A hypergraph H=(V(H),E(H)) is a Berge copy of graph F, if V(F)⊂V(H) and there bijection f:E(F)→E(H) such that for any e∈E(F) we have e⊂f(e). Berge-F-free it does not contain copies F. We address the saturation problem concerning hypergraphs, i.e. what minimum number satr(n,Berge-F) hyperedges in an r-uniform H with property adding new hyperedge (of size r) to creates F? prove grows linearly n F...

A graph $G=(V,E)$ is $\gamma$-excellent if $V$ a union of all $\gamma$-sets $G$, where $\gamma$ stands for the domination number. Let $\mathcal{I}$ be set mutually nonisomorphic graphs and $\emptyset \not= \mathcal{H} \subsetneq \mathcal{I}$. In this paper we initiate study $\mathcal{H}$-$\gamma$-excellent graphs, which define as follows. $G$ following hold: (i) every $H \in \mathcal{H}$ each $...

We let h denote a real or complex nilpotent Lie algebra and V a nite dimensional complex h-module. For X 2 h let X V = (v 7 ! Xv): V ! V. We set h C = h if the ground eld K is C and let h C denote the complexiication of h if K = R. Recall that a linear form : h C ! C is a weight if there is a nonzero v 2 V such that for some natural number n we have (X V ? (X)1 V) n v = 0 for all X 2 h. The ele...

ing this computation, for given k-vectorspace V with non-degenerate alternating form 〈, 〉, put a Lie algebra [2] structure h on V ⊕ k by Lie bracket [v ⊕ z, v′ ⊕ z′] = 0⊕ 〈v, v′〉 In exponential coordinates on H, the exponential map h→ H with H ≈ V ⊕ k is notated exp(v ⊕ z) = v ⊕ z with Lie group structure on H by (v ⊕ z) · (v′ ⊕ z′) = (v + v′)⊕ (z + z′ + 〈v, v ′〉 2 ) (exponential coordinates in...

and Applied Analysis 3 For given nonlinear operators T, g, h, we consider the problem of finding u ∈ H : h u ∈ K such that 〈 Tu, g v − h u 〉 ≥ 0, ∀v ∈ H : g v ∈ K, 2.1 which is called the extended general variational inequality. Noor 13–16 has shown that the minimum of a class of differentiable nonconvex functions on hg-convex set K in H can be characterized by extended general variational ineq...

abstract background and aims: the burden of hiv infection and disease continues to be a major global public health concern all over the world. this study was conducted to measure igg antibody against ebv viral capsid antigen (ebv-vca igg), herpes simplex type1, and 2 to determine the seroprevalence of this infection in hiv-positive population. materials and methods: a cross-sectional study betw...

u ′t + Aut = ft, t ∈ 0,T u0 = u0, where Au,vH = Bu,v ∀u,v ∈ V ⊂ H ⊂ V ′. We showed that if the bilinear form B is coercive then the linear mapping A is an isomorphism from V onto V’. Recall that there exists a family of H-orthonormal eigenfunctions for A such that ||Awk ||H = |λk| ||wk ||H = |λk|→ ∞ as k → ∞. Then A is clearly not bounded as a mapping from H into H. If we define D...

We recently identified a chronic lymphocytic leukemia (CLL) subgroup using the immunoglobulin variable heavy-chain (V(H)) gene V(H)3-21 with almost identical heavy-chain complementarity determining region 3s (HCDR3s) and preferential variable light-chain (V(L)) gene usage, suggesting recognition of a common antigen epitope in this subset. To further explore the B-cell receptors (BCRs) in CLL, w...

by growing the population and need for settlement, many cities have been built on soft sediments and seismic areas. it emphasizes the need for a careful and reliable assessment of site effect phenomena. beyond the methods of studying site effects, microtremor recordings has become popular over the last decades as it offers a convenient, practical and low cost tool to be used in urbanized areas....