We consider the space of graph connections (lattice gauge fields) which can be endowed with a Poisson structure in terms of a ciliated fat graph. (A ciliated fat graph is a graph with a fixed linear order of ends of edges at each vertex.) Our aim is however to study the Poisson structure on the moduli space of locally flat vector bundles on a Riemann surface with holes (i.e. with boundary). It ...

For a graph $G = (V, E)$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_k}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ or both for every $V_i, V_j in pi$, whenever $i neq j$. The textit{upper domatic number} $D(G)$ is the maximum order of an upper domatic partition. We study the properties of upper domatic number and propose an up...

Abstract Let $A$ be a finitely presented associative monomial algebra. We study the category $\textsf{qgr}(A)$, which is quotient of graded $A$-modules by finite-dimensional ones. As this plays role coherent sheaves on corresponding noncommutative variety, we consider its bounded derived $\textbf{D}^b(\textsf{qgr}(A))$. calculate categorical entropy Serre twist functor $\textbf{D}^b(\textsf{qgr...

Let 0 < k ∈ Z and let n = 2k + 1. A rooted binary tree T is presented whose nodes are the classes mod n of the weight-k n-tuples over F2. Lexical 1-factorizations of the middle-levels graphs Mk allow to present an equivalent form of T via nodes that are the classes mod n of the weight-(k + 1) n-tuples over F2. This in turn allows to present a quotient graph Rk of Mk via reverse complementation ...

Let G be a group. The power graph of G is a graph with the vertex set G, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique/chromatic number. Furthermore, it is proved that for every grou...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose order is the number of oriented spanning trees rooted at a fixed vertex. In the case when G is regular of degree k, we show that the sandpile group of G is isomorphic to the quotient of the sandpi...

in this paper by using concepts of graph theory, forces method and substructure ing method for analysis of structures, some methods have been introduced for optimal analysis of structures in a large scale, using substructuring method. planar rigid frames assuming linear behavior and small deformations, have been optimal analyzed, by using forces method. thus, a fortran power station computation...

This paper shows that variations in breathing patterns broaden heart rate variability (HRV) spectral bands and increase the power amplitude of low-frequency bands. Because of these influences, spectral markers for HRV signals, such as the quotient between spectral power at different frequency bands, should be compared only under controlled breathing conditions or after considering the effect of...