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Abstract: Abstract In this paper, we first construct a fast Euler-Maruyama (EM) method based on the sum-of-exponentials approximation for a class of nonlinear fractional stochastic differential equations whose coefficients satisfy a linear growth condition and the Lipschitz continuity. Then the strong convergence of this fast EM method is proved with the order \(\alpha -\frac{1}{2}\) , where \(\alpha \in (\frac{1}{2},1)\) is the index of Caputo fractional derivative. Finally, numerical experiments are given to verify the theoretical results and demonstrate that the computational efficiency of the fast EM scheme has overwhelming advantages over the original EM method. PubDate: 2022-05-11
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Abstract: Abstract MDS symbol-pair codes forms an optimal class of symbol-pair codes for their best error-correction capability. \(\psi \) -constacyclic codes of length \(p^s\) over \(\mathfrak {R}=\mathbb {F}_{q}+ u\mathbb {F}_{q} + u^{2}\mathbb {F}_{q}\,\, (u^3=0)\) , where \(q=p^m \) , \(\psi \) is a nonzero element of \(\mathbb {F}_{q}\) , are precisely the ideals of the ring \( {\mathfrak {R}[x]}/{\langle x^{p^s}-\psi \rangle } \) which is a local finite non chain ring with the non principal maximal ideal \(\langle u, x-\varphi \rangle \) , where \( \varphi \in \mathbb {F}_{q} \) satisfying \( \psi =\varphi ^{p^s} \) . In this paper, all MDS symbol-pair \(\psi \) -constacyclic codes of length \(p^s\) over \(\mathfrak {R}\) are established. PubDate: 2022-05-05
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Abstract: Abstract This article discussed and analyzed a numerical technique based on fractional-order Lagrange polynomials to solve a class of fractional-order non-linear Volterra-Fredholm integro-differential equations. The fractional derivative has been considered of Caputo type. The existence and uniqueness of the continuous solution have been discussed for the given problem. In this approach, first using the Laplace transform, fractional-order Lagrange polynomials operational matrices of fractional integration have been derived. Then using these operational matrices, the continuous problem has been reduced into a system of algebraic equations. The error analysis also has been carried out and an upper error bound estimate for the approximate solution has been given in \(L^2\) -norm. It is also shown that as the number of fractional-order Lagrange polynomials increases, the approximation error approaches to zero rapidly. Further, some numerical examples are discussed to verify the accuracy and efficiency of the proposed numerical technique and to validate our theoretical findings. PubDate: 2022-05-05
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Abstract: Abstract In this paper, we first construct two infinite families of new two-weight codes over \(\mathbb {Z}_{2^m}\) with respect to homogeneous metric and Lee metric by their generator matrices, which generalizes the results in Shi et al (Des Codes Cryptogr 88(3):1–13, 2020) from two different directions. We construct some optimal codes over \(\mathbb {Z}_{2^m}\) and prove all codes in one of these two families are self-orthogonal. Finally, we determine the linearity of the Gray images of the codes we constructed for Lee metric completely. PubDate: 2022-05-04
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Abstract: Abstract This paper deals with a mathematical model for HTLV-I infection by considering the role of imprecise essence of the biological parameters. The considered imprecise biologically realistic parameters are taken as a form of triangular fuzzy number. Then the imprecise parameters are transformed to the associated intervals and then with the aid of interval mathematics the corresponding differential equations is changed to two equations. Next, by utilizing utility function method the transformed differential equations is converted to a differential equation. The dynamics of fuzzy HTLV-I model is studied with the help of the utility function method. We explored the qualitative features of HTLV-I model including positivity, boundedness, uniform persistence and biologically feasible equilibrium points, namely disease-free equilibrium point, HTLV-I free steady state and an interior equilibrium point. Our theoretical analysis demonstrates that local and global stability are examined by two critical parameters \(R_0\) and \(R_1\) , basic reproduction numbers due to viral infection and for cytotoxic-T-lymphocytes response, respectively. By using geometric approach, we performed global stability of the endemic equilibrium point which is not only theoretically significant but also important in forecasting the development of HTLV-I infection in the long-run so that involvement strategies can be effectively sketched. Some numerical illustrations are presented to support our theoretical analysis under imprecise biological parameters. PubDate: 2022-05-04
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Abstract: Abstract In this paper, we have developed a fully discrete Alikhanov finite element method to solve the time-fractional Schrödinger equation with non-smooth solution. The proposed scheme uses the Alikhanov formula on graded meshes to approximate the Caputo fractional derivative in temporal direction and the standard finite element method in spatial direction. Furthermore, the \(L^2(\Omega )\) -norm stability and the optimal convergent result for the computed solution are derived. Finally, a numerical example is presented to verify the accuracy of the proposed scheme. PubDate: 2022-04-29
