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In this work, inverse problem for an elliptic equation is studied. We gave a numerical solution of inverse elliptic problem by differential transform method in test example. [ABSTRACT FROM AUTHOR]

This paper presents a computation and discuss on non-polynomial spline of fractional order to solve the differential equations with Caputo fractional derivative. Taylor series is applied to discretize the time derivative of the function. Several examples are considered to confirm the accuracy of the spline method and to show the completion of non-polynomial spline. In addition, we discuss the numerical computations provident and can be used to solve complex problems, also the results are obtained to be in a nice error estimation with known exact solutions. [ABSTRACT FROM AUTHOR]

A numerical approach is defined to get the solution of the regularized long wave (RLW) equation. The hyperbolic- trigonometric tension (HTT) B-spline is adapted as a trial function to the Galerkin method. Space integration of the RLW equation is managed trough HTT B-spline Galerkin method over the finite elements. Resulting system of ordinary differential equations is integrated using the Crank Nicolson technique. Thus RLW equation is fully integrated into system of nonlinear algebraic equations. Solution of this system gives the approximate solution of the RLW equation over the given problem domain. [ABSTRACT FROM AUTHOR]

We establish large deviation inequalities with exponential decay for the maximum of partial sums of subgaussian random variables. Applying our result to acceptable sequences of bounded mean zero random variables, we strengthen a well-known inequality of Hoeffding. As a consequence we prove a bounded law of iterated logarithm for this class of random variables. The obtained method, also allows us to state a strong integrability property for weighted series of negatively dependent random variables. [ABSTRACT FROM AUTHOR]

A Galerkin finite element method is constructed for computing solution of the Fisher equation. Hyperbolic-trigonometric tension (HTT) B-splines are used as weight and shape functions in the Galerkin approach. Fully discretization of the Fisher equation is fulfilled via Crank-Nicolson method in time and Galerkin method in space. Travelling wave front solution is studied to show robustness of the presented scheme on Fisher equation. The numerical results obtained with the present method are satisfactory with regard to its accuracy. [ABSTRACT FROM AUTHOR]

In this paper, Rayleigh Gamma Gompertz (RGGom), as a new compound distribution, is introduced. Various fundamental statistical properties of RGGom distribution, including explicit expressions for the non-central rth moment, characteristic function, quantile function and simulated data, Shannon and relative entropies, and reliability stress strength model, were studied and inspected. The unknown parameters of RGGom have been estimated using the estimation method of maximum likelihood. Furthermore, the RGGom distribution is applied upon a simulation study and two real-life data sets to assess its usefulness and flexibility. [ABSTRACT FROM AUTHOR]

Fractal image coding is one of the active techniques for image compression. It always motivates for designing efficient algorithms to optimize the search space and reduce computation efforts, which is the main disadvantage of this technique. Hybridizing the metaheuristic methods has a vital interest in the optimization field. In this work, an intelligent search technique based on combining of crowding genetic and scattered search methods is proposed, in which the essential steps (generating a collection of diverse trial solutions, and the combined solutions method) in scattered search replaced by the two essential steps (the recombination and the mutation) in crowding method. Satisfactory results in reducing the computation cost of the fractal image compression technique are obtained. [ABSTRACT FROM AUTHOR]

In paper, we consider a system of Kirchhoff type with logarithmic nonlinearity. We prove the global existence of weak solutions by using the potential well method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a new flexible compound distribution named Marshal Olkin Marshal Olkin Gompertz (MOMOGo) distribution. Reliability characteristics besides several statistical properties of the proposed distribution have discussed. The maximum likelihood method, under a complete sample, is used to estimate the distribution parameters. Furthermore, two real data sets are considered to investigate the applicability of the proposed MOMOGo distribution. [ABSTRACT FROM AUTHOR]

The goal of this article is to present double almost lacunary statistical convergence of weight of g in 2-normed spaces. Furthermore, we examine some inclusion theorems and variations. [ABSTRACT FROM AUTHOR]

A multi-dimensional QTRU public-key cryptosystem improves NTRU by replacing the original ring in NTRU by quaternion algebra. In this paper, we introduce QMNTR an improvement of QTRU by using a new mathematical structure of two public keys and five private keys. This modification has enhanced the public key system to be more robust and secure. [ABSTRACT FROM AUTHOR]

