<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">OLGA RAHNEVA</style></author><author><style face="normal" font="default" size="100%">TODORKA TERZIEVA</style></author><author><style face="normal" font="default" size="100%">ANGEL GOLEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INVESTIGATIONS ON THE ZUBAIR–FAMILY WITH BASELINE GHOSH–BOURGUIGNON’S EXTENDED BURR XII CUMULATIVE SIGMOID. SOME APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword><keyword><style  face="normal" font="default" size="100%">68N30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/27/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study the one-sided Hausdorff approximation of&amp;nbsp;the shifted Heaviside step function by a class of the Zubair-family of cumulative distribution with baseline Ghosh–Bourguignon’s extended Burr XII c.d.f. The estimates&amp;nbsp;of the value of the best Hausdorff approximation obtained in this article can be used&amp;nbsp;in practice as one possible additional criterion in ”saturation” study.&lt;/p&gt;

&lt;p&gt;We will illustrate the advances of this new model for approximation and modelling&amp;nbsp;of data for Witty worm for entire world and for USA [1] (see, also [16]) and ”cancer&amp;nbsp;data” (for some details see, [19], [20]).&lt;/p&gt;

&lt;p&gt;Numerical examples, illustrating our results are presented using programming environment &lt;em&gt;CAS Mathematica&lt;/em&gt;.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">11</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MD SHAFIQUL ISLAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN ALTERNATIVE ELEMENTARY METHOD FOR APPROXIMATION OF INVARIANT MEASURES FOR RANDOM MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37A05</style></keyword><keyword><style  face="normal" font="default" size="100%">37E05</style></keyword><keyword><style  face="normal" font="default" size="100%">37H99</style></keyword><keyword><style  face="normal" font="default" size="100%">37M25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we describe an alternative elementary method of approximating&amp;nbsp;invariant measures for random maps. Instead of computing Ulam’s matrices&amp;nbsp;associated with the Frobenious-Perron operator for random map we compute&amp;nbsp;matrices which approximate Ulam’s matrices.&lt;br /&gt;
Let $T = \{\tau_1(x), \tau_2(x), . . . , \tau_K(x); p_1, p_2, . . . , p_K\}$ be a random map which posses a&amp;nbsp;unique absolutely continuous invariant measure $\hat\mu$&amp;nbsp;with probability density function $\hat f$. With our elementary method it is possible to develop and implement algorithms&amp;nbsp;for the approximation of the invariant measure $\hat\mu$&amp;nbsp; with a given bound on the error&amp;nbsp;of the approximation. One of the main advantages of our method is that we do not&amp;nbsp;need to deal with the inverse of the component maps of the random maps. Our result&amp;nbsp;is a generalization of the result of Galatolo and Nisoli (see the paper [12] Galatolo,&amp;nbsp;S. and Nisoli, I, An elementary approch to rigorous approximation of Invariant&amp;nbsp;measures, &lt;em&gt;SIAM J. Appl. Dynamical Systems&lt;/em&gt;, &lt;strong&gt;13&lt;/strong&gt;, No. 2 (2014), 958-985) of&amp;nbsp;single piecewise&amp;nbsp; expanding maps to results of random maps. We present a numerical&amp;nbsp;example.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">31</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">OLGA RAHNEVA</style></author><author><style face="normal" font="default" size="100%">HRISTO KISKINOV</style></author><author><style face="normal" font="default" size="100%">HRISTO MELEMOV</style></author><author><style face="normal" font="default" size="100%">MARTIN STIEGER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE APPROXIMATION OF ONE CLASS OF IMPULSE FUNCTIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/3/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we consider a new class of cumulative distribution functions belonging to the important class of functions arising from the theory of impulse techniques, neural networks and debugging theory.&lt;/p&gt;

&lt;p&gt;By this new family of cumulative functions we study the Hausdorff approximation of the impulse function σ&lt;sup&gt;∗∗&lt;/sup&gt;(t).&lt;/p&gt;

&lt;p&gt;Numerical examples, illustrating our results using the programming environment CAS MATHEMATICA are presented.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">237</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SVETOSLAV MARKOV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE APPROXIMATION OF THE CUT FUNCTIONS BY HYPER–LOG–LOGISTIC FUNCTION</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">08/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/2/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We study the uniform approximation of the sigmoid cut function&amp;nbsp;by smooth sigmoid functions such as the Hyper-log–logistic function. The limiting&amp;nbsp;case of the interval-valued step function is discussed using Hausdorff metric. Various expressions for the error estimates of the corresponding uniform and Hausdorff&amp;nbsp;approximations are obtained. Numerical examples are presented using &lt;em&gt;CAS MATHEMATICA&lt;/em&gt;.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">169</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">D. KUMAR</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A COLLOCATION SCHEME FOR SINGULAR BOUNDARY VALUE PROBLEMS ARISING IN PHYSIOLOGY</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">65L10</style></keyword><keyword><style  face="normal" font="default" size="100%">65L12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/1/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;A new collocation method for the solution of a class of second-order two-point boundary value problems associated with physiology and other areas with a singular point at one endpoint is constructed. The singularity of the differential equation is modified by L’Hôpital’s rule and the boundary condition ${ y′(0)=0}$ . Quintic B-spline functions on equidistant collocation points are used to approximate the solution. The quasi-linearization technique is used to reduce a non-linear problem to a sequence of linear problems. The system obtained on discretization is transformed to the system of linear algebraic equations which is easy to be solved. It is proved that the proposed algorithm converges to a smooth approximate solution of the singular boundary value problems and the error estimates are given. To check the theory and to demonstrate the efficiency of the proposed method, several numerical illustrations from physical model problems have been carried out. To show the effectiveness of the proposed method comparisons with several existing methods has also been done.