We classify, up to homeomorphism, all closed manifolds having the homotopy type of a connected sum of two copies of real projective n-space. 1. Statement of results Let P = Pn(R) be real projective n-space. López de Medrano [LdM71] and C.T.C. Wall [Wal68, Wal99] classified, up to PL homeomorphism, all closed PL manifolds homotopy equivalent to P when n > 4. This was extended to the topological ...

We investigate how human observers make use of three candidate cues in their lightness judgments. Each cue potentially provides information about the spatial distribution of light sources in complex, rendered 3D scenes. The illumination (lighting model) of each scene consisted of a punctate light source combined with a diffuse light source. The cues were (1) cast shadows, (2) surface shading, a...

One of the key directions in complexity theory which has also filtered through to cryptographic research, is the effort to classify related but seemingly distinct notions. Separation or reduction arguments are the basic means for this classification. Continuing this direction we identify a class of problems, called “matching problems,” which are related to the class of “decision problems.” In m...

We introduce compactness theorems for generalized colorings and derive several particular compactness theorems from them. It is proved that the theorems and many of their consequences are equivalent in ZF set theory to BPI, the Prime Ideal Theorem for Boolean algebras. keywords: generalized graph colorings, compactness, prime ideal theorem MSC: 05C15; 03E25 .

For two differential systems, an algorithm which permits us to say whether reflecting functions of these systems coincide or not is given. It allows studying qualitative properties of these two systems simultaneously. © 2009 Elsevier Ltd. All rights reserved.

This work shows that the following problems are equivalent, both in theory and in practice: • median filtering : given an n-element vector, compute the sliding window median with window size k, • piecewise sorting : given an n-element vector, divide it in n/k blocks of length k and sort each block. By prior work, median filtering is known to be at least as hard as piecewise sorting: with a sing...

an efficient, simple and convenient route is described for the synthesis of biscoumarin (3,3'-(arylmethylene) bis (4-hydroxy-2h-chromen-2-one)) by using of recyclable catalyst tio2@ksf. in this method, we synthesis biscoumarin derivatives via 3multi-component reactions (3mcrs) of two equivalent 4-hydroxycoumarin with one equivalent of aromatic aldehydes using 20 mg nano tio2@ksf as homogen...

An efficient, simple and convenient route is described for the synthesis of biscoumarin (3,3'-(arylmethylene) bis (4-hydroxy-2H-chromen-2-one)) by using of recyclable catalyst TiO2@KSF. In this Method, we synthesis biscoumarin derivatives via 3multi-component reactions (3MCRs) of two equivalent 4-hydroxycoumarin with one equivalent of aromatic aldehydes using 20 mg nano TiO2@KSF as homogeneous ...

In this paper, we present new blind signature schemes based on the factorization problem. They are the first blind signature schemes proved secure relatively to factorization. By security, we mean that no “one-more forgery” is possible even under a parallel attack. In other terms, a user that receives k electronic coins cannot manufacture k + 1. Those security definitions have been introduced b...