and Applied Analysis 3 (ii) The scalar C-pseudomonotonicity in Definition 2 is weaker than C-pseudomonotonicity in Definition 1(ii). In fact, for any ξ ∈ C∗ \ {0}, x, y ∈ X, if ⟨ξ(u∗), y − x⟩ ≥ 0, then we have ⟨u∗, y − x⟩ ∉ − intC. Then, it follows from the Cpseudomonotonicity of T that ⟨V∗, y − x⟩ ∈ C, which implies that ⟨ξ(V∗), y − x⟩ ≥ 0. Definition 5. The topological space E is said to be c...

Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f:X → Y is a Frechet differentiable function and F:X ⇉ 2 is a set-valued mapping with closed graph. Uniform convergence of Chord method for solving generalized equation y ∈ f x + F x ...... . (∗), where y ∈ Y a parameter, is studied in the present paper. More clearly, we obtain the uniform convergence of the se...

we prove that the class of profinite groups $g$ that have a factorization $g=ab$‎ ‎with $a$ and $b$ abelian closed subgroups‎, ‎is closed under taking inverse limits‎ ‎of surjective inverse systems‎. ‎this is a generalization of a recent result by k. h. hofmann and f. g. russo‎. ‎as an application we reprove their generalization of iwasawa's structure theorem for‎ ‎quasihamiltonian pro-$p$...

The signed edge domination number of a graph is an edge variant of the signed domination number. The closed neighbourhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having a common end vertex with e. Let f be a mapping of the edge set E(G) of G into the set {−1, 1}. If ∑ x∈N [e] f(x) 1 for each e ∈ E(G), then f is called a signed edge dominating function on G. T...

Consider the exterior boundary value problem (V* + k’) u = 0, in R, k > 0. u lr. = k where T is a smooth closed connected surface in Ip’, u exp(ik 1x1) Ixl-‘f(k, n) as Ix/ + co, n =x lx]-‘, f is called the radiation pattern. We prove that when h runs through any dense set in L’(r) the corresponding radiation pattern f(k, n) runs through a dense set in L*(S’) for any k > 0, where S* is the unit ...

Let F be a function field of one variable over an algebraically closed field of characteristic zero, X a geometrically irreducible smooth projective variety over F , and L a line bundle on X. In this note, we will prove that if Ω X/F is ample and X is non-isotrivial, then there are a proper closed algebraic set Y of X and a constant A > 0 such that hL(P ) ≤ A · d(P ) + O(1) for all P ∈ X(F̄ )\Y ...

Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper ...

Proof. (5.2) implies that the set of permutations is closed under com­ position of functions. We check the three axioms for a group. We already proved that composition of functions is associative. Let i : S −→ S be the identity function from S to S. Let f be a permutation of S. Clearly f ◦ i = i ◦ f = f . Thus i acts as an identity. Let f be a permutation of S. Then the inverse g of f is a perm...

We are interested in the following problem: to describe the closed translation-invariant subspaces of lp(Z). For l2 there is a complete solution due to Wiener, in terms of zeros of Fourier transform. However, the situation when p 6= 2 is much harder. In this talk we will present a proof of Malliavin’s theorem which shows the difficulty of characterizing all invariant subspaces of l1. We will us...