The purpose of this article is to show that the bivariant algebraic A-cobordism groups considered previously by author are independent chosen base ring A. This result proven analyzing ideal generated so called snc relations, and, while alternative characterization we obtain for interesting itself because its simplicity, perhaps more importantly it allows us easily extend definition cobordism di...

Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré Duality and the Dold-Thom Theorem to establish existence of Nash Equilibria under fairly general topological hypotheses. The Dold-Thom Theorem provides us ...

This paper presents an executable semantics of OO models. We made it possible to conduct both simulation and theorem proving on the semantics by implementing its underlying heap memory structure within the expressive intersection of the functional language ML and the theorem prover HOL. This paper also presents a verification system ObjectLogic which supports simulation and theorem proving of O...

We give a new proof of Delsarte, Goethals and Mac williams theorem on minimal weight codewords of generalized Reed-Muller codes published in 1970. To prove this theorem, we consider intersection of support of minimal weight codewords with affine hyperplanes and we proceed by recursion.

We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal ...

The well-known Erdős–Ko–Rado Theorem states that if F is a family of k-element subsets of {1, 2, . . . , n} (n ≥ 2k) satisfying S, T ∈ F ⇒ |S ∩ T | ≥ 1, then |F| ≤ ( n−1 k−1 ) . The theorem also provides necessary and sufficient conditions for attaining the maximum. We present elementary methods for deriving generalizations of the Erdős– Ko–Rado Theorem on several classes of combinatorial objec...

The goal of this paper is to prove Bézout’s Theorem for algebraic curves. Along the way, we introduce some basic notions in algebraic geometry such as affine and projective varieties and intersection numbers of algebraic curves. After proving Bézout’s Theorem, we investigate Max Noether’s Fundamental Theorem and construct the group law on a plane cubic which is the first step in studying the ar...

The main topic of this paper is various " hyperbolic " generalizations of the Edmonds-Rado theorem on the rank of intersection of two matroids. We prove several results in this direction and pose a few questions. We also give generalizations of the Obreschkoff theorem and recent results of J. Borcea and B. Shapiro.