On networks with a uniquely determined flow

On uniquely k-determined permutations

Motivated by a new point of view to study occurrences of consecutive patterns in permutations, we introduce the notion of uniquely k-determined permutations. We give two criteria for a permutation to be uniquely k-determined: one in terms of the distance between two consecutive elements in a permutation, and the other one in terms of directed hamiltonian paths in the certain graphs called path-...

Sets uniquely determined by projections on axes II Discrete case

Fishburn, P. A subset S of N " = { 1,2,. , N} " is a discrete set of uniqueness if it is the only subset of N " with projections P,, Sets of uniqueness and additive sets are characterized by the absence of certain configurations in the lattice N ". The characterization shows that every additive set is a set of uniqueness. If n = 2, every set of uniqueness is also additive. However, when II 3 3,...

Generalized metrics and uniquely determined logic programs

Can optimized effective potentials be determined uniquely?

Local ~multiplicative! effective exchange potentials obtained from the linear-combinationof-atomic-orbital ~LCAO! optimized effective potential ~OEP! method are frequently unrealistic in that they tend to exhibit wrong asymptotic behavior ~although formally they should have the correct asymptotic behavior! and also assume unphysical rapid oscillations around the nuclei. We give an algebraic pro...

A note on uniquely (nil) clean ring

A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.