A two layer Implicit method on hexagonal grids is proposed for approximating the solution to first type boundary value problem of heat equation on rectangle. It is proven that the given implicit scheme is unconditionally stable and converges to the exact solution on the grids of order O (h 4 + τ 2) where, h and 3 2 h are the step sizes in space variables x1 and x2 respectively and τ is the step size in time. The method is applied on a test results. [ABSTRACT FROM AUTHOR]

Second order degenerate Chiral oscillator Lagrangian is reduced into first order Lagrangian and Hamiltonian analysis of this formalism is performed by means of the DiracBergmann constraint algorithm. [ABSTRACT FROM AUTHOR]

The case k = 3 of a complete k-partite graph is called a complete tripartite graph Tp,q,r. It is a graph that its vertices are decomposed into three disjoint sets such that, no two graph vertices within the same set are adjacent. It has recently attracted much attention due to its important in several applications, especially, in chemistry where some of the molecular orbital compounds are correspondents to the tripartite graph structure. One method of capturing graph structure is through computing of the characteristic polynomial for the matrix characterization M of a graph, which is defined as the determinant | λI – M | where I is the identity matrix and λ is the variable of the polynomial. The general technique of the characteristic polynomials evaluation of graphs with large number of vertices is considered as an extremely tiresome problem when it is based on matrix, because its computational complexity is high. In this paper, a new approach for the characteristic polynomial of a complete tripartite graph Ti,i,n−2i, for n ≥ 4, based on the adjacency matrix is introduced. It shows good efficiency because it reduces the complexity and the difficulty of computation in comparing to some well-known methods especially, for the graphs with large number of vertices. [ABSTRACT FROM AUTHOR]

The dependence on technology, digital transformation and the need to work remotely are increasing day by day. It is predicted to increase further after this COVID-19 pandemic. The desire to digitize every object also leads to the need to develop or update many application software. It is very difficult with traditional software development methods to produce flexible solutions to such dynamic and changing demands on time. At the same time, there are problems such as finding qualified human resources and high cost in writing and updating corporate program codes that can be considered complex on a large scale. Low-code software development platforms provide solutions for such problems. These platforms aim to produce flexible and less costly programs in a shorter time by using drag-and-drop components through visual interfaces without requiring deep programming knowledge. This study is based on the examination of the SetXRM platform, which is one of the new generation low-code applications that helps to produce more flexible and short-term solutions to the increasing software needs of the enterprise. [ABSTRACT FROM AUTHOR]

This paper proposes a stabilization method to approximate analytical solutions of magnetohydrodynamics (MHD) equations. The method adds two modular grad-div steps into fully-discrete finite element MHD solver. The main idea in these intrusive steps is to penalize the divergence of the velocity/magnetic fields both in L2 and H1-norms. The paper confirms the optimal convergence of the method, and gives numerical experiments which reveal positive effect of the method as in the usual grad-div stabilization. [ABSTRACT FROM AUTHOR]

Diabetic Retinopathy (DR) is a vascular disorder affecting the retina due to prolonged diabetes. DR is one of the causes of vision defection. The risk of blindness can be reduced significantly in patients by early screening of diabetic patients for the development of diabetic retinopathy. In this study, vascular structure was extracted from fundus images using the Kirsch's method. Gaussian filter has been applied to the extracted vascular structure and removed from its noise. In this way, the detection of DR by pre-trained artificial intelligence has been made significantly easier. [ABSTRACT FROM AUTHOR]

Recently, Big Data is gathered from various sources in different types, and it is not easy to analyze them by traditional methods. Apache Hadoop is a robust solution to the problems of saving and processing large datasets by providing HDFS (Hadoop Distributed File System) and MapReduce for storing and processing data. One of the essential methods for analyzing big data to discover new patterns is the clustering algorithms. In this paper, we have used the canopy clustering algorithm provided by Distributed Machine Learning with Apache Mahout as preprocessing step for the k-means clustering algorithm. The results showed that using Canopy as a preprocessing step has sped up the time of managing the massive scale of the healthcare insurance dataset, and it also reduces the execution time of the k-means by providing initial centroids for the given dataset. [ABSTRACT FROM AUTHOR]

