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If we consider G = (V, E) to be a connected graph, with v is an element of V and e = uw is an element of E, then d(G)(e, v) = min{d(G)(u, v), d(G) (w, v)} has been defined as the distance between a vertex v and an edge e. The card...
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If we consider G = (V, E) to be a connected graph, with v is an element of V and e = uw is an element of E, then d(G)(e, v) = min{d(G)(u, v), d(G) (w, v)} has been defined as the distance between a vertex v and an edge e. The cardinality of the smallest subset S subset of V which can assign a unique distance vector to every edge of G is referred to as edge metric dimension (EMD) given by edim(G). A k multiwheel graph W-1,W- n,W- k is composed of k cycles C-n along with a central vertex x such that x is adjacent to each of the vertices of C-1 and the corresponding vertices of the two consecutive cycles C-i and Ci+i are also adjacent for all 1 收起
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The optimal control for vibration suppression of a plate by distributed piezoelectric actuators is considered. A performance index in the form of a weighted quadratic functional of the dynamic response of a rectangular simply supp...
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The optimal control for vibration suppression of a plate by distributed piezoelectric actuators is considered. A performance index in the form of a weighted quadratic functional of the dynamic response of a rectangular simply supported plate will be minimized within a prescribed time duration using piezoelectric patches (voltages). The minimization of the performance index over these voltages is subject to the equation of motion governing the plate's structural vibration and a set of initial and boundary conditions. The solution method is a combination of modal space expansion and direct state parameterization. Modal space expansion will transform the optimal control of a distributed parameter system into the optimal control of a lumped parameter system. Using Legendre wavelets, the quadratic optimization problem is transformed into a mathematical programming problem, where the objective is to minimize a set of unknown coefficients to obtain the optimal trajectory and the optimal control. Numerical examples will be provided to illustrate the effectiveness and the efficiency of the proposed method.
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In this paper, we consider the plate equation with both weak frictional damping and viscoelastic damping acting simultaneously and complementarily in the domain. An energy decay rate formula is obtained under nonrestrictive hypoth...
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In this paper, we consider the plate equation with both weak frictional damping and viscoelastic damping acting simultaneously and complementarily in the domain. An energy decay rate formula is obtained under nonrestrictive hypotheses on the relaxation function and the frictional damping term. Our results improve and generalize previous results existing in the literature.
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Cryptocurrencies are decentralized electronic counterparts of government-issued money. The first and best-known cryptocurrency example is bitcoin. Cryptocurrencies are used to make transactions anonymously and securely over the in...
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Cryptocurrencies are decentralized electronic counterparts of government-issued money. The first and best-known cryptocurrency example is bitcoin. Cryptocurrencies are used to make transactions anonymously and securely over the internet. The decentralization behavior of a cryptocurrency has radically reduced central control over them, thereby influencing international trade and relations. Wide fluctuations in cryptocurrency prices motivate the urgent requirement for an accurate model to predict its price. Cryptocurrency price prediction is one of the trending areas among researchers. Research work in this field uses traditional statistical and machine-learning techniques, such as Bayesian regression, logistic regression, linear regression, support vector machine, artificial neural network, deep learning, and reinforcement learning. No seasonal effects exist in cryptocurrency, making it hard to predict using a statistical approach. Traditional statistical methods, although simple to implement and interpret, require a lot of statistical assumptions that could be unrealistic, leaving machine learning as the best technology in this field, being capable of predicting price based on experience. This article provides a comprehensive summary of the previous studies in the field of cryptocurrency price prediction from 2010 to 2020. The discussion presented in this article will help researchers to fill the gap in existing studies and gain more future insight.
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It is well known that numerical simulations of the cardiac monodomain model require fine mesh resolution, which increases the computational resources required. In this paper, we construct three operator-splitting alternating direc...