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">95</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JEWGENI  DSHALALOW</style></author><author><style face="normal" font="default" size="100%">KIZZA  NANDYOSE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONTINUOUS TIME INTERPOLATION OF MONOTONE MARKED RANDOM MEASURES WITH APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60G25</style></keyword><keyword><style  face="normal" font="default" size="100%">60G50</style></keyword><keyword><style  face="normal" font="default" size="100%">60G51</style></keyword><keyword><style  face="normal" font="default" size="100%">60G52</style></keyword><keyword><style  face="normal" font="default" size="100%">60G55</style></keyword><keyword><style  face="normal" font="default" size="100%">60G57</style></keyword><keyword><style  face="normal" font="default" size="100%">60K05</style></keyword><keyword><style  face="normal" font="default" size="100%">60K35</style></keyword><keyword><style  face="normal" font="default" size="100%">60K40</style></keyword><keyword><style  face="normal" font="default" size="100%">90B10</style></keyword><keyword><style  face="normal" font="default" size="100%">90B15</style></keyword><keyword><style  face="normal" font="default" size="100%">90B18</style></keyword><keyword><style  face="normal" font="default" size="100%">90B25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/2/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We study a class of monotone delayed marked point processes that model stochastic networks (under attacks), status of queueing systems during vacation modes, responses to cancer treatments (such as chemotherapy and radiation), hostile ambushes in economics and warfare. We are interested in the behavior of such a process about a fixed threshold. It presents an analytic challenge, because of the arbitrary nature of random marks. We target the first passage time, pre-first passage time, the status of the associated continuous time parameter process between these two epochs, and the status of the process upon these two epochs. A joint functional of these stochastic quantities is investigated in the transient mode. Analytically tractable formulas are obtained and demonstrated on special cases of marked Poisson processes.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">119</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SYED ABBAS</style></author><author><style face="normal" font="default" size="100%">ANIBAL CORONEL</style></author><author><style face="normal" font="default" size="100%">MANUEL PINTO</style></author><author><style face="normal" font="default" size="100%">SWATI TYAGI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXPONENTIAL APPROXIMATION OF SOLUTIONS OF BIDIRECTIONAL NEURAL NETWORKS MODEL WITH POSITIVE DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">approximate solution</style></keyword><keyword><style  face="normal" font="default" size="100%">delay differential equation</style></keyword><keyword><style  face="normal" font="default" size="100%">neural networks</style></keyword><keyword><style  face="normal" font="default" size="100%">piecewise constant argument of generalized type</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/1/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">30</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, a class of bidirectional neural network containing delay&amp;nbsp;has been studied. Based on the theory of differential calculus and the generalized&amp;nbsp;Gronwall inequality, the solution of the corresponding neural network model is approximated&amp;nbsp;using discretization method and a sufficient condition is established for&amp;nbsp;its stability. Some easily verifiable sufficient conditions are obtained ensuring that&amp;nbsp;every solution of the discrete-time analogue converges exponentially to the unique&amp;nbsp;solution. In the last section, two numerical example are also presented to validate the&amp;nbsp;feasibility of the proposed results and illustrate the advantages of the discrete-time&amp;nbsp;analogues in numerically simulating the continuous-time networks.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. PRATHUSHA</style></author><author><style face="normal" font="default" size="100%">S. JYOTHI</style></author><author><style face="normal" font="default" size="100%">D.M. MAMATHA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A HYBRID IMPLEMENTATION OF MULTICLASS RECOGNITION ALGORITHM FOR CLASSIFICATION OF CRABS AND LOBSTERS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">GLCM</style></keyword><keyword><style  face="normal" font="default" size="100%">KNN</style></keyword><keyword><style  face="normal" font="default" size="100%">ROI/NROI</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/1/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Crabs and lobsters have a major share in the production of sea food. Among the marine foods available along the coasts of south India, crabs occupy the major role for fetching economy to the farmers in fishing Industry. The problem faced by many fishing farmers is the manual sorting of the sea food available. Because of the huge variations in the price of the marine fauna it will be beneficial to farmers if they are classified and packaged. The proposed technique in this paper uses a hybrid implementation of multi class crab recognition system. The crab features are extracted using reduced gray level co-occurrence matrix (GLCM) with less feature set in contrast to traditional huge feature set and a multiclass training vector is created. Further, Crab images are classified using KNN classification. Test crab samples (images) features are matched with the stored database by various matching techniques such as Euclidean distance, cosine and city block distances. The experiments are carried on images collected from various coasts of south India and result shows that hybrid multiclass approach using KNN classifier has better recognition accuracy. It uses hybrid approach of GLCM with less features , Segmentation with ROI/NROI technique and KNN classifier and K-fold cross validation. Dimensionality Reduction is applied which is a significant improvement in multiclass recognition process. This paper successfully proposes a hybrid multi-class recognition algorithm which uses less feature set compared to traditional feature set. Further it reduces the feature set to minimal set and achieved good accuracy for multiclass problems. The proposed technique is tested with KNN classifier with various distance measures like Euclidian, cosine and city block. The novelty of the proposed multiclass recognition algorithm lies in training with minimal feature set.