Jensen and Toft [10] conjectured that every 2-edge-connected graph without a K5minor has a nowhere zero 4-flow. Walton and Welsh [24] proved that if a coloopless regular matroid M does not have a minor in {M(K3,3),M(K5)}, then M admits a nowhere zero 4-flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K5),M(K5)}, then M admits a nowhere zero 4-flow....

In 1940, Ulam proposed the general Ulam stability problem see 1 . Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for all x, y ∈ G1 then there is a homomorphism H : G1 → G2 with d h x ,H x < ε for all x ∈ G1? In 1941, this problem was solved by Hyers 2 i...

we develop a theory of stratified $lm$-filters which generalizes the theory of stratified $l$-filters. our stratification condition explicitly depends on a suitable mapping between the lattices $l$ and $m$. if $l$ and $m$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $l$-filters. based on the stratified $lm$-filters, a general theory of lattice-v...

For a given weighted mean $\mathscr{M}$ defined on subinterval of $\mathbb{R}_+$ and sequence weights $\lambda=(\lambda_n)_{n=1}^\infty$ we define Hardy constant $\mathscr H(\lambda)$ as the smallest extended real number such that $$ \sum_{n=1}^\infty \lambda_n \mathscr{M}\big((x_1,\dots,x_n),(\lambda_1,\dots,\lambda_n)\big) \le \mathscr H(\lambda) \cdot x_n \text{ for all }x \in \ell^1(\lambda...

We consider the concepts of colored terms and multihypersubstitutions. If t ∈ Wτ (X) is a term of type τ , then any mapping αt : Pos (t) → IN of the non-variable positions of a term into the set of natural numbers is called a coloration of t. The set W c τ (X) of colored terms consists of all pairs 〈t, αt〉. The set Hyp(τ) of all hypersubstitutions of type τ is a countable monoid. If M is a subm...

The genus Microbacterium was proposed by Orla-Jensen in 1919. Four species were described, viz., Microbacterium lacticum, Microbacterium flavum, Microbacterium liquefaciens, and Microbacterium mesentericum. The organisms of this genus presented a physiological gradient with the saccharolytic acid former (M. lacticum) at one extreme and the proteolytic gelatin liquefier (M. liquefaciens) at the ...

We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-v...