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Abstract: A space-filling (SF) design gives a good representation of experimental region with even fewer points by selecting its points everywhere in the region with as few gaps as possible. Elsawah (J Comput Appl Math 384:113164, 2021) presented the multiple tripling (MT) technique for constructing a new class of three-level designs, called multiple triple designs (MTDs). The MT technique showed its superiority over the widely used techniques by constructing new large optimal MTDs in an efficient manner using small initial designs (InDs). This paper gives a closer look at the SF behavior of MTDs after all of its factor projections and level permutations (FPs-LPs) that alter their statistical inference abilities. The selection of optimal designs by FPs-LPs of such large MTDs needs millions of trials to test all the possible cases. This paper tries to solve this hard computational problem by building theoretical bridges between the SF behavior of the MTD after all of its FPs-LPs and the behavior of the corresponding InD, which is investigated based on the similarity among its runs, confounding among its factors, and uniformity of its points. This study provides benchmarks to guide the experimenters before using FPs-LPs for improving the SF behavior of MTDs in the full dimension and any low dimension. Moreover, the construction of non-isomorphic MTDs is discussed and a lower bound of the number of non-isomorphic MTDs is given. Finally, numerical studies to support the interesting theoretical findings are provided. PubDate: 2022-05-17

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Abstract: In this study, a source identification problem for elliptic differential equation with integral type non-local condition is discussed. The second order of accuracy difference scheme for elliptic non-local source identification problem is studied. Using spectral resolution of a self-adjoint operator, stability and coercive stability estimates for solution of difference scheme are established. Subsequently, difference scheme for an approximate solution of multi-dimensional boundary-value problem with integral type non-local and first kind boundary conditions is investigated for stability. Numerical results for 2D and 3D examples are illustrated. PubDate: 2022-05-16

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Abstract: The mean curvature-based image deblurring model is widely used in image restoration to preserve edges and remove staircase effect in the resulting images. However, the Euler–Lagrange equations of the mean curvature model lead to the challenging problem of solving a nonlinear fourth order integro-differential equation. Furthermore the discretization of the Euler–Lagrange equations produces a nonlinear ill-conditioned system which affects the convergence of the numerical algorithms such as Krylov subspace methods (GMRES, etc.) In this paper, we have treated the high order nonlinearity by converting the nonlinear fourth order integro-differential equation into a system of first order equations. To speed up convergence by GMRES method, we have introduced a new circulant preconditioned matrix. Fast convergence is assured by the proved analytical property of our proposed new preconditioner. The first order error estimates are also established for the finite difference discretization. The effectiveness of our algorithm can be observed through fast convergence rates in numerical examples. PubDate: 2022-05-16

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Abstract: This study gives more attention to soliton wave solutions of the nanoparticle hybrid system through two recent (generalized rational (GRat) and Kudryashov (GKud)) schemes. Because of the hybrid model’s nanoscale size, the nanoparticles in these new solitonic liquid wave structures exhibit unique electrical and optical characteristics crucial to several applications. The constructed results are numerically simulated in polar, contour, two, and three-dimensional graphs to demonstrate the dynamic behavior of an inviscid, incompressible, and non-rotating flow of fluid of constant depth h. Moreover, the obtained solutions’ accuracy is also checked by implementing two precise numerical (quintic-B-spline (QBS) and septic-B-spline (SBS)) schemes. The matching between computational and approximate solutions is explained through some distinct graphs in two-dimensional and distribution graphs. The novelty of our results is also elucidated by comparing our results with those constructed previously. PubDate: 2022-05-16

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Abstract: Conjugate gradient method is one of the most efficient methods for large-scale unconstrained optimization and has attracted focused attention of researchers. With the emergence of more and more large-scale problems, subspace technique becomes particularly important. Recently, many scholars have studied subspace minimization conjugate gradient methods, where the iteration direction is generally obtained by minimizing a quadratic approximate model in a specific subspace. Considering that the conic model contains more information than the quadratic model, and may perform better when the objective function is not close to quadratic, in this paper, a improved conjugate gradient method is presented. Specially, in each iteration, a quadratic or conic model is dynamically selected. The search direction is obtained by minimizing the selected model in a three-dimensional subspace spanned by the current gradient and latest two search directions. It is proved that the search direction satisfies the sufficient descent condition under given conditions. With the modified nonmonotone Wolfe line search, we establish the global convergence and the R-linear convergence of the proposed method under mild assumptions. Numerical experiments indicate that the proposed method is efficient. PubDate: 2022-05-16