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">75</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZVI  KONIGSBERG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MODELING AND VERIFICATION ANALYSIS OF A FLEXIBLE MANUFACTURING SYSTEM: A MODAL LOGIC APPROACH</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">08A99</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword><keyword><style  face="normal" font="default" size="100%">93D35</style></keyword><keyword><style  face="normal" font="default" size="100%">93D99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;A flexible manufacturing system is an efficient production line with versatile machines, an automatic transport system and a sophisticated decision making system. This paper proposes a formal modeling and verification analysis methodology, which consists in representing the flexible manufacturing system by means of a modal logic formula. Then, using the concept of logic implication, and transforming this logical implication relation into a set of clauses, a modal resolution qualitative method for verification (satisfiability) as well as performance issues, for some queries is applied.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">65</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ONYANGO  OMONDI</style></author><author><style face="normal" font="default" size="100%">OGADA  ACHIENG</style></author><author><style face="normal" font="default" size="100%">THIRIKA  MWENDE</style></author><author><style face="normal" font="default" size="100%">LAWI G.O.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MODELING MALARIA AND ROTAVIRUS CO-INFECTION</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/2/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">26</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A mathematical model has been developed to explore the co-infection of rotavirus and malaria. A qualitative and comprehensive mathematical analysis has been carried out. A rotavirus only model is considered first. In its analysis, the basic reproduction number ${ (R_0)}$ is calculated. The existence of a disease free and a unique positive endemic equilibria is established and are proved to be both globally stable when ${ R_0 &amp;lt; 1}$&amp;nbsp; and ${ R_0 &amp;gt; 1 }$ respectively. The basic reproduction number ${ (R_{mr} ) }$ of the co-infection model has also been established. The disease free equilibrium is proved to be locally stable whenever ${ R_{mr} \ &amp;lt; 1}$&amp;nbsp; but not globally stable due to coinfection. However, it has been observed that if maximum protection is given against co-infection, then global stability may be achieved. Analysis of co-infection model indicates that it may undergo a forward bifurcation. Numerical simulations using reasonable parameter values indicate that the co-infection persists whenever ${ R_{mr} }$ is greater than unity and dies out when ${ R_{mr} }$ is less than unity.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">143</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">OLGA RAHNEVA</style></author><author><style face="normal" font="default" size="100%">HRISTO KISKINOV</style></author><author><style face="normal" font="default" size="100%">HRISTO MELEMOV</style></author><author><style face="normal" font="default" size="100%">MARTIN STIEGER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MODELLING THE DYNAMICS OF RADICALIZATION WITH GOVERNMENT INTERVENTION</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/2/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we introduce and consider a new class of cumulative distribution functions.&amp;nbsp;This class belongs to the important class of functions arising from the theory of impulse techniques, neural networks and debugging theory.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;By this family we study the Hausdorff approximation of the impulse function $\sigma^{\ast \ast}(t)$.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;Numerical examples, illustrating our results using the programming environment &lt;em&gt;CAS MATHEMATICA&lt;/em&gt; are presented.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">225</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NEW IMPROVEMENT EUCLIDEAN ALGORITHM FOR GREATEST COMMON DIVISOR. I</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">11A05</style></keyword><keyword><style  face="normal" font="default" size="100%">68W01</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/3/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this note we gave new realization of Euclidean algorithm for calculation of greatest common divisor (GCD). Our results are extension of results given&amp;nbsp;in [1]-[26], [41]-[64]. For computer implementation Visual C# 2017 programming&amp;nbsp;environment is used. We optimize about 40% and about 10% Knuth’s recursive and&amp;nbsp;iterative algorithms respectively.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">355</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">VESSELIN KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">HRISTO KISKINOV</style></author><author><style face="normal" font="default" size="100%">OLGA RAHNEVA</style></author><author><style face="normal" font="default" size="100%">GEORGI SPASOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NOTE ON THE EXPONENTIATED EXPONENTIAL–POISSON SOFTWARE RELIABILITY MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/3/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we consider an application to the debugging theory of&amp;nbsp;a class of cumulative exponentiated exponential–Poisson distribution functions introduced by Ramos, Dey, Louzada and Lachos.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;By this family of cumulative distribution functions we study the Hausdorff approximation of the shifted Heaviside step function.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;Numerical examples, illustrating our results using the programming environment&amp;nbsp;Mathematica are presented.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;As application in the field of debugging and test theory are given examples with&amp;nbsp;real data including compatibility modifications, operating system upgrade and signaling message processing from year 2000 using the new software reliability model.