<abstract xml:lang="en"><title style='display:none'>Diagonal Scaling of Ill-Conditioned Matrixes by Genetic Algorithm</title>The purpose of this article is to use genetic algorithm for finding two invertible diagonal matrices <italic>D</italic>1 and <italic>D</italic>2 such that the scaled matrix <italic>D</italic>1<italic>AD</italic>2 approaches to minimum condition number.</abstract>

Diagonal Scaling of Ill-Conditioned Matrixes by Genetic Algorithm

<abstract><title style='display:none'>Abstract</title>Motivated by the substantial development in the theory of digamma function, we derive some new identities for the digamma function. These new identities enable us to compute the values of the digamma function for fractional orders in an analogous manner. Also, we mention two errata, found in Jensen’s article (An elementary exposition of the theory of the Gamma function, 1916), and present their correct forms.</abstract>

Analytic computation of digamma function using some new identities

<abstract><title style='display:none'>Abstract</title>The use of geometrical methods in statistics has a long and rich history highlighting many different aspects. These methods are usually based on a Riemannian structure defined on the space of parameters that characterize a family of probabilities. In this paper, we consider the finite dimensional case but the basic ideas can be extended similarly to the infinite-dimensional case. Our aim is to understand exponential families of probabilities on a finite set from an intrinsic geometrical point of view and not through the parameters that characterize some given family of probabilities.For that purpose, we consider a Riemannian geometry defined on the set of positive vectors in a finite-dimensional space. In this space, the probabilities on a finite set comprise a submanifold in which exponential families correspond to geodesic surfaces. We shall also obtain a geometric/dynamic interpretation of Jaynes’ method of maximum entropy.</abstract>

Geometry of the probability simplex and its connection to the maximum entropy method

<abstract><title style='display:none'>Abstract</title> We present a particle-based approach for animating multiple interacting liquids that can handle number of immiscible fluids as well as number of miscible fluids in our simulation framework. We solve the usual problem of robust interface tracking, between immiscible fluids, by reconstructing the zero level set of our novel composite implicit function, see Fig. 1 left and center. It’s recurrent formulation handles directly interfaces between any number of liquids including the free surfaces. We model the miscible fluids by tracking concentrations of dissolved materials in the vicinity of each particle. Flick’s law is applied for the Laplacian-based diffusion of concentrations, see Fig. 1 right. Particle sedimentation is achieved by directional advection along the settling velocity. The diffusion-advection equation is discretized by particles using the Lagrangian formulation. The proposed improvements can be easily implemented into the common Smoothed Particle Hydrodynamics (SPH) simulations framework</abstract>

Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava, Slovak Republic http://www.fmph.uniba.sk

Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava, Slovak Republic; http://www.sccg.sk/~durikovic

Animating multiple interacting miscible and immiscible fluids based on particle simulation

<abstract><title style='display:none'>Abstract</title> Humans recognize objects visually on the basis of material composition as well as shape. To acquire a certain level of photorealism, it is necessary to analyze, how the materials scatter the incident light. The key quantity for expressing the directional optical effect of materials on the incident radiance is the bidirectional reflectance distribution function (BRDF). Our work is devoted to the BRDF measurements, in order to render the synthetic images, mostly of the metallic paints. We measured the spectral reflectance off multiple paint samples then used the measured data to fit the analytical BRDF model, in order to acquire its parameters. In this paper we describe the methodology of the image synthesis from measured data. Materials such as the metallic paints exhibit a sparkling effect caused by the metallic particles scattered within the paint volume. Our analysis of sparkling effect is based on the processing of the multiple photographs. Results of analysis and the measurements were incorporated into the rendering process of car paint</abstract>

Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava, Slovak Republic http://www.fmph.uniba.sk

Metallic paint appearance measurement and rendering

<abstract><title style='display:none'>Abstract</title> In the present paper we study properties of pre-complete class of Boolean functions - monotone Boolean functions. We discuss interval graph, the abbreviated d.n.f., a minimal d.n.f. and a shortest d.n.f. of this function. Then we present a d.n.f. with the highest number of conjunctionsand we determinate the exact number of them. We count the number of monotone Boolean functions with some special properties. In the end we estimate the number of Boolean functionthat are monotone and self-dual at the same time.</abstract>

