where n = |V |. Let G = (V,E) be a 3-regular hypergraph; i.e. E is a subset of subsets of V of size 3. We consider the space, L2(V ), of real valued functions on V with the usual inner product; let e1, . . . , en be the standard basis for L2(V ), where ei takes the value 1 on the i-th vertex of V and 0 elsewhere. It is natural to construct from G a trilinear form, that is a map from τ , mapping...

where n = |V |. Let G = (V,E) be a 3-uniform hypergraph; i.e. E is a subset of subsets of V of size 3. We consider the space, L(V ), of real valued functions on V with the usual inner product; let e1, . . . , en be the standard basis for L(V ), where ei takes the value 1 on the i-th vertex of V and 0 elsewhere. It is natural to construct from G a trilinear form, that is a map from τ , mapping t...

where F is a monotone operator. Recently, Lu et al. [] were concerned with a special class of variational inequalities in which the mapping F is the complement of a nonexpansive mapping and the constraint set is the set of fixed points of another nonexpansive mapping. Namely, they considered the following type of monotone variational inequality (VI) problem: Find x∗ ∈ Fix(T), such that 〈(I –V ...

Introduction: Venus host two distinctive terrains, one tectonic, the other volcanic. These two terrain types, ribbon tessera terrain and shield terrain are both extensively preserved across the surface of Venus, and they might also show a spatial correlation, which may, in turn reflect a genetic relationship. Geology: Ribbon tessera terrain (rtt) represents the oldest locally exposed unit acros...

This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will prove Needham’s theorem in a more general version. 1. Fixed point indices of holomorphic mappings Let C be the complex vector space of dimension n, let U be a...

Let G∗ = (V, E) be a simple graph and A any nonempty set of parameters. subset R A×V an arbitrary relation from to V. mapping ᵖ(V) written as F:A → can defined F(x) { y ∈ V/xRy} ᵖ(E) K:A K(x) {uv E/{u, v} ⊆ F(x)}. The pair (F, A) is soft over V the (K, E. Obviously (F(a), K(a)) subgraph for all A. 4-tuple G ( G∗, F, K, called G. In this paper we discuss different graphs such Complete graph, Sta...