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">257</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">OLGA RAHNEVA</style></author><author><style face="normal" font="default" size="100%">HRISTO KISKINOV</style></author><author><style face="normal" font="default" size="100%">ANNA MALINOVA</style></author><author><style face="normal" font="default" size="100%">GEORGI SPASOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NOTE ON THE LEE–CHANG–PHAM–SONG SOFTWARE RELIABILITY MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/3/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study the Hausdorff approximation of the shifted Heaviside step function $h_{t_0}(t)$&amp;nbsp;by sigmoidal function based on the Lee--Chang--Pham--Song cumulative function and find an expression for the error of the best approximation.&amp;nbsp;We give real examples with small on--line data provided by IBM entry software package using the model.&amp;nbsp;The potentiality of the software reliability models is analyzed. Lee--Chang--Pham--Song's idea of including the characteristic $t^{\ast}$ (the time when debugging starts after modifying the code causing syntax errors) in the study of models in debugging theory can be successfully expanded.&amp;nbsp;For instance, for the Goel (1980) software reliability model.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">297</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. RAM MOHAN RAO</style></author><author><style face="normal" font="default" size="100%">A. MOUNIKA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">RECOMMENDED SYSTEM OF COLLABORATIVE FILTERING BASED IN SOCIAL NETWORKS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/3/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;&amp;nbsp;Sharing Information Among Friends Using different online Social&amp;nbsp;Network such as What’s Up, Twitter Face book between two are more friends not&amp;nbsp;only sharing profile update ,Audio, Videos with her ,his direct friends are mutual&amp;nbsp;Friends ,Online Social Network connect with globally direct are Indirect Friends Using&amp;nbsp;Online social network sharing any product are comment and ranking it process&amp;nbsp;Unique Challenge and opportunities for recommendation. This Experiment with real&amp;nbsp;online voting trace and we demonstrate the OSN Network group of people seeing the&amp;nbsp;Information online voting and their personal opinion will be Shared in that OSN Network&amp;nbsp;Scalability and Real information gathered from their personal friend and mutual&amp;nbsp;friend feedback participate in online Voting process. In our experiments End to end&amp;nbsp;user information we know that we can simply identify the fake user are Real user can&amp;nbsp;while users interest for hot voting can be better mined then we further purpose a&amp;nbsp;hybrid RS bagging different approaches to achieve the best top-k hit.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">247</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NIKOLAY PAVLOV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SENSITIVE ANALYSIS ON SOME TRANSFORMATIONS TO CONSTRUCT A GENERALIZED 2–COMPONENT WEIBULL DISTRIBUTION</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword><keyword><style  face="normal" font="default" size="100%">68N30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/3/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In literature, several transformations exists to obtain a new cumulative distribution function (cdf) using other(s) well-known cdf(s).&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;In this paper we study the important ”saturation” characteristic for the generalized&amp;nbsp;2–component Weibull c.d.f. in the Hausdorff sense.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;We will conduct a sensitive analysis of this family of cumulative functions.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;The results have independent significance in the study of issues related to life&amp;nbsp;time analysis, insurance mathematics, biochemical kinetics, population dynamics and&amp;nbsp;debugging theory.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;Numerical examples, illustrating our results are presented using programming environment Mathematica.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">269</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARIA MALINOVA</style></author><author><style face="normal" font="default" size="100%">ANGEL GOLEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SPEEDING UP THE GENERATION OF NEAR-RINGS ON FINITE CYCLIC GROUPS USING PARALLEL PROCESSING IN C#</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">16Y30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/3/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The main purpose of this article is to reduce the generation time&amp;nbsp;of near-rings on finite cyclic groups using the parallel processing provided by C#.&amp;nbsp;We divide the near-rings into independent subsets and generate them simultaneously.&amp;nbsp;The calculations are further accelerated after refactoring and defining appropriate&amp;nbsp;compiler optimizations.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">345</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANDREY ANTONOV</style></author><author><style face="normal" font="default" size="100%">SVETOSLAV NENOV</style></author><author><style face="normal" font="default" size="100%">TSVETELIN TSVETKOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STATE-SPACE SYSTEM IDENTIFICATION PROBLEM FOR SOME NONLINEAR BIOLOGICAL MODELS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">dynamical systems</style></keyword><keyword><style  face="normal" font="default" size="100%">first integral</style></keyword><keyword><style  face="normal" font="default" size="100%">Lotka-Volterra system</style></keyword><keyword><style  face="normal" font="default" size="100%">numerical examples</style></keyword><keyword><style  face="normal" font="default" size="100%">problem of parameter estimation</style></keyword><keyword><style  face="normal" font="default" size="100%">state-space system identification</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/3/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The article is concerned with the problem of parameter estimation&amp;nbsp;in the general case of dynamical systems in the form of state-space. Supposing the&amp;nbsp;existence of first integral(s) of the system, we proved some conditions for solvability&amp;nbsp;of the problem.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;As a set of examples, we considered the classical Lotka-Volterra system. We&amp;nbsp;proved that a solution of state-space identification problem is also a solution of a set&amp;nbsp;of nonlinear equations. Based on this result, some applications (using CAS Maple)&amp;nbsp;are presented.