Studies of stability of fluid flowa using variational methods

The study of stability problems is relevant to the study of structure of a physical system. It 1S particularly important when it is not possible to probe into its interior and obtain information on its structure by a direct method. The thesis states about stability theory that has become of dominant importance in the study of dynamical systems. and has many applications in basic fields like meteorology, oceanography, astrophysics and geophysics- to mention few of them. The definition of stability was found useful 1n many situations, but inadequate in many others so that a host of other important concepts have been introduced in past many years which are more or less related to the first definition and to the common sense meaning of stability. In recent years the theoretical developments in the studies of instabilities and turbulence have been as profound as the developments in experimental methods. The study here Points to a new direction for stability studies based on Lagrangian formulation instead of the Hamiltonian formulation used by other authors.

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.

Connection space approach to ambiguities of gauge theories

Two distinct gauge potentials can have the same field strength, in which case they are said to be copies of each other. The consequences of this ambiguity for the general affine space A of gauge potentials are examined. Any two potentials are connected by a straight line in A, but a straight line going through two copies either contains no other copy or is entirely formed by copies. Copyright © 2005 Hindawi Publishing Corporation.

The spatial sign covariance matrix and its application for robust correlation estimation

8 pages, 2 figures, to be published in the conference proceedings of 11th international conference "Computer Data Analysis & Modeling 2016"

New lower bounds for the topological complexity of aspherical spaces

Date of Acceptance: 5/04/2015 15 pages, 4 figures

Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

Notebook concerning mathematical equations : manuscript, 1769-1774

Notes on measuring height and distance, trigonometry, spherical projection, and other mathematical equations. Probably William Winthrop (1753-1825; Harvard AB 1770).

Proceedings of the Section of Sciences

Mode of access: Internet.

Proceedings of the section of sciences.

Vols. 46-48 issued combined.

Proceedings of the section of sciences.

Volumes 46-48 issued combined.

Conference of the Academy of Sciences of the USSR on the peaceful uses of atomic energy, July 1-5, 1955. : In English translation.

Includes bibliographies.

On the forced matching numbers of bipartite graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matching of G. This notion has arisen in the study of finding resonance structures of a given molecule in chemistry. Similar concepts have been studied for block designs and graph colorings under the name defining set, and for Latin squares under the name critical set. There is some study of forcing sets of hexagonal systems in the context of chemistry, but only a few other classes of graphs have been considered. For the hypercubes Q(n), it turns out to be a very interesting notion which includes many challenging problems. In this paper we study the computational complexity of finding the forcing number of graphs, and we give some results on the possible values of forcing number for different matchings of the hypercube Q(n). Also we show an application to critical sets in back circulant Latin rectangles. (C) 2003 Elsevier B.V. All rights reserved.

Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

Mathematical modelling

The development of a new process model of cement grinding in two-stage mills is discussed. The new model has been used to simulate cement grinding and predicting mill performance in open and closed circuit configuration. The new model considered the two-compartment mill as perfectly mixed slices in series. The breakage rate function uses the back calculation technique to determine offline using drop weight and abrasion tests.

Generalization by symbolic abstraction in cascaded recurrent networks

Generalization performance in recurrent neural networks is enhanced by cascading several networks. By discretizing abstractions induced in one network, other networks can operate on a coarse symbolic level with increased performance on sparse and structural prediction tasks. The level of systematicity exhibited by the cascade of recurrent networks is assessed on the basis of three language domains. (C) 2004 Elsevier B.V. All rights reserved.