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Abstract: In this paper, we consider the following generalized nonlinear k-Hessian system $$\left\{ {\matrix{{{\cal G}\left( {S_k^{{1 \over k}}(\lambda ({D^2}{z_1}))} \right)S_k^{{1 \over k}}(\lambda ({D^2}{z_1})) = \varphi (\left x \right ,{z_1},{z_2}),\,\,\,x \in {\mathbb{R}^N},} \cr {{\cal G}\left( {S_k^{{1 \over k}}(\lambda ({D^2}{z_2}))} \right)S_k^{{1 \over k}}(\lambda ({D^2}{z_2})) = \varphi (\left x \right ,{z_1},{z_2}),\,\,\,x \in {\mathbb{R}^N},} \cr } \,} \right.$$ where \({\cal G}\) is a nonlinear operator and S k (λ(D 2 z)) stands for the k-Hessian operator. We first are interested in the classification of positive entire k-convex radial solutions for the k-Hessian system if φ(∣x∣, z 1, z 2) = b(∣x∣)φ(z 1, z 2) and ψ(∣x∣, z 1, z2) = h(∣x∣)ψ(z 1). Moreover, with the help of the monotone iterative method, some new existence results on the positive entire k-convex radial solutions of the k-Hessian system with the special non-linearities ψ,φ are given, which improve and extend many previous works. PubDate: 2021-10-01
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Abstract: Although there are many papers on variable selection methods based on mean model in the finite mixture of regression models, little work has been done on how to select significant explanatory variables in the modeling of the variance parameter. In this paper, we propose and study a novel class of models: a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The problem of variable selection for the proposed models is considered. In particular, a modified Expectation-Maximization(EM) algorithm for estimating the model parameters is developed. The consistency and the oracle property of the penalized estimators is established. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. An example is illustrated by the proposed methodologies. PubDate: 2021-10-01
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Abstract: In this paper, we investigate the CUSUM statistic of change point under the negatively associated (NA) sequences. By establishing the consistency estimators for mean and covariance functions respectively, the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge, which extends the results obtained under the case of an independent normal sample and the moving average processes. Finally, the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis. PubDate: 2021-10-01
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Abstract: Particle Swarm Optimization, a potential swarm intelligence heuristic, has been recognized as a global optimizer for solving various continuous as well as discrete optimization problems. Encourged by the performance of Gompertz PSO on a set of continuous problems, this works extends the application of Gompertz PSO for solving binary optimization problems. Moreover, a new chaotic variant of Gompertz PSO namely Chaotic Gompertz Binary Particle Swarm Optimization (CGBPSO) has also been proposed. The new variant is further analysed for solving binary optimization problems. The new chaotic variant embeds the notion of chaos into GBPSO in later stages of searching process to avoid stagnation phenomena. The efficiency of both the Binary PSO variants has been tested on different sets of Knapsack Problems (KPs): 0–1 Knapsack Problem (0-1 KP) and Multidimensional Knapsack Problems (MKP). The concluding remarks have made on the basis of detailed analysis of results, which comprises the comparison of results for Knapsack and Multidimensional Knapsack problems obtained using BPSO, GBPSO and CGBPSO. PubDate: 2021-10-01
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Abstract: We introduced the fuzzy axioms of choice, fuzzy Zorn’s lemma and fuzzy well-ordering principle, which are the fuzzy versions of the axioms of choice, Zorn’s lemma and well-ordering principle, and discussed the relations among them. As an application of fuzzy Zorn’s lemma, we got the following results: (1) Every proper fuzzy ideal of a ring was contained in a maximal fuzzy ideal. (2) Every nonzero ring contained a fuzzy maximal ideal. (3) Introduced the notion of fuzzy nilpotent elements in a ring R, and proved that the intersection of all fuzzy prime ideals in a commutative ring R is the union of all fuzzy nilpotent elements in R. (4) Proposed the fuzzy version of Tychonoff Theorem and by use of fuzzy Zorn’s lemma, we proved the fuzzy Tychonoff Theorem. PubDate: 2021-10-01
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Abstract: In this article, we are exploring the hemodynamics of nanofluid, flowing through a bifurcated artery with atherosclerosis in the presence of a catheter. For treating obstruction in the artery, one can use the catheter whose outer surface is carrying the drug coated with nano-particles. The resultant solvent is considered as blood nano-fluid. Blood being a complex fluid, is modeled by couple stress fluid. In the presence of nano-particles, the temperature and the concentration distribution are understood in a bifurcated stenotic artery. The concluded mathematical model is governed by coupled non-linear equations, and are solved by using the homotopy perturbation method. Consequently, we have explored is the effects of fluid and the embedded geometric parameters on the hemodynamics characteristics. It is also realized that high wall shear stress exists for couple stress nano-fluid when compared to Newtonian nanofluid. which is computed at a location corresponding to maximum constriction (z = 12.5) of the artery. PubDate: 2021-10-01
