Let G be a graph on n vertices. Its Laplacian matrix is the n-by-n matrix L(G) - D(G) - A(G), where A(G) is the familiar (0, 1) adjacency matrix, and D(G) is the diagonal matrix of vertex degrees. This is primarily an...
Let G be a graph on n vertices. Its Laplacian matrix is the n-by-n matrix L(G) - D(G) - A(G), where A(G) is the familiar (0, 1) adjacency matrix, and D(G) is the diagonal matrix of vertex degrees. This is primarily an expository article surveying some of the many results known for Laplacian matrices. Its six sections are: Introduction, The Spectrum, The Algebraic Connectivity, Congruence and Equivalence, Chemical Applications, and Immanants.
In this paper we show that if the fuzzy graph (sigma,mu) is a cycle, then it is a fuzzy cycle if and only if (sigma,mu) is not a fuzzy tree. We also examine the relationship between fuzzy bridges and cycles. We introd...
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In this paper we show that if the fuzzy graph (sigma,mu) is a cycle, then it is a fuzzy cycle if and only if (sigma,mu) is not a fuzzy tree. We also examine the relationship between fuzzy bridges and cycles. We introduce and examine the concepts of chords, twigs, 1-chains with boundary zero, cycle vectors, coboundary, and cocycles for fuzzy graphs. We show that although the set of cycle vectors, fuzzy cycle vectors, cocycles, and fuzzy cocycles do not necessarily form vector spaces over the field Z(2) of integers module 2, they nearly do. This allows us to introduce the concepts of (fuzzy) cycle rank and (fuzzy) cocycle rank for fuzzy graphs in a meaningful way.
With the rapid improvement of medical consumer electronics (CE), the transmission of multiple images has become increasingly common in the medical field. During the transmission and storage of image data, sensitive in...
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This paper deals with a coupled system of reaction-diffusion equations modeling the competition of two species with cross diffusion. We discuss the existence of positive steady-state solutions in relation to the intri...
This paper deals with a coupled system of reaction-diffusion equations modeling the competition of two species with cross diffusion. We discuss the existence of positive steady-state solutions in relation to the intrinsic birth rates a(1), a(2) of species and the cross diffusion coefficients beta(12), beta(21). Our results show that positive steady-state solutions exist if a(1) and a(2) lie in certain range, or if beta(12) and beta(21) are sufficiently large. (C) 1996 Academic Press, Inc.
In this paper, the problem of finding inputs which generate zero outputs in linear time-invariant control systems of the formE(dx/dt) =Ax+Buis considered whereEandAare not necessarily square matrices. This problem is ...
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In this paper, the problem of finding inputs which generate zero outputs in linear time-invariant control systems of the formE(dx/dt) =Ax+Buis considered whereEandAare not necessarily square matrices. This problem is solved using the theory of matrix generalized inverses.
We give an introduction into the three AI-fields: logic and automated reasoning, expert systems and blackboard architecture, neural networks, and also discuss some of their practical applications.
We give an introduction into the three AI-fields: logic and automated reasoning, expert systems and blackboard architecture, neural networks, and also discuss some of their practical applications.
Non-invasive brain stimulation (NIBS) techniques, such as transcranial infrared (tNIR) stimulation, offer promising advancements in sleep monitoring and regulation. To enhance sleep stage classification without relyin...
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A similarity between finite state machines and directed graphs can be seen from the natural way a directed graph can be associated with a finite state machine to describe the state transition of the finite state machi...
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A similarity between finite state machines and directed graphs can be seen from the natural way a directed graph can be associated with a finite state machine to describe the state transition of the finite state machine. Likewise, there is a similarity between fuzzy finite state machines and fuzzy directed graphs. As a matter of fact, all four of these concepts, together with that of information retrieval systems and fuzzy systems, share this similarity, namely that of the notion of successor. This paper gives an axiomatic treatment of the notion of successor in such a way that all of the above systems fall under this axiomatic approach. (C) Elsevier science Inc. 1996
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