The Number of Monotone and Self-Dual Boolean Functions

<abstract>
<title style='display:none'>Abstract</title>
In this study, a new generalization of Samade distribution has been proposed. The weighted Samade distribution (WSD) is a new distribution designed for modeling real-life data. The survival function, hazard function, moments, moment-generating function, order statistics, and entropies of this distribution have all been determined. The parameters of the suggested model are estimated using the maximum likelihood estimation technique. Finally, the helpfulness and application of the distribution have been demonstrated by lung cancer data.
</abstract>

A new generalization of Samade distribution with properties and its application to lung cancer data

<abstract>
<title style='display:none'>Abstract</title>
In this article, we proposed a new probability distribution called length-biased Chris-Jerry distribution in which length-biased distribution is a specific case of weighted distribution. Also, we determined the structural properties of length-biased Chris-Jerry distribution and the unknown parameters were estimated by maximum likelihood estimator and tested by likelihood ratio test. Finally, we emphasized a real lifetime data set to reveal how the proposed distribution worked in it.
</abstract>

A new extension of Chris-Jerry distribution with its properties

<abstract>
<title style='display:none'>Abstract</title>
Serious games are becoming a more commonly utilized tool in training, education, and learning. On the other hand, Petri nets, a well-known formalism for process modeling, seem to be a promising tool for describing learning activity scenarios for serious games and virtual environments. Thanks to their graphical form and easy-to-understand nature, it can be assumed that participants from different backgrounds should be able to understand and use Petri nets for their scenarios. A present study presented here investigates how this assumption corresponds to reality. In the study, a short explanation of Petri nets and a set of related tasks were given to a sample of 31 participants (n = 31). The participants were students of Computer Science (16) and Humanities (15). The results collected and statistically analyzed demonstrate both similarities and distinctions in the reactions to problem-solving assignments among individuals in the two groups. These findings and their analysis have been condensed and presented in visual form.
</abstract>

Petri nets for Adaptive learning scenarios in Serious games

<abstract>
<title style='display:none'>Abstract</title>
This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coefficients are independently and identically distributed as standard normal variates. Additionally, the paper provides a clear exposition of the developed methodology. To establish our results, we develop a novel approach utilizing the classical Cauchy’s bounds for the zeros of a deterministic polynomial with complex coefficients. We also corroborate our analytical results with extensive simulations. The methodology developed in the paper can potentially be applied to a broad class of problems regarding bounds and the distribution of zeros in the theory of random polynomials.
</abstract>

Probabilistic zero bounds of certain random polynomials

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we propose a modification that improves efficiency, robustness and reliability of the famous HS conjugate gradient method. In particular, we propose a hybrid of the HS and DHS methods, where DHS is another recent modification of the HS method. Irrespective of the line search, the search direction of the proposed method is sufficiently descent. Moreover, the new approach guarantees global convergence for general functions under the strong Wolfe line search. Numerical results and performance profiles are reported, and indicate that the new approach outperforms three similar methods in the literature. We also give a practical application of the new approach in minimizing risk in portfolio selection.
</abstract>

Application of a globally convergent hybrid conjugate gradient method in portfolio optimization

<abstract>
<title style='display:none'>Abstract</title>
The notion of Plithogenic vertex domination and Plithogenic edge domination in Plithogenic product fuzzy graphs (PPFGs) has been newly introduced and discussed based on P-weights of P-vertices and P-edges respectively with properties, results and examples. Plithogenic vertex domination number and Plithogenic edge domination number for a Plithogenic product fuzzy graph (PPFG), and the bounds and algorithms for and the maximum and minimum values and algorithms for the same are also investigatedthe same are also investigated. Perfect Plithogenic vertex domination and perfect Plithogenic edge domination are presented as special cases of Plithogenic vertex domination and Plithogenic edge domination respectively. It is observed that the P-vertex (P-edge) with the maximum P-weight exists in every Plithogenic vertex (edge) dominating set of a Plithogenic product fuzzy graph. The novelty in these ideas of domination is that a better perception of reality can be obtained through the analysis of both, Plithogenic vertex domination and Plithogenic edge domination, in any Plithogenic product fuzzy graphical structure.
</abstract>