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Abstract: Abstract R. Hofer and A. Winterhof proved that the 2-adic complexity of the two-prime (binary) generator of period pq with two odd primes \(p\ne q\) is close to its period and it can attain the maximum in many cases. When the two-prime generator is applied to producing quaternary sequences, we need to determine the 4-adic complexity. It is proved that there are only two possible values of the 4-adic complexity for the two-prime quaternary generator, which are at least \(pq-1-\max \{\log _4(pq^2),\log _4(p^2q)\}\) . Examples for primes p and q with \(5\le p, q <10000\) illustrate that the 4-adic complexity only takes one value larger than \(pq-\max \{\log _4(p),\log _4(q)\}\) , which is close to its period. So it is good enough to resist the attack of the rational approximation algorithm. PubDate: 2022-04-28
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Abstract: Abstract In this paper, compact finite difference schemes with \((3-\alpha )\) -th order accuracy in time and fourth order accuracy in space based on the L1 method are constructed for time-fractional diffusion-wave equations with time delay, where \(\alpha \in (1,2)\) is the fractional order. When solving the two dimensional situation, we adopt the alternating direction implicit (ADI) method to improve the computing efficiency. The convergence and stability of the difference schemes are proved based on some crucial skills. In the end, some numerical examples demonstrate our theoretical statement. PubDate: 2022-04-28
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Abstract: Abstract A discrete-time predator–prey model is investigated in this paper. In considered model, the population is assumed to follow the model suggested by Ricker 1954. Existence and stability of equilibria are studied. Numerical simulations reveal that, depending on the parameters, the system has complicated and rich dynamics and can exhibit complex patterns. Also the bifurcation diagrams are presented. PubDate: 2022-04-27
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Abstract: Abstract In this paper, we develop a new two-sex mosquito population suppression model including stage structure and a reproduction delay. Sterile mosquitoes are introduced to suppress the development of wild mosquito populations and a special function \(M_s(t)\) is used as a control function to describe the number of sterile mosquitoes in the field. Firstly, the dynamic behaviors of the system when the control function is a constant function, a general continuous function and a periodic pulse function are analyzed theoretically, and the existence and stability of the equilibria of the system are determined. In particular, the conditions for the global stability of the wild mosquito-extinction equilibrium, that is, the conditions for the successful suppression of wild mosquitoes, are found. Then, a series of numerical simulations are carried out which on the one hand verify the theoretical results obtained, and on the other hand supplement the imperfections of the theoretical study. Finally, a brief conclusion is given, and the focus of further research is pointed out. PubDate: 2022-04-22
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Abstract: Abstract Tuberculosis is an infectious disease caused by bacteria that most commonly affects the lungs. Due to its high mortality, it remains a global health issue, and it is one of the leading causes of death in the majority of sub-Saharan African countries. We formulate a six-compartmental deterministic model to investigate the impact of vaccination on the dynamics of tuberculosis in a given population. The qualitative behaviors of the presented model were examined, and the respective threshold quantity was obtained. The tuberculosis-free equilibrium of the system is said to be locally asymptotically stable when the effective reproduction number \(\mathcal {R}_{0}<1\) and unstable otherwise. Furthermore, we examined the stability of the endemic equilibrium, and the conditions for the existence of backward bifurcation are discussed. A numerical simulation was performed to demonstrate and support the theoretical findings. The result shows that reducing the effective contact with an infected person and enhancing the rate of vaccinating susceptible individuals with high vaccine efficacy will reduce the burden of tuberculosis in the population. PubDate: 2022-04-22
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Abstract: Abstract Considering that one of the most significant challenges for oil industry planners is developing an effective schedule plan that reduces costs, increases profitability, and enhances customer satisfaction, this article improves a formulation for scheduling multi-product pipelines. The primary goal is to minimize operational expenses, which include inventory and shortages, interfaces, and labor. Consideration is given to batch sizing limits, inventory carrying costs, backlog, and settlement periods. Additionally, certain parameters have been classified as having the belief degree-based type of uncertainty due to a lack of relevant historical data. As solution strategies, three separate conversion approaches are used. The model's efficiency and dependability, as well as the proposed methodologies, are demonstrated numerically. Sensitivity analysis shows that objective function values are highly dependent on changes in confidence levels, so the best technique is implemented. PubDate: 2022-04-18