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">311</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ALI BOUSSAYOUD</style></author><author><style face="normal" font="default" size="100%">ABDELHAMID ABDERREZZAK</style></author><author><style face="normal" font="default" size="100%">PHILIP B. ZHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SYMMETRIC FUNCTIONS FOR FAMILIES OF GENERATING FUNCTIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">05E05</style></keyword><keyword><style  face="normal" font="default" size="100%">11B39</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/1/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we show how the action of the symmetrizing operators $L_{e_{1}e_{2}}^{k}\ $to the series $\sum_{j=0}^{\infty }S_{j}\left( -A\right) e_{1}^{j}z^{j}$ allows the obtention of an alternative approach for the determination of Fibonacci numbers and Chebychev polynomials of the first and second kind.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">53</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DOUGLAS  NG</style></author><author><style face="normal" font="default" size="100%">ANITA  WONG</style></author><author><style face="normal" font="default" size="100%">FION  CHEUNG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CANCER GROWTH MODELS AND ITS TREATMENT</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The success of radiotherapy treatment relies in accurately localizing the target region&lt;br /&gt;
close to tumor as well as avoiding damage to the nearby healthy organ. In order to control the tumor&lt;br /&gt;
growth and minimize side effects to the patient, it is crucial to make some substantial modifications&lt;br /&gt;
on the patient’s anatomy due to the reduction of the patient’s weight; shrinkage of the tumor; and&lt;br /&gt;
the edema of the tissue before the treatment. For surgery consideration, an efficient registration&lt;br /&gt;
method to delineate the clinically critical objects in computed tomography images obtained from&lt;br /&gt;
the radiation treatment process is needed. Over the last decades, the Deformable Image Registration&lt;br /&gt;
Model has undergone intensive investigation from researchers in the fields of computer vision, remote&lt;br /&gt;
sensing, and etc. Despite the significant progress that has been made, deformable registration&lt;br /&gt;
remains a challenging problem in the field of radiotherapy. In this paper, we discuss several Cancer&lt;br /&gt;
Growth Models, as well as the Deformable Image Registration techniques used in Radiotherapy&lt;br /&gt;
treatment and finally, the model of Quenching-induced deactivation of photosensitizer to improve&lt;br /&gt;
phototherapy of cancer will be introduced.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">107</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SIQING LI</style></author><author><style face="normal" font="default" size="100%">MING LI</style></author><author><style face="normal" font="default" size="100%">G.R.  LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONVERGENCE ANALYSIS AND UPPER BOUND PROPERTY OF NS-RPIM WITH PURE RBFS USING VORONOI SMOOTHING DOMAINS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, a nodal based smoothed point interpolation method (NS-RPIM) is implemented using Voronoi smoothing domains to solve elliptic partial differential equations with different node selection strategies. Shape functions for field variable approximation are built using the radial point interpolation method (RPIM) with pure radial basis functions (RBFs) without polynomial basis. The smoothed Galerkin weak form is applied to construct the discretized system equations. Triangle background cells with voronio smoothing domains and quadrilateral mesh with smoothing domains of equally-shared areas are used. It is found that in all cases that the NS-RPIM provides results with higher convergency rates for distorted mesh compared with the standard FEM. In addition, in all numerical examples, solutions for the energy norm by NS-RPIM are found to be upper bounds with respect to the FEM counterparts and even to exact solutions. In terms of accuracy, however, NS-RPIM could be more or less accurate than that of FEM dependent on the problem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">115</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HAIYAN TIAN</style></author><author><style face="normal" font="default" size="100%">ANDREAS GRUNEWALD</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A DELTA-SHAPED BASIS METHOD FOR ILL-POSED NONHOMOGENEOUS ELLIPTIC BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">65N21</style></keyword><keyword><style  face="normal" font="default" size="100%">65N35</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, a Delta-shaped basis method is coupled with the method of fundamental solutions and Tikhonov regularization for solving ill-posed nonhomogeneous elliptic boundary value problems. Delta-shaped basis functions are used to approximate the source function since they can effectively handle scattered data and give rapidly convergent approximation. This approach also results in an easy derivation of a particular solution for a general type elliptic operator. The associated homogeneous problem is solved by the method of fundamental solutions with Tikhonov regularization. The approach is mesh free and is effective for domains of irregular shapes. Numerical results show that this method is accurate and stable against perturbed data.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">W.Y. CHAN</style></author><author><style face="normal" font="default" size="100%">H.T. LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FINDING THE CRITICAL DOMAIN OF MULTI-DIMENSIONAL QUENCHING PROBLEMS WITH NEUMANN BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35J47</style></keyword><keyword><style  face="normal" font="default" size="100%">35J60</style></keyword><keyword><style  face="normal" font="default" size="100%">35K20</style></keyword><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Let ${Ω}$ be a disc in ${ R^2}$&amp;nbsp; with the center (0, 0) and radius a, ${ ∂Ω }$ and ${ \bar{Ω} }$&amp;nbsp; be its boundary and closure, respectively.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;Suppose that ${u}$ is a function of ${ τ, χ,}$ and ${ ζ.