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Abstract: In this paper, a new class of hemivariational inequalities is introduced. It concerns Laplace operator on locally finite graphs together with multivalued nonmonotone nonlinearities expressed in terms of Clarke’s subdifferential. First of all, we state and prove some results on the subdifferentiability of nonconvex functionals defined on graphs. Thereafter, an elliptic hemivariational inequality on locally finite graphs is considered and the existence and uniqueness of its weak solutions are proved by means of the well-known surjectivity result for pseudomonotone mappings. In the end of this paper, we tackle the problem of hemivariational inequalities of parabolic type on locally finite graphs and we prove the existence of its weak solutions. PubDate: 2022-05-13

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Abstract: In this study, traveling wave solutions have been explored with the newly developed improved tanh method and modified \(\left( {1/G^{\prime}} \right)\) -expansion method for the Fractional foam drainage equation, which is famous for modeling physical phenomena such as heat conduction and acoustic waves. Abundant solutions are successfully achieved which have not been appeared ever in the literature. The found solutions are represented graphically to bring out the appearances of different types solitons. In addition, three important points are highlighted in the result and discussion section. First, the comparison of the applied methods, second, the association of the obtained solutions with the literature, and finally the effect of the change in the parameters with physical properties on the wave behavior are discussed. PubDate: 2022-05-12

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Abstract: We propose a new model for removing the Salt and Pepper Noise (SPN) by combining the high-order total variation overlapping group sparsity with the nuclear norm regularization. Since the proposed model is convex, non-smooth, and separable, the alternating direction method of multipliers (ADMM) can be employed to solve it and the convergence can be kept. Numerical comparisons with some related state-of-the-art models show that the proposed model can significantly improve the restored quality in terms of the signal to noise ratio (SNR) and the structural similarity index measure (SSIM). PubDate: 2022-05-12

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Abstract: In this paper, we study the algebraic structure of a new family of linear codes over the mixed alphabet \({\mathbb {Z}}_2\mathrm {R}\) , where \(\mathrm {R}={\mathbb {Z}}_2+u{\mathbb {Z}}_2+u^2{\mathbb {Z}}_2+u^3{\mathbb {Z}}_2, \ u^4=0\) . We present generator and parity-check matrices of \({\mathbb {Z}}_2\mathrm {R}\) -linear codes in standard form. We define a \({\mathbb {Z}}_2\mathrm {R}\) -cyclic code of length (r, s) as a \(\mathrm {R}[x]\) -submodule of \(\frac{{\mathbb {Z}}_2[x]}{\langle x^r-1 \rangle } \times \frac{\mathrm {R}[x]}{\langle x^s-1 \rangle }\) and determine its generator polynomial. Also, we determine the size of a \({\mathbb {Z}}_2\mathrm {R}\) -cyclic code by giving a minimal spanning set. Furthermore, we present the generator polynomial of dual code of a \({\mathbb {Z}}_2\mathrm {R}\) -cyclic code of length (r, s) for odd s, while r is set arbitrary. Finally, optimal binary codes are constructed from Gray images of \({\mathbb {Z}}_2\mathrm {R}\) -cyclic codes. PubDate: 2022-05-11

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Abstract: Data including significant losses are a pervasive issue in general insurance. The computation of premiums and reinsurance premiums, using deductibles, in situations of heavy right tail for the empirical distribution, is crucial. In this paper, we propose a mixture model obtained by compounding the Birnbaum–Saunders and gamma distributions to describe actuarial data related to financial losses. Closed-form credibility and limited expected value premiums are obtained. Moment estimators are utilized as starting values in the non-linear search procedure to derive the maximum-likelihood estimators and the asymptotic variance–covariance matrix for these estimators is determined. In comparison to other competing models commonly employed in the actuarial literature, the new mixture distribution provides a satisfactory fit to empirical data across the entire range of their distribution. The right tail of the empirical distribution is essential in the modeling and computation of reinsurance premiums. In addition, in this paper, to make advantage of all available data, we create a regression structure based on the compound distribution. Then, the response variable is explained as a function of a set of covariates using this structure. PubDate: 2022-05-11

