It has previously been shown that there exists a minimum degree ordering for regular grids that is considerably worse than nested dissection in terms of ll-in and operations for factorization 1]. This paper proves the existence of a minimum degree ordering for regular grids that has the same optimal asymptotic order complexity for ll-in and operation count as nested dissection. The analysis is ...

Consider an entire (absolutely convergent in $\mathbb{C}$) Dirichlet series $F$ with the exponents $\lambda_n$, i.e., of form $F(s)=\sum_{n=0}^\infty a_ne^{s\lambda_n}$, and, for all $\sigma\in\mathbb{R}$, put $\mu(\sigma,F)=\max\{|a_n|e^{\sigma\lambda_n}:n\ge0\}$ and $M(\sigma,F)=\sup\{|F(s)|:\operatorname{Re}s=\sigma\}$. Previously, first authors M.M.~Sheremeta proved that if $\omega(\lambda)...

We use a discrete-time formulation of the asymmetric avalanche process (ASAP) [Phys. Rev. Lett. 87, 084301 (2001)]] of p particles on a finite ring of N sites to obtain an exact expression for the average avalanche size as a function of toppling probabilities and particle density rho=p/N. By mapping the model onto driven interface problems, we find that the ASAP incorporates the annealed Kardar...

Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2  functions. The class of prox-regular functions covers all convex functions, lower C2  functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...

A model for cleaning a graph with brushes was recently introduced. Let α = (v1, v2, . . . , vn) be a permutation of the vertices of G; for each vertex vi let N (vi) = {j : vjvi ∈ E and j > i} and N−(vi) = {j : vjvi ∈ E and j < i}; finally let bα(G) = ∑n i=1 max{|N+(vi)|−|N−(vi)|, 0}. The Broom number is given by B(G) = maxα bα(G). We consider the Broom number of d-regular graphs, focusing on th...

We propose a network of generalized Toffoli gates with multiple EXORs for the realization of reversible functions. If implemented as a quantum circuit, the cost of such gates is shown to be only marginally higher than the cost of a Toffoli gate with a single EXOR and the same number of controls. The main result is a regular synthesis procedure which allows for the creation of asymptotically opt...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

I present further analytic time symmetric initial data for five dimensions describing “bubbles of nothing” which have no Kaluza-Klein circle asymptotically. The new solutions consist of a large family of single bubbles in both asymptotically flat and asymptotically AdS space. I also numerically construct gravitational solitons in AdS where the usual boundary conditions are modified geometricall...

In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and  fuzzy gener...