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Abstract: In this article, some new rigorous perturbation bounds for the SR decomposition under normwise or componentwise perturbations for a given matrix are derived. Also, the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach. Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature. PubDate: 2021-10-01
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Abstract: The nonlinear conformable time-fractional Zoomeron equation is an important model to describe the evolution of a single scalar field. In this paper, new exact solutions of conformable time-fractional Zoomeron equation are constructed using the Improved Bernoulli Sub-Equation Function Method (IBSEFM). According to the parameters, 3D and 2D figures of the solutions are plotted by the aid of Mathematics software. The results show that IBSEFM is an efficient mathematical tool to solve nonlinear conformable time-fractional equations arising in mathematical physics and nonlinear optics. PubDate: 2021-10-01
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Abstract: The motivation behind this paper is a sequence Sn of generalized Szász operators using multiple Appell polynmials. The purpose of the present paper is to find the image of the polynomials under these operators. We find that as n → ∞, Sn (tm; x) approaches to xm for every m ∈ ℕ. Finally, We prove the image of a polynomial of degree m under these operators is another polynomial of degree m by using the linearity of these operators. PubDate: 2021-10-01
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Abstract: Allergy due to toxic pollutants present in the environment has become a major public health threat affecting the lives of more than one billion people worldwide. Its prevalence and impact are on the rise due to urbanization and growing chemical industries, on the other hand emerging toxic allergens heavily impact the budgets of public health systems. In the current work, the dynamical model of allergy due to pollution is constructed and studied. Moreover, the basic reproduction number is formulated to calculate the threshold value of allergic diseases. The model is stabilized locally and globally, besides the conditions that emerged from stability theory are used to study the effects of various parameters. Z-type control mechanism has been used to optimize the stability of the model. Numerical simulations validate, that chaotic oscillated compartments are stabilized under the effect of Z-control which shows that allergic diseases due to the polluted environment can be controlled. PubDate: 2021-10-01
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Abstract: In [3], Chen, Deng, Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces Lp(ℝn), Hardy spaces Hp(ℝn) and general mixed norm spaces, which implies almost everywhere convergence of such operator. In this paper, we study the rate of convergence on fractional power dissipative operator on some sobolev type spaces. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-3901-8
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Abstract: We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions. Consequently, we get the results for many dependent structures, such as END, ϱ*-mixing, ϱ−-mixing and φ-mixing, etc. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-3816-4
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Abstract: Based on the quantile regression, we extend Koenker and Xiao (2004) and Ling and McAleer (2004)’s works from finite-variance innovations to infinite-variance innovations. A robust t-ratio statistic to test for unit-root and a re-sampling method to approximate the critical values of the t-ratio statistic are proposed in this paper. It is shown that the limit distribution of the statistic is a functional of stable processes and a Brownian bridge. The finite sample studies show that the proposed t-ratio test always performs significantly better than the conventional unit-root tests based on least squares procedure, such as the Augmented Dick Fuller (ADF) and Philliphs-Perron (PP) test, in the sense of power and size when infinite-variance disturbances exist. Also, quantile Kolmogorov-Smirnov (QKS) statistic and quantile Cramer-von Mises (QCM) statistic are considered, but the finite sample studies show that they perform poor in power and size, respectively. An application to the Consumer Price Index for nine countries is also presented. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-4187-6
