Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

具有四个素因子的奇亏完全数

设n为自然数,σ(n)表示n的所有正因子和函数.令d是n的真因子,若n满足σ(n)=2n-d,则称n为亏因子为d的亏完全数.本文给出了具有四个素因子的奇亏完全数的一些性质的刻画.     

High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics

In this paper, we present a class of high‐order accurate cell‐centered arbitrary Lagrangian–Eulerian (ALE) one‐step ADER weighted essentially non‐oscillatory (WENO) finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two‐dimensional unstructured triangular meshes. High order of accuracy in space is achieved by a WENO reconstruction algorithm, while a local space–time Galerkin predictor allows the schemes to be high order accurate also in time by using an element‐local weak formulation of the governing PDE on moving meshes. The mesh motion can be computed by choosing among three different node solvers, which are for the first time compared with each other in this article: the node velocity may be obtained either (i) as an arithmetic average among the states surrounding the node, as suggested by Cheng and Shu, or (ii) as a solution of multiple one‐dimensional half‐Riemann problems around a vertex, as suggested by Maire, or (iii) by solving approximately a multidimensional Riemann problem around each vertex of the mesh using the genuinely multidimensional Harten–Lax–van Leer Riemann solver recently proposed by Balsara et al. Once the vertex velocity and thus the new node location have been determined by the node solver, the local mesh motion is then constructed by straight edges connecting the vertex positions at the old time level tⁿ with the new ones at the next time level t^{n + 1}. If necessary, a rezoning step can be introduced here to overcome mesh tangling or highly deformed elements. The final ALE finite volume scheme is based directly on a space–time conservation formulation of the governing PDE system, which therefore makes an additional remapping stage unnecessary, as the ALE fluxes already properly take into account the rezoned geometry. In this sense, our scheme falls into the category of direct ALE methods. Furthermore, the geometric conservation law is satisfied by the scheme by construction. We apply the high‐order algorithm presented in this paper to the Euler equations of compressible gas dynamics as well as to the ideal classical and relativistic magnetohydrodynamic equations. We show numerical convergence results up to fifth order of accuracy in space and time together with some classical numerical test problems for each hyperbolic system under consideration. Copyright © 2014 John Wiley & Sons, Ltd.     

An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD

We propose an improved framework for dynamic mode decomposition (DMD) of 2‐D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD‐based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

Modified extended BDF scheme for the discontinuous Galerkin solution of unsteady compressible flows

In this paper, a high‐order DG method coupled with a modified extended backward differentiation formulae (MEBDF) time integration scheme is proposed for the solution of unsteady compressible flows. The objective is to assess the performance and the potential of the temporal scheme and to investigate its advantages with respect to the second‐order BDF. Furthermore, a strategy to adapt the time step and the order of the temporal scheme based on the local truncation error is considered. The proposed DG‐MEBDF method has been evaluated for three unsteady test cases: (i) the convection of an inviscid isentropic vortex; (ii) the laminar flow around a cylinder; and (iii) the subsonic turbulent flow through a turbine cascade. Copyright © 2014 John Wiley & Sons, Ltd.     

Confined crystallization of polymers within anodic aluminum oxide templates

In this article, a review of recent literature on confined crystallization within nanoporous anodic aluminum oxide (AAO) templates is presented. For almost all infiltrated polymeric materials, crystal orientation within the nanopores is a function of pore diameter. T_c and T_m usually decrease and are a function of pore size. When no pore interconnection remains, the crystallization occur at large supercoolings in heterogeneity free environments. Hence, the nucleation mechanism changes from heterogeneous to surface or homogeneous nucleation. The crystallization kinetics of infiltrated polymers should be close to first order, since in confined environments nucleation is the determining step of the overall crystallization and Avrami indexes (n) of ～1 (or lower in some cases) should be obtained. Examples are provided where these conditions have been met and first order kinetics (n = 1) were measured as opposed to higher orders (n = 3?4) for the same polymer in the bulk. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1179–1194     

Measurement of Large Dipolar Couplings of a Liquid Crystal with Terminal Phenyl Rings and Estimation of the Order Parameters

NMR spectroscopy is a powerful means of studying liquid‐crystalline systems at atomic resolutions. Of the many parameters that can provide information on the dynamics and order of the systems, ¹H–¹³C dipolar couplings are an important means of obtaining such information. Depending on the details of the molecular structure and the magnitude of the order parameters, the dipolar couplings can vary over a wide range of values. Thus the method employed to estimate the dipolar couplings should be capable of estimating both large and small dipolar couplings at the same time. For this purpose, we consider here a two‐dimensional NMR experiment that works similar to the insensitive nuclei enhanced by polarization transfer (INEPT) experiment in solution. With the incorporation of a modification proposed earlier for experiments with low radio frequency power, the scheme is observed to enable a wide range of dipolar couplings to be estimated at the same time. We utilized this approach to obtain dipolar couplings in a liquid crystal with phenyl rings attached to either end of the molecule, and estimated its local order parameters.     

High‐performance liquid chromatographic separations of stereoisomers of chiral basic agrochemicals with polysaccharide‐based chiral columns and polar organic mobile phases

The separation of the stereoisomers of 23 chiral basic agrochemicals was studied on six different polysaccharide‐based chiral columns in high‐performance liquid chromatography with various polar organic mobile phases. Along with the successful separation of analyte stereoisomers, emphasis was placed on the effect of the chiral selector and mobile phase composition on the elution order of stereoisomers. The interesting phenomenon of reversal of enantiomer/stereoisomer elution order function of the polysaccharide backbone (cellulose or amylose), type of derivative (carbamate or benzoate), nature, and position of the substituent(s) in the phenylcarbamate moiety (methyl or chloro) and the nature of the mobile phase was observed. For several of the analytes containing two chiral centers all four stereoisomers were resolved with at least one chiral selector/mobile phase combination.     

(2‐Aminopyrimidine‐κN1)aqua(pyridine‐2,6‐dicarboxylato‐κ3O2,N,O6)copper(II): X‐ray and DFT calculated structure

In the title compound, [Cu(C₇H₃N₂O₄)(C₄H₅N₂)(H₂O)], (I), pyridine‐2,6‐dicarboxylate (pydc²⁻), 2‐aminopyrimidine and aqua ligands coordinate the Cu^II centre through two N atoms, two carboxylate O atoms and one water O atom, respectively, to give a nominally distorted square‐pyramidal coordination geometry, a common arrangement for copper complexes containing the pydc²⁻ ligand. Because of the presence of Cu...X_bridged contacts (X = N or O) between adjacent molecules in the crystal structures of (I) and three analogous previously reported compounds, and the corresponding uncertainty about the effective coordination number of the Cu^II centre, density functional theory (DFT) calculations were used to elucidate the degree of covalency in these contacts. The calculated Wiberg and Mayer bond‐order indices reveal that the Cu...O contact can be considered as a coordination bond, whereas the amine group forming a Cu...N contact is not an effective participant in the coordination environment.