}$ Further, assume that ${ β }$ is a positive number. In this paper, we investigate&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;the multi-dimensional parabolic quenching problems with the second initial-boundary condition: $$ { \frac{∂u}{∂τ} = \frac{∂^2u}{∂χ^2}&amp;nbsp;+ \frac{∂^2u}{∂ζ^2} +\frac{1}{1 − u} \&amp;nbsp; for&amp;nbsp; \&amp;nbsp;(χ, ζ, τ) ∈ Ω × (0, ∞), }$$ $${&amp;nbsp;u (χ, ζ, 0) = u_0 (χ, ζ) \ for \&amp;nbsp;(χ, ζ) ∈ \bar{Ω}, \frac{∂u (χ, ζ, τ)}{∂n} = − \frac{β}{a} \ for \&amp;nbsp;τ &amp;gt; 0 \ and \ (χ, ζ) ∈ ∂Ω, }$$&amp;nbsp;where ${ u_0 ∈ C^2 \left( \bar{Ω} \right)}$&amp;nbsp;and ${ u_0 (χ, ζ) \ &amp;lt; \ 1}$ &amp;nbsp;for ${&amp;nbsp;(χ, ζ) ∈ \bar{Ω}, }$ and ${&amp;nbsp;∂u/∂n }$ is the outward normal derivative of ${ u }$. We shall determine an approximated critical domain of some ${ u_0 (χ, ζ) }$ of the above problem by using a numerical method.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">19</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">DONGFANG YUN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LEAST SQUARES INTEGRATION-BASED RBF METHOD FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, the method of least square and the recently developed integrationbased radial basis function method are applied for solving partial differential equations. Several boundary value problems defined in rectangular and L-shaped domains with uniform and random nodes are studied. Superiorities like higher accuracy and convergency are shown through comparisons with existing results. Furthermore, a two-dimensional Burgers’ equation is taken as an example to indicate the superior stability and higher accuracy of this proposed method. Numerical results demonstrate that our method works better than classical Kansa’s method and adaptive meshing technique.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">61</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">KA  CHEUNG</style></author><author><style face="normal" font="default" size="100%">LEEVAN LING</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MESHLESS COLLOCATION METHODS WITH GRAPH LAPLACIAN FOR PDES ON FOLDED SURFACE</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This work aims to provide a numerical treatment to deal with PDEs on surfaces with singularity along smooth curves. Previously, we proposed a low-order localized meshless method for discretizing the surface Laplacian operator on surfaces with folded. It is observed that the previously proposed strategy of approximating surface Laplacian at fold does not work with a recently developed high-order embedding meshless method for smooth surface. In this paper, we propose using the graph Laplacian to handel the surface singularity and study how it can be used to solve PDEs on folded surfaces.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">79</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">THIR DANGAL</style></author><author><style face="normal" font="default" size="100%">C.S. CHEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE METHOD OF PARTICULAR SOLUTIONS FOR FINDING CRITICAL DOMAINS FOR QUENCHING PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this work, the method of particular solutions (MPS) has been used for solving nonlinear Poisson-type problems defined on different geometries. The polyharmonic splines is used as the basis function so that no shape parameter is needed in the solution process. The MPS is also applied to compute the sizes of critical domains of different shapes for a quenching problem and compared with the sizes of critical domains obtained from some other numerical methods. Numerical examples are presented to show the efficiency and accuracy of the method.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">135</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">B.K.  GHIMIRE</style></author><author><style face="normal" font="default" size="100%">A.R.  LAMICHHANE</style></author><author><style face="normal" font="default" size="100%">D. WATSON</style></author><author><style face="normal" font="default" size="100%">Z. ZHOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLVING FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS USING RADIAL BASIS FUNCTION COLLOCATION METHODS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">65N35</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we propose a new approach for solving fourth-order partial differential equations (PDEs) which uses an intermediate step so that fourth order PDEs can be reduced to second order PDEs. This method is simple and easy to implement. We compare the numerical result of this method to the Kansa method and the method of approximate particular solutions (MAPS). We also observe the numerical accuracy of the proposed method on the local Kansa method (LKM) and localized method of approximate particular solutions (LMAPS). Numerical results show that this method outperforms the MAPS and Kansa method in both global and local cases.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">91</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LING  YEUNG</style></author><author><style face="normal" font="default" size="100%">MANWAI YUEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME ANALYTICAL SOLUTIONS FOR THE EULER AND EULER-POISSON EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B44</style></keyword><keyword><style  face="normal" font="default" size="100%">35C05</style></keyword><keyword><style  face="normal" font="default" size="100%">35Q35</style></keyword><keyword><style  face="normal" font="default" size="100%">76N10</style></keyword><keyword><style  face="normal" font="default" size="100%">83F05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article, we obtain a family of exact solutions for the 3-dimensional nonisentropic compressible pressureless Euler equations the Euler-Poisson equations with pressure in both the attractive and repulsive cases. Here, the exact solutions for the pressureless Euler equations are with arbitrary function parameters.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">37</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">WEI ZHAO</style></author><author><style face="normal" font="default" size="100%">MARTIN STOLL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY ON INTERPOLATION OF SCATTERED DATA VIA KERNELS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;For an approximation, the inverse inequality can guarantee the smoothness of an approximant based on its rate approximation. The purpose of this paper is to present new inverse inequalities for scattered data interpolation on&amp;nbsp;${ \mathbb{R}^d }$&amp;nbsp;and bounded domain ${ Ω.}$&amp;nbsp; Finally, some numerical experiments are given as well.&lt;/p&gt;

