MATHEMATICAL RESEARCHES
Year:2019 | Volume:4 | Issue:2 |Papers Count:10

Introduction This paper presents an algorithm for covering orthogonal polygons with minimal number of guards. This idea examines the minimum number of guards for orthogonal simple polygons (without holes) for all scenarios and can also find a rectangular area for each guards. We consider the problem of covering orthogonal polygons with a minimum number of r-stars. In each orthogonal polygon P, two points' p and q are called r-visible if these two points are in opposite rectangular corners, then the entire rectangle is placed in P. Now we consider a polygon P to be an r-Star if there is a point p in it so that every point q is r-visible from p. ...

In this paper, we deal with solving systems of linear congruences over commutative CFrings. More precisely, let R be a CF-ring (every finitely generated direct sum of cyclic R-modules has a canonical form) and let I, , In 1 be n ideals of R. We consider the system of linear congruences: ...

Introduction The time dependent Schrö dinger equation with arbitrary potential function is a fundamental equation of quantum mechanics. It is well known that Schrö dinger equation play an essential role in the relativistic and non-relativistic quantum mechanics. This equation arises in many other practical domains of physical and technological interest, e. g. optics, seismology and plasma physics. Many problems of solid state physics, atomic and molecular structure and spectra, molecular dynamics and quantum chemistry require the solution of the nonlinear time dependent Schrö dinger equation. ...

Variational problems and elliptic equations with-growth conditions have been widely investigated in latest years, mainly due to their applications in the theory of elastic mechanics. This fruitful generalization of the classical-Laplace operator is also motivated by questions arising in image restoration as well as in the mathematical modelling of electrorheological fluids. The corresponding functional spaces and enjoy properties similar to those of and, respectively, but there are some crucial differences. ...

During recent years, the theory of fractional calculus has gained notable attention from scientists due to its capability for describing various complicated natural phenomena. Complex processes in natural science can be described more exactly by using the theory of fractional calculus. Many anomalous and complicated phenomena in mechanics, chemistry, physics and other sciences have been mathematically modelled as fractional differential and integral equations. The fractional equations are very powerful mathematical tools to describe the inherent characteristics and hereditary properties of materials and processes. ...

In the analysis of life-testing data which is studied in many fields of applied statistics and medical studies, due to the lack of insufficient financial resources and/or time limitations, the censored data are considered. There are different types of censoring schemes. In this study, type-II censored is used. In this method, the test is continued until the occurrence of the th failure time. The number of failure units is predetermined. Also, the estimation parameter of distribution is one of the important discussions in statistical inference. In this paper, the parameters of Lomax distribution under the censored of the second type data can be estimated using the EM algorithm and the Lindley approximation. ...

The probability density function is a basic concept in statistics, which can be used to study all behaviors of a random variable; several nonparametric methods have been used to estimate the probability density function. One of a nonparametric procedure used to estimate densities is the kernel method. In this paper, to reduce bias of kernel density estimation, methods such as usual kernel (UK), geometric extrapolated usual kernel (GEUK), a bias reduction kernel (BRK) and a geometric extrapolated bias reduction kernel (GEBRK) are introduced. Theoretical properties, including the selection of smoothness parameter and the accuracy of resultant estimators are studied. Accordingly, the mean integrated squared error of GEBRK method achieves a faster convergence rate when kernels are symmetric. ....

Let be a nonempty subset of a normed linear space. A self-mapping is said to be nonexpansive provided that for all. In 1965, Browder showed that every nonexpansive self-mapping defined on a nonempty, bounded, closed and convex subset of a uniformly convex Banach space, has a fixed point. In the same year, Kirk generalized this existence result by using a geometric notion of normal structure. ...

Introduction Optimal control problems occur in engineering, science and many other fields. An optimal control problem is a problem of optimization of an objective functional on a set of state and control variables, which is called the performance index, subject to dynamic constraints on the states and controls. In the case that the dynamic constraints include delay fractional differential equation, the problem is called a delay fractional optimal control problem. In this paper, we consider the following optimal control problem ....

In this study, we use a newly proposed method based on the software structure of the maple, called the Khaters method, and will be introducing exponential, hyperbolic, and trigonometric solutions for one of the Schrö dinger equations, called the nonlinear Schrö dinger equation with the dual power law nonlinearity. Given the widespread use of the Schrö dinger equation in physics and engineering, solving this equation is very important with the above method, which includes a large variety of solutions. Schrö dinger's nonlinear equation is a partial differential equation that plays a significant role in modern physics. ...