In this paper we consider the problem of bounding the Betti numbers, bi(S), of a semi-algebraic set S ⊂ R k defined by polynomial inequalities P1 ≥ 0, . . . , Ps ≥ 0, where Pi ∈ R[X1, . . . , Xk] , s < k, and deg(Pi) ≤ 2, for 1 ≤ i ≤ s. We prove that for 0 ≤ i ≤ k − 1, bi(S) ≤ 1 2 + (k − s) + 1 2 · min{s+1,k−i}

A graph property is any nonempty isomorphism-closed class of simple (finite or infinite) graphs. A graph property P is of finite character if a graph G has a property P if and only if every finite induced subgraph of G has a property P . Let P1,P2, . . . ,Pn be graph properties of finite character, a graph G is said to be (uniquely) (P1,P2, . . . ,Pn)partitionable if there is an (exactly one) p...

Semi-transparent solar cells are emerging as promising devices for building integrated photovoltaics. However, regardless of the technology considered, optical transmission semi-transparent is fixed during fabrication process, and hence, cannot adjust to variations in daylight or weather conditions. This becomes an issue when applications such photovoltaic windows envisioned. Previously, it has...

in this paper, at first we mention to some results related to pi and vertex co-pi indices and then we introduce the edge versions of co-pi indices. then, we obtain some properties about these new indices.

Two equal-length strings S and S′ are a parameterized-match (p-match) iff there exists a one-toone function that renames the characters in S to those in S′. Let P be a collection of d patterns of total length n characters that are chosen from an alphabet Σ of cardinality σ. The task is to index P such that we can support the following operations: search(T ): given a text T , report all occurren...

The pi calculus holds the promise of compile-time checks for whether a given program will have the correct interactive behaviour. The theory behind such checks is called bisimulation. In the synchronous pi calculus, it is well-known that the various natural definitions of (strong) bisimulation yield different relations. In contrast, for the asynchronous pi calculus, they collapse to a single re...

In the present paper, we continue the study on fuzzy soft topological spaces and investigate the properties of fuzzy soft semi connected sets, fuzzy soft semi separated sets and fuzzy soft semi s-connected sets and have established several interesting properties supported by examples. Moreover, we show that a fuzzy soft semi disconnectedness property is not hereditary property in general. Final...

Guang-Hong Chen University of Wisconsin–Madison Department of Medical Physics Madison, Wisconsin 53704 and University of Wisconsin–Madison Department of Radiology Madison, Wisconsin 53792 E-mail: [email protected] Abstract. We present a cone-beam image reconstruction algorithm for helical CT scanning with a tilted gantry and N-PI data acquisition. When the gantry is tilted, the effective source t...