&lt;p&gt;&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&amp;nbsp;&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">45</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RATINAN BOONKLURB</style></author><author><style face="normal" font="default" size="100%">ARTIT SIRIROOP</style></author><author><style face="normal" font="default" size="100%">TAWIKAN TREEYAPRASERT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SUFFICIENT CONDITIONS FOR MULTI-DIMENSIONAL BLOW-UP PROBLEM</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K58</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/25/1/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article studies a multi-dimensional parabolic problem with a concentrated nonlinear source having local and nonlocal features. It is shown that if its solution exists, then it blows up everywhere on the boundary of a ball where the concentrated source is situated. A criterion for the solution to blow up in a finite time is also given.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">29</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANWAR ZEB</style></author><author><style face="normal" font="default" size="100%">SULTAN HUSSAIN</style></author><author><style face="normal" font="default" size="100%">VEDAT  ERTURK</style></author><author><style face="normal" font="default" size="100%">GUL ZAMAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC BEHAVIOR OF DIFFERENT CONTROLS OF HEPATITIS B VIRUS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">49J15</style></keyword><keyword><style  face="normal" font="default" size="100%">91G20</style></keyword><keyword><style  face="normal" font="default" size="100%">92D25</style></keyword><keyword><style  face="normal" font="default" size="100%">93D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-45-54.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we introduce a hepatitis B virus stochastic transition model with vaccination and awareness campaign. The purpose of this work is to show the effect of vaccine and awareness in the affected area of hepatitis B. For this purpose first, we formulate the stochastic model for hepatitis B virus, then investigate the asymptotic behavior of vaccination and awareness campaign, through the unique positive solution of our proposed model. We study the different scenarios in order to identify the best control of this virus. Graphical justification is also presented.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">45</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">VENKATESWARA MUDUNURU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMPARISON OF ACTIVATION FUNCTIONS IN MULTILAYER NEURAL NETWORKS FOR STAGE CLASSIFICATION IN BREAST CANCER</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-83-96.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Artificial Neural Networks (ANNs), recently applied to a number of clinical, business, forecasting, time series prediction, and other applications, are computational systems consisting of artificial neurons called nodes arranged in different layers with interconnecting links. Among the available wide range of neural networks, most research is concentrated around feed forward neural networks called Multi-layer perceptrons (MLPs). One of the important components of an artificial neural network (ANN) is the activation function. This paper discusses properties of activation functions in multilayer neural network applied to breast cancer stage classification. There are a number of common activation functions in use with ANNs. The main objective in this work is to compare and analyze the performance of MLPs which has back-propagation algorithm using various activation functions for the neurons of hidden and output layers to evaluate their performance on the stage classification of breast cancer data.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">83</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZVI  KONIGSBERG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMPUTABILITY POWER OF AN EXTENDED PETRI NET MODEL ( APN )</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">03D10</style></keyword><keyword><style  face="normal" font="default" size="100%">03D20</style></keyword><keyword><style  face="normal" font="default" size="100%">03D60</style></keyword><keyword><style  face="normal" font="default" size="100%">03D78</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-29-44.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The notion of computability has its origin in the works of the logicians Church, Gödel, Kleene, Post and Turing. Several approaches of computation were proposed: recursive functions, Post programs, lambda calculus, Turing machines, register machines, to mention some. It was shown that all these models were equivalent in terms of its computability power. In this paper a new computational paradigm called arithmetic Petri nets (APN) is introduced. APN are Petri nets with inhibitor arcs that perform three types of arithmetical operations; increment, decrement and test for zero. Its equivalence to Turing and therefore to all the other approaches was shown to be true by simulation of a register machine. In this paper a different path is proposed by first proving that all recursive functions are APN computable. The opposite implication is obtained from Kleene’s normal form theorem for APN. The normal form theorem was introduced by Kleene for the general recursive computation paradigm in terms of system of equations. The proof for the APN computational paradigm is based on the idea of computation tree, where each node of such a tree will tell us how a value needed for the arithmetical operations can be inductively obtained. Then, using arithmetization plus course of value recursion a primitive recursive predicate is defined from which by means of a primitive recursive function the desired characterization for the value of the output function is established.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">29</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JEWGENI  DSHALALOW</style></author><author><style face="normal" font="default" size="100%">KENNETH IWEZULU</style></author><author><style face="normal" font="default" size="100%">RYAN WHITE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DISCRETE OPERATIONAL CALCULUS IN DELAYED STOCHASTIC GAMES</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60G51</style></keyword><keyword><style  face="normal" font="default" size="100%">60G55</style></keyword><keyword><style  face="normal" font="default" size="100%">60G57</style></keyword><keyword><style  face="normal" font="default" size="100%">60K05</style></keyword><keyword><style  face="normal" font="default" size="100%">82B41</style></keyword><keyword><style  face="normal" font="default" size="100%">91A05</style></keyword><keyword><style  face="normal" font="default" size="100%">91A10</style></keyword><keyword><style  face="normal" font="default" size="100%">91A60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-55-64.