Second set of spaces

2020

Electronics and Communications in Japan (Part I: Communications), 1985

Proceedings of the 44th IEEE Conference on Decision and Control, 2005

In this paper a novel software for analysis and design of multivariable 2x2 control systems is presented. The 2x2 Individual Channel Design MATLAB® Toolbox is a valuable aid for analysing and designing multivariable control systems under the framework of the Multivariable Structure Function (MSF) and Individual Channel Design (ICD). Given a set of specifications for a 2-input 2-output multivariable control system the appropriate use of the toolbox can lead to successful and robust controllers. The process is based on an iterative procedure. Closed loop simulations (in SIMULINK®) are included so results can be tested. Final stability margins and robustness measures are also assessed. A design example is included for completeness. The development of the general m x m case is in progress.

Lecture Notes in Computer Science, 2002

... 1 CWI, Amsterdam, The Netherlands farhad@cwi.nl 2 University of Waterloo, Ontario, Canada fmavadda@math.uwaterloo.ca ... For convenience, we represent a channel by the pair of its source and sink ends, ie, ab represents the channel whose source and sink ends are ...

2017

G06F 3/16 (2006.01) (57) ABSTRACT G06F 3/00 (2006.01) H04B I/00 (2006.01) Techniques for mixing multiple input channel signals into HO3G 3/20 (2006.01) multiple output channel signals are provided. A graphical (52) U.S. Cl. ....................... 715/727; 715/716; 381/119; user interface (GUI), which includes multiple indicators, is 381/61 displayed. The input channel signals are mixed to produce (58) Field of Classification Search ................. 715/727; multiple output channel signals. The mixing is performed 381/119, 61: 700/94 based on the distance between the indicators’ positions in the See application file for complete search history. GUI. According to one embodiment of the invention, the mixing is also performed based on the angle formed between (56) References Cited the indicators. Thus, the extent to which an input channel U.S. PATENT DOCUMENTS signal is carried by an output channel signal is, in one embodi ment of the invention, a function of both the distance between...

Channel changes with respect to time and space play a significant role in stream flow dynamics. The rambling and trailing of channels in the studied region have been studied through systematic analysis and interpretation of diverse channel configuration and multi-channel orientation using multi-temporal Topographical maps and Satellite images for a period spanning nearly 80 years . For this specific purpose the lower course of Diana River in the Jaldhaka-Diana river system has been selected in the Duars region of the Jalpaiguri district, West Bengal, which is virtually a zone of transition between the Himalayan Mountains and the North Bengal plain. The prime objective of the study is to reveal the spatio-temporal sequences of channel changes, consequent movement of confluence point and the factors and causes of such movement. For this particular extraction, a base map has been generated with the help of SOI Topographical maps and satellite images of the respective area. For this purpose an updated version of ERDAS Imaging is employed as image processing tool for enhancing, merging and to update the spatial information of channel configuration and Arc GIS is used for final product generation. Following the specific objective of the study it has been deduced that during this span the confluence point has moved and re-oriented both upstream and downstream on a historical time scale and new confluence points have been created by repeated shifting and migration of channels. No definite trend is observed in the movement of the confluence points. However, it is noticed that some distinct flow dynamics and channel maintaining processes are actively performing in this spatio-temporal analysis of channel changes. (g) Palaeochannels and spillways between Diana and Rangati. (The photographs were taken during field surveys from 2010-2012. The precise location of each photo has been pointed out on the image of the study area).

Journal of Graph Theory, 1997

A (k; g)-graph is a k-regular graph with girth g. Let f (k; g) be the smallest integer ν such there exists a (k; g)-graph with ν vertices. A (k; g)-cage is a (k; g)-graph with f (k; g) vertices. In this paper we prove that the cages are monotonic in that f (k; g 1) < f(k; g 2) for all k ≥ 3 and 3 ≤ g 1 < g 2. We use this to prove that (k; g)-cages are 2-connected, and if k = 3 then their connectivity is k.

We have discussed the basic properties of connected spaces regarding subspaces, product spaces, preservation under mappings etc. Also we have given several characterizations of these spaces. We begin our research paper of topological properties by making the idea of being connected that is being in one piece. It turns out to be easier to think about the property that is opposite of connectedness, namely the property of being in two or more pieces. I. INTRODUCTION Two important and interrelated strands in the practice of the exact sciences in the 19th century will be considered in which topological ideas came to be relevant for natural philosophy. In this way, light can be thrown on a part of the causal weave of events that eventually led to the emergence-of topology as a discipline, a part which has largely been neglected up until now in-the historical literature. The first of these two strands was concerned with topological issues that arose in the context of a dynamical theory of physical phenomena, a theory-advocated in particular by British natural philosophers during the last third of the 19 th century. These developments will be discussed in the first part of our study. The second strand of events related to speculations about the large-scale topological structure of space will be the focus of the second part of this article. The emergence of an entirely new discipline within mathematics is a rare event-in the history of science. The creation of topology the science of properties of spaces-and figures that remain unchanged under continuous deformations represents a phenomenon of this kind, but of a distinctly modern variety. Topology bears comparison-with the calculus, probability theory or number theory in that the first ideas about a new field called Analysis Situs or Geometria Situs were communicated among a handful of mathematically minded intellectuals in the late seventeenth and early eighteenth centuries. However, unlike the calculus and number theory, but similar to probability theory, the basic ideas underlying Analysis Situs reveal no ancient roots. Notoriously, ancient-authors treated questions of continuity hardly at all, and if so, then mainly as physical-questions linked to the phenomenon of motion. Moreover, in sharp contrast to these three other fields, during the 18th century no clearly defined domain of mathematical-problems was delineated that should and could be treated by Analysis Situs. Rather, a vague idea about an analysis which dealt not with magnitude, but " position, " left it to-individual mathematicians to decide what should belong to the new field. Only gradually over the course of the 19th century was a consensus reached about the nature of-problems in topology. Nevertheless, after crossing the threshold to a scientific discipline in the full sense of the word in the first decades of this century, topology became one of the core research fields of mathematics, and topological arguments have come to play a role in virtually every other field in mathematics and the mathematical sciences. If one may reasonably speak of genuinely modern mathematical disciplines, then topology-certainly belongs among them. These late beginnings may be one reason why the emergence of topology has only begun to attract historiographical attention comparable to that received by fields like the calculus, number theory, or probability theory. While the invention of the calculus has long since been the object of historical study, and while the emergence of number theory and probability theory have recently been treated from a wide variety of perspectives, the number of historical monographs devoted to the formation of topology remains very small. Apart from these, we have a few survey articles and several research papers-dealing with particular topics within or closely related to topology. II. REVIEW OF LITERATURE Connectedness plays a very significant role in the study of topological spaces. The first attempt to give a precise definition of these spaces was made by Weierstrass who infact introduced the notion of arcwise connectedness. However, the notion of connectedness which we use today was introduced by Cantor (1883). Since then a host of leading toplogists notably Jordan (1893), Schoenfliesz (1902), F. Riesz (1906), Lennes (1911), Mazurkiewicz (1920), Vaidyanathaswamy (1947) studies these spaces very extensively and also introduced various generalization too of these spaces.