For the signed circuits of a regular oriented matroid (and more particular of a digraph) the above questions have been studied very well in past. From graph theory it is known that the dimension of the circuit space of a connected digraph is |E| − |V | + 1, that the circuit space L(C) is regular and that the elementary circuits {C(B, e)}e∈E\B form a basis of L(C) for any basis B of O. For gener...

In [2], a family of stochastic flows of kernels on S 1 called " sticky flows " is described. Sticky flows are defined by their " moments " which are consistent systems of transition kernels on S 1. In this note, a discrete version of sticky flows is presented in the case the sticky flows are associated with a system of Brownian particles on S 1. This discrete model is defined by products of Bet...

We study different renormalization group flows for scale-dependent effective actions, including exact and proper-time renormalization group flows. These flows have a simple one-loop structure. They differ in their dependence on the full field-dependent propagator, which is linear for exact flows. We investigate the inherent approximations of flows with a nonlinear dependence on the propagator. ...

Let D be a t-(v, k, λ) design and let Ni(D), for 1 ≤ i ≤ t, be the higher incidence matrix of D, a (0, 1)-matrix of size ( v i ) × b, where b is the number of blocks of D. A zero-sum flow of D is a nowhere-zero real vector in the null space of N1(D). A zero-sum k-flow of D is a zero-sum flow with values in {±1, . . . ,±(k− 1)}. In this paper we show that every non-symmetric design admits an int...

Let κ be a regular uncountable cardinal and λ > κ a singular strong limit cardinal. We give a new characterization of the nonstationary subsets of Pκ(λ) and use this to prove that the nonstationary ideal on Pκ(λ) is nowhere precipitous. 0 Introduction Let κ be a regular uncountable cardinal and λ > κ a singular cardinal. Let Iκ,λ (respectively, NSκ,λ) denote the ideal of noncofinal (respectivel...

The number of nowhere zero ZQ flows on a graph G can be shown to be a polynomial in Q, defining the flow polynomial ΦG(Q). According to Tutte’s five-flow conjecture, ΦG(5) > 0 for any bridgeless G. A conjecture by Welsh that ΦG(Q) has no real roots for Q ∈ (4,∞) was recently disproved by Haggard, Pearce and Royle. These authors conjectured the absence of roots for Q ∈ [5,∞). We study the real r...

A graph G = (V,E) has a nowhere-zero k-flow if there exists an orientation H = (V,A) of G and an integer flow φ : A → Z such that for all a ∈ A, 0 < |φ(a)| < k. A (1, 2)-factor of G is a set F ⊆ E such that the degree of any vertex v in the subgraph induced by F , denoted by dF (v), is 1 or 2. The main result of this work is the following. A bridgeless cubic graph G has a nowhere-zero 5-flow if...