Computational scheme for solving nonlinear fractional stochastic differential equations with delay

Abstract

This paper studies the numerical solution of fractional stochastic delay differential equations driven by Brownian motion. The proposed algorithm is based on linear B-spline interpolation. The convergence and the numerical performance of the method are analyzed. The technique is adopted for determining the statistical indicators of stochastic responses of fractional Langevin and Mackey-Glass models with stochastic excitations.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

Assessing Number Sense of Students in Australia,Sweden, Taiwan,and the United States

This paper reports selected findings from a study of number sense proficiency of students aged 8 to 14 years in Australia, Sweden, United States, and Taiwan. It comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Some implications for classrooms of the findings are then discussed.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.     

Decompositions for edge-coloring join graphs and cobipartite graphs

An edge-coloring is an association of colors to the edges of a graph, in such a way that no pair of adjacent edges receive the same color. A graph G is Class 1 if it is edge-colorable with a number of colors equal to its maximum degree Δ(G). To determine whether a graph G is Class 1 is NP-complete [I. Holyer, The NP-completeness of edge-coloring, SIAM J. Comput. 10 (1981) 718-720]. First, we propose edge-decompositions of a graph G with the goal of edge-coloring G with Δ(G) colors. Second, we apply these decompositions for identifying new subsets of Class 1 join graphs and cobipartite graphs. Third, the proposed technique is applied for proving that the chromatic index of a graph is equal to the chromatic index of its semi-core, the subgraph induced by the maximum degree vertices and their neighbors. Finally, we apply these decomposition tools to a classical result [A.J.W. Hilton, Z. Cheng, The chromatic index of a graph whose core has maximum degree 2, Discrete Math. 101 (1992) 135-147] that relates the chromatic index of a graph to its core, the subgraph induced by the maximum degree vertices.     

\mathfrak D -parallelism of normal and structure Jacobi operators for hypersurfaces in complex two-plane Grassmannians

In this paper, we give non-existence theorems for Hopf hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C }^{m+2})$ with $\mathfrak D $ -parallel normal Jacobi operator ${\bar{R}}_N$ and $\mathfrak D $ -parallel structure Jacobi operator $R_{\xi }$ if the distribution $\mathfrak D $ or $\mathfrak D ^{\bot }$ component of the Reeb vector field is invariant by the shape operator, respectively.     

Higher order symmetric spaces and the roots of the identity in a Lie group

Let denote the set of all -roots of the identity in a Lie group . We show that is always an embedded submanifold of , having the conjugacy classes of its elements as open submanifolds. These conjugacy classes are examples of -symmetric spaces and we show, more generally, that every -symmetric space of a Lie group is a covering manifold of an embedded submanifold of . We compute also the Hessian of the inclusions of and into , relative to the natural connection on the domain and to the symmetric connection on .