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.     

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 .

     

Solving multiple-objective problems in the objective space

Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.This work was partially sponsored by grants from CNP_q and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments.     

Measurements in Situ and Spectral Analysis of Wind Flow Effects on Overhead Transmission Lines

In the paper an important issue of vibrations of the transmission line in real conditions was analyzed. Such research was carried out by the authors of this paper taking into account the cross-section of the cable being in use on thetransmission line. Analysis was performed for the modern ACSR high voltage transmission line with span of 213.0 m. The purpose of the investigation was to analyze the vibrations of the power transmission line in the natural environmentand compare with the results obtained in the numerical simulations. Analysis was performed for natural and wind excited vibrations. The numerical model was made using the Spectral Element Method. In the spectral model, for variousparameters of stiffness, damping and tension force, the system response was checked and compared with the results of the accelerations obtained in the situ measurements. A frequency response functions (FRF) were calculated. Thecredibility of the model was assessed through a validation process carried out by comparing graphical plots of FRF functions and numerical values expressing differences in acceleration amplitude (MSG), phase angle differences (PSG) and differences in acceleration and phase angle total (CSG) values. Particular attention was paid to the hysteretic damping analysis. Sensitivity of the wave number was performed for changing of the tension force and section area of thecable. The next aspect constituting the purpose of this paper was to present the wide possibilities of modelling and simulation of slender conductors using the Spectral Element Method. The obtained results show very good accuracy in the range of both experimental measurements as well as simulation analysis. The paper emphasizes the ease with which the sensitivity of the conductor and its response to changes in density of spectral mesh division, cable cross-section,tensile strength or material damping can be studied.     

Acetone powder from dormant seeds of Ricinus communis L

The influence of several factors on the hydrolytic activity of lipase, present in the acetone powder from dormant castor seeds (Ricinus communis) was evaluated. The enzyme showed a marked specificity for short-chain substrates. The best reaction conditions were an acid medium, Triton X-100 as the emulsifying agent and a temperature of 30 degrees C. The lipase activity of the acetone powder of different castor oil genotypes showed great variability and storage stability of up to 90%. The toxicology analysis of the acetone powder from genotype Nordestina BRS 149 showed a higher ricin (toxic component) content, a lower 2S albumin (allergenic compound) content, and similar allergenic potential compared with untreated seeds.     

Surfactant-based dispersant for multiwall carbon nanotubes to prepare ceramic composites by a sol-gel method

A dispersant for multiwall carbon nanotubes (MWCNTs) is proposed that fulfils the requirements of creating a uniform dispersion in the matrix and obtaining a good interface between CNTs and the matrix, and is soluble in generic nonpolar solvents. This dispersant is based on a long chain surfactant, called in this work dabcosil stearate, containing a stearate-based 18-carbon alkyl chain as an anion, and a silsesquioxane containing a bridged, positively charged 1,4-diazoniabicyclo[2.2.2]octane group. It provides not only a very good dispersion medium for the MWCNTs, but also a very good interface between MWCNTs and ceramic matrices, such as alumina and zirconia, prepared by the sol-gel method.