Domination in Plithogenic product fuzzy graphs

<abstract><title style='display:none'>Abstract</title>Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.</abstract>

Department of Mathematics, Faculty of Science, Selçuk University, Konya,

Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Hatay,

New Fractional Complex Transform for Conformable Fractional Partial Differential Equations

<abstract><title style='display:none'>Abstract</title> In this note, we obtain new some inequalities of Simpson’s type based on convexity. Some applications for special means of real numbers are also given.</abstract>

Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey

Ataturk University, K.K. Education Faculty, Department of Mathematics, 25240, Campus, Erzurum, Turkey

On New Inequalities of Simpson’s Type for Functions Whose Second Derivatives Absolute Values are Convex

<abstract><title style='display:none'>Abstract</title> In this paper, we establish Hermite-Hadamard type inequalities for s - convex functions in the second sense and m - convex functions via fractional integrals. The analysis used in the proofs is fairly elementary. </abstract>

Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, TURKEY

Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, TURKEY

Department of Mathematics K. K. Education Faculty, Ataturk University, 25640, Kampus, Erzurum, TURKEY

Department of Mathematics, Faculty of Science and Arts, Kahramanmaraş Sütcü Imam University, Kahramanmaraş-TURKEY

The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results

<abstract><title style='display:none'>Abstract</title>The paper presents design, background and experimental results of the IPTables applied in IPv4 and IP6Tables applied in IPv6 network compared through several tested parameters. The experimental testbed environment is based on P2P grid utilized for DDoS attacks. IPTables tool is used for packet filtering and consequently for preventing DoS/DDoS attacks. It allows a system administrator to configure the tables, the chains and rules it stores in order to manage the incoming and outgoing packets. The packets are treated according to the rules’ results provided by the packet processing. A rule in a chain can be bound with another chain in the table etc.We employ the P2P grid environment to carry out as well as to coordinate DDoS attack on the availability of services to simulate real DDoS attack launched indirectly through many compromised computing systems. The same routing protocols as well as the same firewall rules were used for IPv4 and for IPv6 network. The main aim was to analyse pros and cons of new IP6Tables tool compared with IPTables in IPv4 networks in light of the resistance to DDoS attacks which is still one of the most significant threats in the IPv6 networks.</abstract>

Department of Applied Informatics and Mathematics, University of SS. Cyril and Methodius, Slovak Republic

Performance Evaluations of IPTables Firewall Solutions under DDoS attacks

<abstract><title style='display:none'>Abstract</title> In this paper, Riemann-Liouville type fractional integral identity and inequality for differentiable convex mappings are studied. Some applications to special means of real numbers are given. Finally, error estimates for a midpoint formula are also obtained.</abstract>

Department of Mathematics, Guizhou University Guiyang, Guizhou 550025, P.R. China

Department of Mathematical Analysis and Numerical Mathematics Faculty of Mathematics, Physics and Informatics Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia

Department of Mathematics Guizhou University Guiyang, Guizhou 550025, P.R. China

Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula

<abstract><title style='display:none'>Abstract</title>In this work, we apply fractional calculus to analyze a class of economic growth modelling (EGM) of the Spanish economy. More precisely, the Grünwald-Letnnikov and Caputo derivatives are used to simulate GDP by replacing the previous integer order derivatives with the help of Matlab, SPSS and R software. As a result, we find that the data raised from the Caputo derivative are better than the data raised from the Grünwald-Letnnikov derivative. We improve the previous result in [12].</abstract>

Applying Fractional Calculus to Analyze Economic Growth Modelling

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 Journal of Applied Mathematics, Statistics and Informatics (JAMSI) serves as a venue for careful presentation of applied research...