An (h, s, t)-representation of a graph G consists of a collection of subtrees {Sv |v ∈ V (G)} of a tree T , such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at most s, and (iii) there is an edge between two vertices in the graph if and only if the corresponding subtrees in T have at least t vertices in common. For example, chordal graphs correspond to [∞...

We construct a model structure on the category $\mathrm{DblCat}$ of double categories and functors, whose trivial fibrations are functors that surjective objects, full horizontal vertical morphisms, fully faithful squares; fibrant objects weakly horizontally invariant categories. show functor $\mathbb H^{\simeq}\colon \mathrm{2Cat}\to \mathrm{DblCat}$, more homotopical version usual embedding H...

A class A of labelled graphs is weakly addable if if for all graphs G in A and all vertices u and v in distinct connected components of G, the graph obtained by adding an edge between u and v is also in A; the class A is monotone if for all G ∈ A and all subgraphs H of G, we have H ∈ A. We show that for any weakly addable, monotone class A whose elements have vertex set {1, . . . , n}, the prob...

Given a sequence of Galerkin spaces Xh of curl conforming vector fields, we state necessary and sufficient conditions under which it is true that the scalar product uh ·uh of two sequences of vector fields uh, uh ∈ Xh converging weakly in L, converges in the sense of distributions to the right limit, whenever uh is discrete divergence free and curluh is precompact in H−1. The conditions on Xh a...

In this paper, we compute basis elements of certain spaces of weight 0 weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the rank 2 hyperbolic Kac-Moody algebras H(a), a = 4, 5, 6, through Hilbert modular forms explicitly given by Borcherds lifts of the weakly holomorphic modular ...

If G is a locally compact topological group, let BC{G) denote the set of real-valued, bounded, uniformly continuous functions on G with the compact-open topology. Using the fact that the distal (weakly distal) functions are the elements of BC(G) whose orbit closures are compact distal (point-distal) minimal sets, we can characterize compact distal and point-distal minimal transformation groups....

In the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎We also define the concept of weakly related mappings on an ordered space‎. ‎Moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.

in this paper, we prove some common fixed point results for two self mappingsf and g on s-metric space such that f is a g.w.c.m with respect to g.

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

In this paper, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a metric space satisfying a weak Meir-Keeler type contractive condition by using a class of implicit relations. In particular, our result generalizes and improves a result of K. Jha, R.P. Pant, S.L. Singh, by removing the assumption of continuity, relaxing compatibility to weakly com...