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Abstract: Abstract Algebraic systems with positive coefficients appear in several applications. We consider a family of such systems depending on parameters. Using Brouwer’s Theorem, properties of convex functions, and iterative methods we study the existence and the uniqueness of positive solutions for these systems. PubDate: 2022-04-17
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Abstract: Abstract In this paper, we apply the variational technique together with the local linking theory or the fountain theorem to study a class of discrete Kirchhoff type problems with Dirichlet boundary conditions. Examples and numerical simulations are also provided to illustrate applications of our results. PubDate: 2022-04-16
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Abstract: Abstract Two new spectral conjugate gradient methods (ZL1 method and ZL2 method) for solving unconstrained optimization problems are established. Under the standard Wolfe line search, the search direction generated by the ZL1 method is a descent direction. The search direction of the ZL2 method satisfies descent property independent of the line search. The global convergence of the two new methods can be demonstrated under the standard Wolfe line search. Numerical experiments are presented to show that the two methods are effective. PubDate: 2022-04-11
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Abstract: Abstract In this study, we consider a three-dimensional discrete-time model to investigate the interaction between normal host cells with functional immune cells and tumor cells. Fixed point analysis is performed to study the stability of the discrete three-dimensional model and the sensitivity of the system analysis on the initial cell population. Necessary and sufficient conditions for optimal control of tumor cell growth have been created with the introduction of immune-chemotherapy drugs and the chaotic behavior of the system with branching having been demonstrated. The turbulence behavior of the system is shown by branching and Lyapunov power is performed for the integer-order discrete model and the turbulence effect is compared to the different fractional orders of the discrete model. Also, by numerical simulation, validating the theoretical results of the work and the effect of fractional derivative order on system chaos are investigated. PubDate: 2022-04-05
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Abstract: Abstract In this paper, a new conjugacy condition is established to solve unconstrained optimization problems based on a new quasi-Newton equation. We present a modified Dai–Liao conjugate gradient method to solve unconstrained optimization problems with a new value of the parameter t based on the new conjugacy condition. The presented algorithm has the following properties: (i) the modified Dai–Liao conjugate gradient method considers both the gradient and function value information. (ii) The global convergence is achieved for the modified Dai–Liao conjugate gradient method under some suitable assumptions. (iii) Numerical experiments on unconstrained optimization problems and image restoration problems are conducted, and the numerical results show that our method is efficient. PubDate: 2022-04-01
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Abstract: Abstract The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones. PubDate: 2022-04-01
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Abstract: Graph invariants provide an outstanding tool for investigation of abstract structures of graphs. They contain global and general information about a graph and its particular substructures. In this paper, the graph invariants such as vertex connectivity, metric dimension, minimum vertex degree, independence number, domination number, Laplacian energy and Zagreb indices of line graph of zero-divisor graph over the rings \(\mathbb {Z}_{pq}\) and \(\mathbb {Z}_{p^n}\) (where p and q are prime) are determined. Moreover, we provide a MATLAB code for calculating Laplacian energy and Zagreb indices of line graph of \(\varGamma (\mathbb {Z}_{n})\) . PubDate: 2022-04-01
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Abstract: Abstract The concept of energy of a graph was first introduced by I. Gutman [5] in 1978. The energy E(G) of a simple graph G is defined to be the sum of the absolute values of the eigenvalues of G. The tree dendrimer d(n, k) is a finite connected cycle free graph, also known as Bethe lattice. The each vertex in d(n, k) is connected to \((k-1)\) . It is a rooted tree, with all other vertices arranged in shells around the root vertex, also called the central vertex. In this paper, the reduction formula for the characteristic polynomial of d(2, k) and d(3, k) is obtained. By using these reduction formulas, the energy of these graphs is also calculated. The comparison of energy for different values of n and k is also given. PubDate: 2022-04-01
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