Here are two of our main results: Theorem 1. Let X be a normal space with dimX = n and m ≥ n + 1. Then the space C∗(X,R m ) of all bounded maps from X into R m equipped with the uniform convergence topology contains a dense Gδ-subset consisting of maps g such that g(X) ∩Π is at most (n+ d −m)-dimensional for every d-dimensional plane Π in R m , where m − n ≤ d ≤ m. Theorem 2. Let X be a metriza...

This survey discuss approaches that integrate Decision Diagrams inside High Order Logic based Theorem provers. The approaches can be divided in two kinds, one is based on building a translation between model checker and theorem prover, the second is based on embedding the model checker algorithms inside the theorem prover. A comparison between both is discussed in detail. The paper also tries t...

A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove 3-dimensional analogue: simply-connected 2-complex every link which is locally flat 3-sphere, if it one at all. This can be thought as generalisation Schoenflies theorem.

We prove that every homogeneously Souslin set is coanalytic provided that either (a) 0long does not exist, or else (b) V = K, where K is the core model below a μ-measurable cardinal. 1 Homogeneously Souslin sets. In this paper we shall deal with homogeneously Souslin sets of reals, or rather with sets of reals which admit an ω-closed embedding normal form. Definition 1.1 (Cf. [4, p. 92].) Let A...

introduction:in this study, ecg signals have been embedded into medical images to create a novel blind watermarking method. the embedding is done when the original image is compressed using the ezw algorithm. the extraction process is performed at the decompression time of the watermarked image. materials and methods: the multi-resolution watermarking with a secret key algorithm developed in th...

We show the faithful embedding of common knowledge logic CKL into game logic GL, that is, CKL is embedded into GL and GL is a conservative extension of the fragment obtained by this embedding. Then many results in GL are available in CKL, and vice versa. For example, an epistemic consideration of Nash equilibrium for a game with pure strategies in GL is carried over to CKL. Another important ap...

Let F be a p-dimensional polyhedron and let Ç be a PL qmanifold without boundary. (Neither is necessarily compact.) The purpose of this paper is to prove that, if q — p > 3, then any topological embedding of P into Q can be pointwise approximated by PL embeddin-gs. The proof of this theorem uses the analogous result for embeddings of one PL manifold into another obtained by Cernavskii and Mille...

An embedding of a 3-regular graph in a surface is called polyhedral if its dual is a simple graph. An old graph-coloring conjecture is that every 3-regular graph with a polyhedral embedding in an orientable surface has a 3-edge-coloring. An affirmative solution of this problem would generalize the dual form of the Four Color Theorem to every orientable surface. In this paper we present a negati...

Ritt’s theorem of zeroes and Siedenberg’s embedding are classical results in differential algebra allowing to connect algebraic model-theoretic on nonlinear PDEs the realm analysis. However, existing proofs these use sophisticated tools from constructive (characteristic set theory) analysis (Riquier’s existence theorem). In this paper, we give new short for both theorems relying only basic fact...

There is recent interest in compressing data sets for non-sequential settings, where lack of obvious orderings on their data space, require notions of data equivalences to be considered. For example, Varshney & Goyal (DCC, 2006) considered multiset equivalences, while Choi & Szpankowski (IEEE Trans. IT, 2012) considered isomorphic equivalences in graphs. Here equivalences are considered under a...