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It is well known that numerical simulations of the cardiac monodomain model require fine mesh resolution, which increases the computational resources required. In this paper, we construct three operator-splitting alternating direction implicit (ADI) schemes to efficiently solve the nonlinear cardiac monodomain model. The main objective of the proposed methods is to reduce the computational time and memory consumed for solving electrocardiology models, compared to standard numerical methods. The proposed methods have second order accuracy in both space and time while evaluating the ionic model only once per time-step. Several examples using regular wave, spiral wave reentry, and nonsymmetrical scroll wave are conducted, and the efficiency of the proposed ADI methods is compared to the standard semi-implicit Crank-Nicolson/ Adams-Bashforth method. Large-scale twoand three-dimensional simulations are performed.
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We compute for the first time, the number of fuzzy topologies defined on a finite set and having a small number of open sets. Certain cases, where the number of open sets is large, are also considered. Several well known results a...
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We compute for the first time, the number of fuzzy topologies defined on a finite set and having a small number of open sets. Certain cases, where the number of open sets is large, are also considered. Several well known results are obtained as corollaries. The paper is ended by some questions for future investigations. (C) 2016 Elsevier B.V. All rights reserved.
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In this paper, we establish several results concerning chains in Y-X, the lattice of mappings from a finite set X into a finite totally ordered set Y. We compute the total number and the cardinalities of several collections of cha...
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In this paper, we establish several results concerning chains in Y-X, the lattice of mappings from a finite set X into a finite totally ordered set Y. We compute the total number and the cardinalities of several collections of chains. As a byproduct we determine the total number of chained Y-fuzzy topologies defined on X. Several related and other well known results are obtained as corollaries. Also some natural questions are presented for further investigations. (C) 2018 Elsevier Inc. All rights reserved.
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In this work, a new alternative uniformly convergent iterative scheme is presented and applied for the solution of an extended class of linear and nonlinear third order boundary value problems that arise in physical applications. ...
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In this work, a new alternative uniformly convergent iterative scheme is presented and applied for the solution of an extended class of linear and nonlinear third order boundary value problems that arise in physical applications. The method is based on embedding Green's functions into well-known fixed point iterations, including Picard's and Krasnoselskii-Mann's schemes. Convergence of the numerical method is proved by manipulating the contraction principle. The effectiveness of the proposed approach is established by implementing it on several numerical examples, including linear and nonlinear third order boundary value problems. The results show highly accurate approximations when compared to exact and existing numerical solutions. (C) 2015 Elsevier Inc. All rights reserved.
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Regular plane tessellations can easily be constructed by repeating regular polygons. This design is of extreme importance for direct interconnection networks as it yields high overall performance. The honeycomb and the hexagonal n...
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Regular plane tessellations can easily be constructed by repeating regular polygons. This design is of extreme importance for direct interconnection networks as it yields high overall performance. The honeycomb and the hexagonal networks are two such popular mesh-derived parallel networks. The first and second Zagreb indices are among the most studied topological indices. We now consider analogous graph invariants, based on the second degrees of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for the Hex, Hex derived and some honeycomb networks.
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A numerical scheme aimed at solving a broad class of second-order nonlinear boundary value problems (BVPs) is presented, described, and then applied to a problem that appears in chemical reactor theory. In particular, the steady-s...
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A numerical scheme aimed at solving a broad class of second-order nonlinear boundary value problems (BVPs) is presented, described, and then applied to a problem that appears in chemical reactor theory. In particular, the steady-state solution of the equation governing the model of the adiabatic tubular chemical reactor is investigated. The proposed method is based on expressing the particular solution of the governing equation in terms of an integral involving Green's function. Then, the Krasnoselskii-Mann's fixed-point scheme is implemented to an amended version of the resulting integral operator. The convergence of the iterative scheme is proved and its efficiency and applicability are demonstrated by solving the equation for selected values of the parameters that appear in the model. Residual error computation is adopted to confirm the accuracy of the results. In addition, the numerical outcomes of the proposed method are compared with those obtained by other existing numerical approaches.
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