Applied Mathematics-a Journal Of Chinese Universities Series B最新文献

In this paper, we introduced a numerical approach for solving the fractional differential equations with a type of variable-order Hilfer-Prabhakar derivative of order μ(t) and ν(t). The proposed method is based on the Jacobi wavelet collocation method. According to this method, an operational matrix is constructed. We use this operational matrix of the fractional derivative of variable-order to reduce the solution of the linear fractional equations to the system of algebraic equations. Theoretical considerations are discussed. Finally, some numerical examples are presented to demonstrate the accuracy of the proposed method.

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.

Polygon clipping is of great importance in computer graphics. One of the popular algorithms to clip a polygon is Cohan—Sutherland Hodgeman algorithm which is based on line clipping. Cohan—Sutherland Hodgeman algorithm clips the polygon against the given rectangular clip window with the help of line clipping method. Cohan—Sutherland algorithm requires traversing the polygon in anti clockwise direction (positive orientation). In this work we propose an efficient polygon clipping algorithm against a rectangular clip window. Proposed algorithm uses parametric representation of polygon edges. Using the concept of point clipping, we can find required intersection points of edges of polygon with clip window boundaries. Well suited numerical illustrations are used to explain the proposed polygon clipping method. The proposed algorithm is computationally less expensive and comprehensive.

A series of detailed quantitative results is established for the family of demi-distributions which is a large extension of the family of usual distributions.

In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.

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.

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.

The motivation behind this paper is a sequence S_n 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 → ∞, S_n (t^m; x) approaches to x^m 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.

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.

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.