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Abstract: To increase competition, control price, and decrease inefficiency in the carbon allowance auction market, limitations on bidding price and volume can be set. With limitations, participants have the same cap bidding price and volume. While without the limitations, participants have different values per unit of carbon allowance; therefore, some participants may be strong and the other week. Due to the impact of these limitations on the auction, this paper tries to compare the uniform and discriminatory pricing in a carbon allowance auction with and without the limitations utilizing a multi-agent-based model consisting of the government and supply chains. The government determines the supply chains' initial allowances. The supply chains compete in the carbon auction market and determine their bidding strategies based on the Q-learning algorithm. Then they optimize their tactical and operational decisions. They can also trade their carbon allowances in a carbon trading market in which price is free determined according to carbon supply and demand. Results show that without the limitations, the carbon price in the uniform pricing is less than or equal to the discriminatory pricing method. At the same time, there are no differences between them in the case with limitations. Overall, the auction reduces the profit of the supply chains. This negative effect is less in uniform than discriminatory pricing in the case without the limitations. Nevertheless, the strong supply chains make huge profits from the auction when mitigation rate is high. PubDate: 2022-05-10

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Abstract: The aim of the present work is to obtain numerical solutions of the solitary wave, undular bore and boundary-forced problems for Regularized Long Wave (RLW) equation. For this purpose, low-order modified cubic B-spline is chosen as base functions. Crank–Nicolson formulae combined with efficient space discretization method have been applied. With the aid of Rubin and Graves type linearization technique, nonlinear terms are linearized and a solvable linear equation system has been obtained. Three significant test problems in the literature are solved successfully. The present algorithm has obtained high accurate numerical solutions of the RLW equation. Numerical results are compared with those of some earlier ones and given. The rates of the convergence are also investigated. PubDate: 2022-05-10

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Abstract: As two mathematical tools for dealing with uncertainty, the covering rough set theory and the evidence theory have close relationships with each other. Different covering rough set models are characterized by evidence theory. The purpose of this paper is to interpret belief functions with two pairs of covering approximation operators. The two pairs of covering approximation operators are equivalent to a pair of relation approximation operators. Then, based on a necessary and sufficient condition for a belief structure to be the belief structure induced by the pair of relation approximation operators, necessary and sufficient conditions for a belief structure to be the belief structure induced by the covering approximation operators are presented. Moreover, two kinds of covering reductions in covering information systems defined from the two pairs of covering approximation operators are characterized by the belief and plausibility functions. PubDate: 2022-05-07

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Abstract: Sylvester-type matrix equations have wide applications in system science, control theory, and so on. In this paper, we consider a constrained system of Sylvester-type matrix equations over the quaternions. We first derive the necessary and sufficient conditions for the system to have a solution and propose a formula of its general solution when it is solvable. As an application, we then investigate the \(\eta \) -Hermitian solution of a system. Moreover, we also give a numerical example to illustrate the main findings of this paper. PubDate: 2022-05-06

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Abstract: In this study, a shape optimization problem for the two-dimensional stationary Navier–Stokes equations with an artificial boundary condition is considered. The fluid is assumed to be flowing through a rectangular channel, and the artificial boundary condition is formulated so as to take into account the possibility of ill-posedness caused by the usual do-nothing boundary condition. The goal of the optimization problem is to maximize the vorticity of the said fluid by determining the shape of an obstacle inside the channel. Meanwhile, the shape variation is limited by a perimeter functional and a volume constraint. The perimeter functional was considered to act as a Tikhonov regularizer and the volume constraint is added to exempt us from possible topological changes. The shape derivative of the objective functional was formulated using the rearrangement method, and this derivative was later on used for gradient descent methods. Additionally, an augmented Lagrangian method and a class of solenoidal deformation fields were considered to take into account the goal of volume preservation. Lastly, numerical examples based on gradient descent and the volume preservation methods are presented. PubDate: 2022-05-06