In this paper, the effect of the simultaneous rotation of two different groups, hydroxyl (OH) and hydroxymethyl (CH2OH) groups, on the basic properties of Glycerol are comprehensively studied. Relative energies are reported at the HF/ aug-cc-pVDZ, b3lyp/ aug-cc-pVDZ levels with corrections for zero-point vibrational energies. Structural parameters, Electric Dipole Moment and HOMO-LUMO energy gap of the identified conformers are also tabled. An inverse correlation between the relative energy and HOMO-LUMO energy gap is seen. [ABSTRACT FROM AUTHOR]

"Fake News (FNs) is defined as a made-up story to deceive or to mislead." The problem of FNs spread widely in recent years, especially on social media such as Facebook, Twitter, and other sources like webs and blogs. It has become a significant problem in society as a result of changing people's ideas and opinions about the direction of this news. In this paper, FNs detection can be proposed by using the Term Frequency-Inverse Document Frequency (TF-IDF) as features extraction, and Multi-Layer perceptron (MLP) algorithm as a classifier. Two phases (feed-forward and back-propagation) are used with a three-layers, which are (input layer, one hidden layer, and output layer). After running our proposed algorithm on a FNs dataset, the classification accuracy achieved equals 95.47%. [ABSTRACT FROM AUTHOR]

In today's world where the effects of Covid-19 are felt intensely all over the world, change in traditional retail has become necessary. Traditional merchandising based on physical contact Covid-19 is not suitable. People do not shop from places that are not safe for health. Technological innovations in the retail sector paved the way for information and digital-based commerce. Instant data obtained from the devices used are transferred to central databases over networks. With the machine learning method based on artificial intelligence, more efficient and faster business activities are performed on these data. Sensor and camera-assisted deep learning-based IoT applications play a very important role in combating the epidemic. Shopping environments without contact, waiting, cashier, store assistant, cash flow and credit card applications are a great advantage for the Covid-19 period. Less human contact and hygienic environments that are not crowded are critical in this period. In this study, the use of contactless payments, artificial intelligence-supported digital innovations and Covid-19 measures were examined in the retail sector. [ABSTRACT FROM AUTHOR]

Facial expression recognition has become an increasingly important area of research in recent years. Neural network- based methods have made amazing progress in performing recognition-based tasks, winning competitions set up by various data science communities, and achieving high performance on many datasets. Miscellaneous regularization methods have been utilized by various researchers to help combat over-fitting, to reduce training time, and to generalize their models. In this paper, by applying the Haar Cascade classifier to crop faces and focus on the region of interest, we hypothesize that we would attain a fast convergence without using the whole image to analyze facial expressions. We also apply label smoothing and analyze its effect on the databases of CK+, KDEF, and RAF. The ResNet model has been employed as an example of a neural network model. Label smoothing has demonstrated an improvement of the recognition accuracy up to 0.5% considering CK+ and the KDEF databases. While the application of Haar Cascade has shown to decrease the achieved accuracy on KDEF and RAF databases with a small margin, fast convergence of the model has been observed. [ABSTRACT FROM AUTHOR]

Well-consolidated servers are needed in the execution of information technology processes. With rapid digitalization, information processing units turn into unplanned, heterogeneous, problematic, cumbersome and complex structures that require too much labor. In these structures, which are difficult to manage and irregular, resources that are not used effectively are wasted. Information technology resources such as CPU, memory, disk, operating system, network and human are costly components. Solutions are produced with virtualization technology against such high cost complex structures. With a well-structured virtualization solution, dynamic structures with flexible structure, low cost, high performance, safe, fast and uninterrupted are created, as well as labor gains in installation, maintenance and management that require technical expertise. This study is on the analysis of the examples of institutions performing virtualization and the research results on virtualization cost savings over an example data server model. [ABSTRACT FROM AUTHOR]

Underwater robots have the ability to go down the sea up to several meters of height without any fear of loss of human lives. These robots need autonomous control systems and guidance to carry out their tasks. One of the main objectives of any underwater robot is to reach a given depth under the water and also be able to maintain that depth throughout the operation period. In this paper a simple full state feedback controller was designed to control the underwater robot's depth, despite all the external forces and disturbances during a given mission. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate ideal strong lacunary ward continuity in 2-normed spaces. A function f on a subset A of a 2-normed space X into X is ideal strongly lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences of points in A. We also studied some other kinds of continuities. [ABSTRACT FROM AUTHOR]