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article deals with classes of antagonistic games with two players. A game is specified in terms of two “hostile” stochastic processes representing mutual attacks upon random times that exert casualties of random magnitudes. The game ends when one of the players is defeated, that is, when the amounts of casualties to the players cross respective tolerance thresholds. We target the first passage time τ&lt;sub&gt;ρ&lt;/sub&gt; of the defeat and the amount of casualties to either player upon τρ. Here we validate our claim of analytic tractability in formulas obtained in [1] under various transforms.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">55</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HEYUAN WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DYNAMICAL BEHAVIORS ANALYSIS AND NUMERICAL SIMULATION OF THE LORENZ-TYPE SYSTEM FOR COUETTE-TAYLOR FLOW</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-65-82.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we investigate the problem of dynamical behaviors and numerical simulation of the Lorenz-type systems for the incompressible flow between two concentric rotating cylinders. The estimation of Hausdorff dimension of its attractor is discussed, and the globally exponentially attractive set and positive invariant set of the chaotic system are studied via Lyapunov function. We present a detailed numerical result of the whole process from bifurcation to chaos, and analyze the evolutionary mechanism of the dynamical behavior of the system. Moreover, by using numerical simulation results of attractors, bifurcation diagram, Lyapunov exponent spectrum and Poincare map, return map of the system we show abundant and complex dynamical behaviors of the system, and explain successive transitions of Couette-Taylor flow from Laminar flow to turbulence in the experiment.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">65</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SOUDABEH SHEMEHSAVAR</style></author><author><style face="normal" font="default" size="100%">KAMBIZ FARAHMAND</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXPECTED NUMBER OF REAL ROOTS OF CERTAIN GAUSSIAN RANDOM TRIGONOMETRIC POLYNOMIALS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-97-106.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let ${ D_n(θ) = \sum^n_{k=0}(A_k cos kθ + B_k sin kθ) }$ be a random trigonometric polynomial where the coefficients ${ A_0, A_1, . . . , A_n}$, and ${ B_0, B_1, . . . , B_n}$, form sequences of Gaussian random variables. Moreover, we assume that the increments ${ ∆_1^k = A_k−A_{k−1}, ∆_2^k = B_k−B_{k−1}, \&amp;nbsp; k = 0, 1, 2, . . . , n,}$ are independent, with conventional notation of ${ A_{−1} = B_{−1} = 0.}$ The coefficients ${ A_0, A_1, . . . , A_n,}$ and ${ B_0, B_1, . . . , B_n,}$ can be considered as n consecutive observations of a Brownian motion. In this paper we provide the asymptotic behavior of the expected number of real roots of ${ D_n(θ) = 0 }$as order ${ \frac{ 2 \sqrt{2}n}{\sqrt{3}}}$&amp;nbsp;. Also by the symmetric property assumption of coefficients, i.e., ${ A_k ≡ A_{n−k}, \&amp;nbsp; B_k ≡ B_{n−k},}$ we show that the expected number of real roots is of order ${ \frac{2n}{\sqrt{3} }.}$&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">97</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. SREENIVASAN</style></author><author><style face="normal" font="default" size="100%">A. KRISHNAMOORTHY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MAP/P H/1 RETRIAL QUEUE WITH CONSTANT RETRIAL RATE, WORKING VACATIONS AND A FINITE BUFFER FOR ARRIVALS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">68K25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-107-120.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we study a MAP/P H/1 retrial queueing model in which the server is subject to taking vacations and serving at a lower rate during vacation. The service is returned to normal rate whenever the vacation gets over. If an arriving customer finds the server busy he joins a finite buffer. If the buffer is also full he joins a pool of unsatisfied customers called orbit. There from he makes retrial for a place in the server or buffer. Inter-retrial times are exponentially distributed with intensity independent of the number of customers in the orbit. The model is analyzed in steady state using matrix analytic methods. Illustrative numerical examples are presented.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">107</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SWARN SINGH</style></author><author><style face="normal" font="default" size="100%">SURUCHI SINGH</style></author><author><style face="normal" font="default" size="100%">RAJNI ARORA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NEW HIGHLY ACCURATE STABLE SCHEMES FOR THE SOLUTION OF TELEGRAPHIC EQUATION WITH NEUMANN BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-01-14.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we present two new three level implicit schemes to solve telegraphic equation with Neumann boundary conditions. The accuracy of the proposed schemes is of ${ O(k^2 + k^2h^2 + h^4 ) }$ and ${O(k^4 + k^4h^2 )&amp;nbsp;}$, where ${ h &amp;gt; 0 }$ and ${ k &amp;gt; 0 }$ are the mesh sizes in the space and time directions respectively. The proposed schemes are shown to be solvable and unconditionally stable. Numerical experiments are presented to demonstrate the accuracy and efficiency of the new schemes.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">YUMI YAHAGI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A PROBABILISTIC CONSIDERATION ON ONE DIMENSIONAL KELLER SEGEL SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K15</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-15-28.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we perform a consideration on partial differential equations known as the Keller Segel system (KS) through both probabilistic and numerical methods. Stochastic differential equation (SDE), having a correspondence with (KS) is the main tool of our probabilistic consideration. In our main theorem, by using probabilistic expressions of ${ (u, v) }$&amp;nbsp;with&amp;nbsp;&amp;nbsp;${ u = u(x, t), \&amp;nbsp; v = v(x, t),}$ the solution of (KS), by means of expectation of functionals of the SDE, we derive a set of bounds for ${ (u, v)}$&amp;nbsp; which gives a good estimate of ${ (u, v) }$ around time zero.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">15</style></section></record></records></xml>