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Abstract: Low-rank matrix recovery from an observation data matrix has received considerable attention in recent years, which has a wide range of applications in pattern recognition and computer vision, such as face denoising, background/foreground separation, gait recognition, image alignment, etc. However, existing algorithms suffer from the interference of small noise, for example, low-level Gaussian noise, which makes their performance not satisfactory. To address this issue, we are based on the unconstrained nonconvex relaxed minimization model for low-rank and sparse matrices recovery using low-rank matrix decomposition, and propose a novel efficient and effective solving algorithm in terms of direction matrices and step sizes alternating iteration in this paper. The three direction matrices are deduced using Newton method, Taylor expansion and so forth, and the appropriate step size of the direction sparse matrix is searched by the nonmonotonous step size linear search technique efficiently. In theory, we provide the convergence theorem of the proposed algorithm. Experimentally, its efficiency and effectiveness are illustrated under appropriate conditions. PubDate: 2022-05-05

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Abstract: The intention along this study is to provide an analytical approach to model a flame propagation formulated with a non-linear diffusion. The proposed model can be used to characterize the flame behaviour, and has been previously discussed with a linear diffusion with accurate results. Nonetheless, along this analysis, the non-linear diffusion is introduced supported by the mathematical properties induced by the porous medium equation theory formulated within the partial differential equations theory. First of all, regularity, existence and uniqueness of solutions are shown to hold. Afterwards, asymptotic solutions are obtained with purely analytical techniques. Particular solutions for the flame pressure and temperature variables are provided. Aiming the search of travelling waves (TW) profiles, a minimal travelling wave speed is provided to ensure a purely monotone travelling wave behaviour free of oscillation. In addition, the geometric perturbation theory is explored to show the normal hyperbolic condition of the manifolds used to obtain the travelling waves profiles. The existence of such profiles are based on a topological argument in the phase plane given by the involved manifolds close the critical point. Afterwards, dedicated travelling wave profiles are obtained showing an exponential behaviour and the existence of a propagating support. Note that the existence of an exponential solution is not trivial in the non-linear diffusion case. Finally, the property known as finite speed of propagation is shown to exist and a precise supersolution has been obtained to model the flame propagation at the beginning of the process. The finite speed precludes the existence of an evolving flame front that has been precisely determined. PubDate: 2022-05-04

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Abstract: Despite the increasing complexity of real-world multi-attribute decision-making (MADM) situations, the decision-makers have no problems in providing some incomplete (also called imprecise or partial) information about attribute (importance) weights. Often, incomplete weight information takes the form of weights bounded between upper and lower limits, ranked weights, etc. In this work, we deal with the important class of multi-attribute choice problems (MACPs) in which incomplete weight information consists of a ranking of weights. Prominent solution methods for such MACPs can be classified into dominance measuring methods (DMMs), or ordinal surrogate-weighting schemes. The object of the present article is to circumvent the shortcomings of the most efficacious solution methods that can be used to solve the MACPs under-ranked weights. To that end, we devise here an original safe sequential screening technique named the "TCA-algo'' method. The newly devised method follows three steps: (1) the decision matrix is normalized (if needed) and Pareto dominated alternatives are screened out, (2) a tentative choice alternative (TCA) is nominated from among Pareto optimal alternatives, and (3) the nominated TCA is tested using an appropriate dominance rule established herein. The second and third steps of the suggested method are repeated until a final choice alternative (FCA) is reached. Numerical examples and experimental results show convincingly that the TCA-algo method outperforms prominent solution methods. PubDate: 2022-05-04

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Abstract: We study the split common fixed point problem for Bregman demigeneralized type mappings in the context of two real Banach spaces. We propose a new self-adaptive method and prove that it converges strongly to a solution of this problem. As consequences of our results, we propose some new self-adaptive methods for solving split feasibility problem, split common null point problem and split equilibrium problem, using some dynamical stepsize techniques, which allow these methods to be easily implemented without prior knowledge of the norm of the bounded linear operator. We perform some numerical experiments to demonstrate implementation and efficiency of our methods. PubDate: 2022-05-03

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Abstract: In this paper, the orthogonal array and Latin square are used to construct authentication codes. First, orthogonal arrays are constructed by mutually orthogonal Latin squares. Then, the orthogonal array is used to establish the mapping between authentication tag and the message set, and a non-splitting Cartesian authentication code and a splitting authentication code are constructed. Furthermore, the coding matrix of the non-splitting Cartesian authentication code is used to establish a connection with the Latin square, and a security authentication code is constructed. These construction methods are of universal significance. The probability of successful impersonation attack and substitution attack of these codes, various distribution probabilities, and information entropy are calculated. Finally, the performance of these authentication codes is analyzed, and it is verified that the constructed codes are perfect and optimal. PubDate: 2022-05-02