In this study, source identification problem for the two dimensional neutron transport equation is studied. For the approximate solution of this problem a first order of accuracy difference scheme is presented. Stability inequalities for the solution of these differential and difference problems are established. Numerical results are given. [ABSTRACT FROM AUTHOR]

In this paper, two stage difference method is presented to solve the Dirichlet problem for the Laplace equation on rectangle. In the first stage, the sum of the pure fourth order derivatives of the required solution is approximated on a square grid. Then, by using the quantities that are determined in the first stage, the system of difference equations which approximates the Dirichlet problem, is computed during the second stage. The difference equations found in the stages are formulated by using the 5-point averaging operator. Due to these facts that, the boundary values are continuous and sixth times differentiable at the edges of the rectangle, the derivatives of them satisfy Hölder condition and at the end, their second and fourth order derivatives meet the matching condition implied by the Laplace equation. We proved that the difference solution of the Dirichlet problem is uniform convergent with the order O(h4), where h denotes the mesh size. [ABSTRACT FROM AUTHOR]

In this work, we discuss a third order of accuracy difference scheme for approximate solution of the elliptic overdeter-mined multi-point problem in the Hilbert space. Functional operator approach is used to study existence and uniqueness of solution of difference problem. Stability, almost coercive stability and coercive stability estimates for solution of difference scheme are established. [ABSTRACT FROM AUTHOR]

In this paper, a numerical approach is proposed for solving one dimensional nonlinear time-space-fractional reaction-advection-diffusion equation with Dirichlet boundary conditions. The fractional derivatives are described in the conformable sense. The numerical scheme is based on shifted Chebyshev polynomials of the fourth kind. The unknown function is written as Cheby-shev series with m terms. The nonlinear space fractional reaction-advection-diffusion equation is reduced to a system of nonlinear ordinary differential equations by using the properties of Chebyshev polynomials and conformable fractional calculus.The finite difference method is applied to solve this system. Finally, numerical example is presented to confirm the reliability and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The present paper studies a Bolza problem of optimal control theory with third-order polyhedral delay-differential inclusions and state constraints. We aim to establish well verifiable sufficient conditions of optimality for the polyhedral third- order delay-differential inclusions. Discrete-approximate inclusions are investigated using the method of discretization to ensure the transition to a continuous problem. The idea for obtaining sufficient conditions of the problem is based on passing the formal limit on the optimality conditions of the discrete-approximation problem. Thus, the sufficient conditions are formulated by using polyhedral Euler-Lagrange inclusions and the distinctive "transversality" conditions. [ABSTRACT FROM AUTHOR]

In this study, the first order of accuracy difference scheme for approximate solution of source identification elliptic problem with integral and second kind boundary conditions is considered. Stability and coercive stability estimates for solution of the difference scheme are described. Moreover, test example with computation results is given. [ABSTRACT FROM AUTHOR]

In the present paper, the initial value problem for the Schrödinger type involutory partial differential equation is studied. Applying Green's function of space operator, we get formula for solution of this problem. In applications, the theorem on stability of this problem is established. Furthermore, this formula is applied to the existence and uniqueness of bounded solution of nonlinear problem with involution. [ABSTRACT FROM AUTHOR]

In the present paper, a source identification problem for elliptic-telegraph equation with non-local condition is studied. Stability estimates for the differential equations of the source identification problem are established. Furthermore, stability estimates for the difference schemes of the source identification problem are presented. [ABSTRACT FROM AUTHOR]

In this study, nonlocal boundary value Schrödinger type problem in a Hilbert space with the self-adjoint positive definite operator is investigated. Single step stable third and fourth order of accuracy difference schemes for the numerical solution of this problem are presented. The main theorems on the stability of these difference schemes are established. In application, theorem on the stability of difference schemes for nonlocal boundary value problems for Schrödinger equations is proved. Numerical results are given. [ABSTRACT FROM AUTHOR]

In the present paper, a space-dependent identification problem for parabolic-elliptic equations is investigated. The second order of accuracy r-modified Crank-Nicholson difference schemes for the numerical solution of the source identification parabolic-elliptic problems are presented. Numerical results are given. [ABSTRACT FROM AUTHOR]

We prove common fixed point theorems for mappings satisfying a general contractive inequality of integral type for generalized metric spaces. Our results extend of the theorem of Branciari (2002) constitutionally and we provide some examples in support of our results. [ABSTRACT FROM AUTHOR]

