The papers [19], [9], [1], [4], [20], [2], [18], [13], [5], [8], [14], [21], [7], [15], [12], [11], [17], [6], [10], [16], and [3] provide the terminology and notation for this paper. For simplicity we follow the rules: M is a metric space, c, g are elements of the carrier of M , F is a family of subsets of the carrier of M , A, B are subsets of the carrier of M , f is a function, n, m, p, k ar...

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. The reconfiguration version of a vertex-subset problem Q asks whether it is possible to transform one feasible solution for Q into another in at most l steps, where each step is a vertex addition or deletion, and each intermediate set is also a feasible solution for Q of size bounded ...

Suppose ( M , γ stretchy="false">) (M, \ga...

Previous studies from this laboratory have demonstrated a statistically significant dysregulation in several key components of the 2',5'-oligoadenylate (2-5A) synthetase/RNase L and PKR antiviral pathways in chronic fatigue syndrome (CFS) (Suhadolnik et al. Clin Infect Dis 18, S96-104, 1994; Suhadolnik et al. In Vivo 8, 599-604, 1994). Two methodologies have been developed to further examine th...

For $(X,\,L)$ a polarized toric variety and $G\subset \mathrm {Aut}(X,\,L)$ torus, denote by $Y$ the GIT quotient $X/\!\!/G$ . We define family of fully faithful functors from category torus equivariant reflexive sheaves on to $X$ show, under genericity assumption $G$ , that slope stability is preserved these if only pair $((X,\,L),\,G)$ satisfies combinatorial criterion. As an application, whe...

In this paper, we study the Chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. In particular, we prove that if T is a remotal subset of an inner product space H, and F is a star-shaped set at a relative Chebyshev centre c of T with respect to F, then llx - qT (x)1I2 2 Ilx-cll2 + Ilc-qT (c) 112 x E F, where qT : F + T is any choice functi...

Let T be a topological structure and let A be a subset of the carrier of T . Then IntA is a subset of T . Let T be a topological structure and let P be a subset of the carrier of T . Let us observe that P is closed if and only if: (Def. 1) −P is open. Let T be a non empty topological space and let F be a family of subsets of T . We say that F is dense if and only if: (Def. 2) For every subset X...

It is the purpose of this paper to prove that if each of X and Y is a compact Hausdorff space containing infinitely many points, and X X Y is the continuous image of a compact ordered space L, then both X and Fare metrizable.2 The preceding theorem is a generalization of a theorem [l ] by Mardesic and Papic, who assume that X, Y, and L are also connected. Young, in [3], shows that the Cartesian...

In this paper we consider the Unary-Subset-Sum problem which is defined as follows: Given integers m1, . . . ,mn and B (written in unary), we define the subset sum problem to be that of determining whether or not there exists an S ⊆ [n] so that ∑ i∈Smi = B (note that for this problem the mi are often assumed to be non-negative). Let C = |B| + ∑n i=1 |xi| + 1. This problem can be solved using a ...

BACKGROUND In adults, exercise is a powerful and natural stimulator of immune cells and adhesion molecules. Far less is known about exercise responses during childhood and adolescence and whether or not exercise in "real life" activities of healthy adolescents influences immune responses. OBJECTIVE To determine if strenuous exercise leads to significant changes in leucocyte number and adhesio...