Extension problem to an invertible matrix

Extension to an invertible matrix in convolution

Let M+ denote the Banach algebra of all complex Borel measures with support contained in [0, +∞), with the usual addition and scalar multiplication, and with convolution ∗, and the norm being the total variation of μ. We show that the maximal ideal space X(M+) of M+, equipped with the Gelfand topology, is contractible as a topological space. In particular, it follows that every left invertible ...

Logical s-t Min-Cut Problem: An Extension to the Classic s-t Min-Cut Problem

Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, ca...

Order of an Invertible Matrix 3

AN EXTENSION TO STOCHASTIC TIME-COST TRADE-OFF PROBLEM OPTIMIZATION WITH DISCOUNTED CASH FLOW

In this paper, an efficient multi-objective model is proposed to solve time-cost trade off problem considering cash flows. The proposed multi-objective meta-heuristic is based on Ant colony optimization and is called Non Dominated Archiving Ant Colony Optimization (NAACO). The significant feature of this work is consideration of uncertainties in time, cost and more importantly interest rate. A ...

MATRIX VALUATION PSEUDO RING (MVPR) AND AN EXTENSION THEOREM OF MATRIX VALUATION

Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...