The present extended abstract considers the differential equations on smooth closed manifolds, investigates and establishes the well-posedness of nonlocal boundary value problems (NBVP) in Hölder spaces. It also establishes new coercivity estimates in various Hölder norms for the solutions of such boundary value problems for parabolic equations. [ABSTRACT FROM AUTHOR]

In the present paper, we study a source identification problem for hyperbolic-parabolic equation with nonlocal conditions. The stability estimates for the solution of this source identification problem are established. Furthermore, we construct the second order of accuracy difference scheme for the approximate solution of the problem under consideration. The stability estimates for the solution of this difference scheme are presented. [ABSTRACT FROM AUTHOR]

In this paper we study the domain of generalized Riesz difference matrix RqΔ(α) of fractional order α in the classical sequence spaces c0 and c and introduced the sequence spaces r 0 q (Δ (α)) and r c q (Δ (α)). We obtain the α−, β− and γ−duals of these spaces and using Hausdorff measure of noncompactness, we characterize certain classes of compact operators on the space r 0 q (Δ (α)). [ABSTRACT FROM AUTHOR]

In this paper, we prove some periodic point results on partial metric spaces. Thus, we generalize famous results existing in the literature such as Boyd-Wong fixed point theorem and Banach fixed point theorem. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce the concepts of Wijsman deferred statistical convergence of order α and Wijsman strong deferred Cesàro convergence of order α for sequences of sets. [ABSTRACT FROM AUTHOR]

In this extended abstract, we introduce the concept of delta quasi Cauchy sequences in metric spaces. A function f defined on a subset of a metric space X to X is called delta ward continuous if it preserves delta quasi Cauchy sequences, where a sequence (xk) of points in X is called delta quasi Cauchy if lim n → ∞ [ d (x k + 2 , x k + 1) − d (x k + 1 , x k) ] = 0. A new type compactness in terms of δ-quasi Cauchy sequences, namely δ-ward compactness is also introduced, and some theorems related to δ-ward continuity and δ-ward compactness are obtained. Some other types of continuities are also discussed, and interesting results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the concept of Abel statistical delta ward compactness and Abel statistical delta ward continuity in metric spaces. A function f defined on a metric space X into X is called Abel statistically delta ward continuous it preserves Abel statistical delta quasi Cauchy sequences, where a sequence (xk) of points in X is called Abel statistically delta quasi Cauchy if lim x → 1 − (1 − x) ∑ k : | d (x k + 2 , x k + 1 − d (x k + 1 , x k ) | ≥ ε x k = 0 for every ε > 0, Some other types of compactnesses are also studied and interesting results are obtained. [ABSTRACT FROM AUTHOR]

The concept of P-convergent double sequence spaces was presented in 1988 by Moricz and Rhoades, and also in 2005, the notion of almost lacunary strongly P-convergent double sequences was introduced by Savas and Patterson, using Orlicz functions. Following these two concepts, we present the double almost lacunary strongly P-convergent of weight g via Orlicz functions in 2-Normed spaces. Additionally, inclusion theorems and extension of existing results in the literature will be established. [ABSTRACT FROM AUTHOR]

In this paper we introduce and study some properties of the new sequence space of order α which is defined using the modulus and ϕ function. Furthermore some connections between V μ α ((T , φ)) - strong summability of sequences and μ− strong convergence of order α with respect to a modulus are studied. [ABSTRACT FROM AUTHOR]

In this study, we introduce and examine the concepts of Δm−weighted statistical convergence and Δm−weighted (N ¯ , p n) −summability. Also some relations between Δm−weighted statistical convergence and Δm−weighted (N ¯ , p n) −summability are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of strong ρ−convergence of order β (or N p β (ρ) −convergence) of sequence of real numbers and give some inclusion relations between the set of all ρ−statistical convergence of order β and strong N p β (ρ)− convergence. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study characterization of strongly λ- invariant regular matrices, uniqueness of generalized limits and inclusion relations of such sequences have been discussed. [ABSTRACT FROM AUTHOR]

In this study, by using definition of ρ-statistical convergence which was defined by Ç akallı[2], we give some inclusion relations between the set of ρ-statistical convergence and strong (S, [ρ]) summability. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of Δα-deferred statistical convergence with the fractional order of α and Δα- strongly convergence with the fractional order of α. Additionally, we give some relations about these concepts. [ABSTRACT FROM AUTHOR]