It is well known that input-to-state stability admits an astonishing number of equivalent characterizations. Here it is shown that for monotone systems on R+ there are some additional characterizations that are useful for network stability analysis. These characterizations include system theoretic properties, algebraic properties, as well as the problem of finding simultaneous bounds on solutio...

In this work we study the asymptotically at, static, and spherically symmetric black-hole solutions of the theory described by the action o ; with n > 3 and arbitrary. We demonstrate the absence of scalar hairs for < 0. For > c = n?2 4(n?1) , we show that there is no scalar hair obeying j(r)j < 1= p or j(r)j > 1= p. For 0 < < c , we prove the absence of scalar hairs such that j(r)j < 1= p or 1 ...

where n ≥ , f : [, ]× (R+)n– → R+ is continuous in which R+ = [,+∞), A and B are right continuous on [, ), left continuous at t = , and nondecreasing on [, ], withA() = B() = ; ∫   v(s)dA(s) and ∫   v(s)dB(s) denote the Riemann-Stieltjes integrals of v with respect to A and B, respectively. Boundary value problems (BVPs for short) for nonlinear differential equations arise in m...

In this paper, we propose a method to obtain fuzzy solutions of duality fully fuzzy linear system (DFFLS) of the form ÃX̃ = B̃X̃ + C̃, where Ã, B̃ are fuzzy matrices and C̃, X̃ are fuzzy number vectors. To this end, we solve the 1-cut of DFFLS (which is a crisp system here) ,then some unknown spreads are allocated to any row of a 1-cut of dual fully fuzzy linear system in 1-cut position. Also, by usin...

2. Max-Cut Revisited As in last week’s lecture, we approximate solutions to Max-Cut using Goemans’s and Williamson’s αGW = 0.878-approximation. Specifically, we seek max ∑ (i,j)∈E 1 4 ∥∥vi − vj∥∥2 subject to the constraint that ∀i, ‖vi‖ = 1. We can visualize this by drawing the vectors restricted to a unit circle, as seen in the figure to the left. There is an appealing geometric intuition here...

We calculate genus one corrections to Hermitian one-matrix model solution with arbitrary number of cuts directly from the loop equation confirming the answer previously obtained from algebro-geometrical considerations and generalizing it to the case of arbitrary potentials.

Abstract. We present a Branch-and-Cut algorithm where the volume algorithm is applied instead of the traditionally used dual simplex algorithm to the linear programming relaxations in the root node of the search tree. This means that we use fast approximate solutions to these linear programs instead of exact but slower solutions. We present computational results with the Steiner tree and Max-Cu...

This paper presents exact solution methods for analyzing vulnerability of electric power networks to a certain kind of undetectable attacks known as false data injection attacks. We show that the problems of finding the minimum number of measurement points to be attacked undetectably reduce to minimum cut problems on hypergraphs, which admit efficient combinatorial algorithms. Experimental resu...

In this paper, we study a class of nonlinear boundary value problems in R+ . By means of minimax method and the Lusternik-Schnirelman category, the criteria of the existence, multiplicity and nonexistence of positive solutions are established.