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Abstract: Multiplicative calculus (MUC) measures the rate of change of function in terms of ratios, which makes the exponential functions significantly linear in the framework of MUC. Therefore, a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC. Taking this as motivation, this paper lays mathematical foundation of well-known classical Gauss-Newton minimization (CGNM) algorithm in the framework of MUC. This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization (MGNM) method along with its convergence properties. The proposed method is generalized for n number of variables, and all its theoretical concepts are authenticated by simulation results. Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions. From simulation results, it has been observed that proposed MGNM method converges for 12972 points, out of 19600 points considered while optimizing multiplicatively-linear exponential function, whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points, respectively. Furthermore, for a given set of initial value, the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods. A similar pattern is observed for multiplicatively-non-linear exponential function. Therefore, it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-3814-6
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Abstract: Fractal interpolation is a modern technique to fit and analyze scientific data. We develop a new class of fractal interpolation functions which converge to a data generating (original) function for any choice of the scaling factors. Consequently, our method offers an alternative to the existing fractal interpolation functions (FIFs). We construct a sequence of α-FIFs using a suitable sequence of iterated function systems (IFSs). Without imposing any condition on the scaling vector, we establish constrained interpolation by using fractal functions. In particular, the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data. The existence of \({{\cal C}^r} - \alpha - {\rm{FIFs}}\) is investigated. We identify suitable conditions on the associated scaling factors so that α-FIFs preserve r-convexity in addition to the \({{\cal C}^r} - {\rm{smoothness}}\) of original function. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-3635-7
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Abstract: As is well known, the definitions of fractional sum and fractional difference of f (z) on non-uniform lattices x(z) = c1z2 + c2z + c3 or x(z) = c1qz + c2q−z + c3 are more difficult and complicated. In this article, for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways. The analogue of Euler’s Beta formula, Cauchy’ Beta formula on non-uniform lattices are established, and some fundamental theorems of fractional calculas, the solution of the generalized Abel equation on non-uniform lattices are obtained etc. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-4013-1
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Abstract: This paper investigates the nonlinear boundary value problem resulting from the exact reduction of the Navier-Stokes equations for unsteady magnetohydrodynamic boundary layer flow over the stretching/shrinking permeable sheet submerged in a moving fluid. To solve this equation, a numerical method is proposed based on a Laguerre functions with reproducing kernel Hilbert space method. Using the operational matrices of derivative, we reduced the problem to a set of algebraic equations. We also compare this work with some other numerical results and present a solution that proves to be highly accurate. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-3761-2
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Abstract: In this note, we show a sharp lower bound of \(\min \left\{{\sum\nolimits_{i = 1}^k {{d_G}({u_i}):{u_1}{u_2} \ldots {u_k}}} \right.\) is a path of (2-)connected G on its order such that (k-1)-iterated line graphs Lk−1(G) are hamiltonian. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-3885-4
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Abstract: In this paper, weak optimal inverse problems of interval linear programming (IvLP) are studied based on KKT conditions. Firstly, the problem is precisely defined. Specifically, by adjusting the minimum change of the current cost coefficient, a given weak solution can become optimal. Then, an equivalent characterization of weak optimal inverse IvLP problems is obtained. Finally, the problem is simplified without adjusting the cost coefficient of null variable. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-4324-2
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Abstract: In this paper, first, Bernstein multi-scaling polynomials (BMSPs) and their properties are introduced. These polynomials are obtained by compressing Bernstein polynomials (BPs) under sub-intervals. Then, by using these polynomials, stochastic operational matrices of integration are generated. Moreover, by transforming the stochastic integral equation to a system of algebraic equations and solving this system using Newton’s method, the approximate solution of the stochastic Itô-Volterra integral equation is obtained. To illustrate the efficiency and accuracy of the proposed method, some examples are presented and the results are compared with other methods. PubDate: 2021-09-01 DOI: 10.1007/s11766-021-3694-9
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