About generalized scaling for passive scalars in fully developed turbulence

In this paper we use a simple normal form approach of scale invariant fields to investigate scaling laws of passive scalars in turbulence. The coupling equations for velocity and passive scalar moments are scale covariant. Their solution shows that passive scalars in turbulence do not generically follow a general scaling observed for velocity field because of coupling effects.

Composite materials dynamic fracture studies by generalized Shmuely difference algorithm

The generalized Shmuely Difference Algorithm (GSDA) is presented here to analyze the dynamic fracture performance of orthogonal-anisotropic composite materials, such as glass fibre reinforced phenolplast. The difference recurrence Formulae and boundary condition difference extrapolation formulae are derived and programmed. The dynamic stress intensity factors (DSIF) of the isotropic and anisotropic centrally cracked plates are computed respectively using GSDA and compared with that published previously. GSDA is proved effective and reliable. Copyright (C) 1996 Elsevier Science Ltd.

Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.

Failure process analysis of cement under explosive loading with a generalized driven nonlinear threshold model

The microstructural heterogeneity and stress fluctuation play important roles in the failure process of brittle materials. In this paper, a generalized driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. As an illustration, the failure process of cement material under explosive loading is analyzed using the model. The result agrees well with the experimental one, which proves the efficiency of the model.

Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Designing Spaces for Effective Learning: A guide to 21st century learning space design

Increasing investment in estate and learning technologies, combined with the need for more cost-effective space utilisation, is making it increasingly important for senior managers to keep abreast of new thinking about the design of technology-rich learning spaces. Designing Spaces for Effective Learning, one of a series of guides, was launched at the JISC Conference 2006 which helped to meet this need. A visually-rich publication, it was designed to promote better understanding of what makes an effective design for the 21 century and to summarise the key points to consider when approaching a refurbishment or new-build project. The publication takes the reader on a ’walk through’ an educational institution, exploring the relationship between learning technologies and innovative examples of physical space design at each stage of the journey. Discussion of the key points is illustrated by ten case studies from further and higher education, and floor plans from AMA Alexi Marmot Associates, architects and space planners, which provide up-to-date guidelines on the integration of technologies into teaching and learning accommodation.

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

12 p.

On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

Sampling and learning the Mallows and Generalized Mallows models under the Cayley distance

[EN]The Mallows and Generalized Mallows models are compact yet powerful and natural ways of representing a probability distribution over the space of permutations. In this paper we deal with the problems of sampling and learning (estimating) such distributions when the metric on permutations is the Cayley distance. We propose new methods for both operations, whose performance is shown through several experiments. We also introduce novel procedures to count and randomly generate permutations at a given Cayley distance both with and without certain structural restrictions. An application in the field of biology is given to motivate the interest of this model.

An R package for permutations, Mallows and Generalized Mallows models

[EN]Probability models on permutations associate a probability value to each of the permutations on n items. This paper considers two popular probability models, the Mallows model and the Generalized Mallows model. We describe methods for making inference, sampling and learning such distributions, some of which are novel in the literature. This paper also describes operations for permutations, with special attention in those related with the Kendall and Cayley distances and the random generation of permutations. These operations are of key importance for the efficient computation of the operations on distributions. These algorithms are implemented in the associated R package. Moreover, the internal code is written in C++.

Effective and Robust Generalized Predictive Speed Control of Induction Motor

14 p.