Effective Hironaka resolution and its Complexity (with appendix on applications in positive characteristic)

Building upon works of Hironaka, Bierstone-Milman, Villamayor and Wlodarczyk, we give an a priori estimate for the complexity of the simplified Hironaka algorithm. As a consequence of this result, we show that there exists canonical Hironaka embedded desingularization and principalization over fields of large characteristic (relative to the degrees of generating polynomials).Comment: 1 figure. arXiv admin note: substantial text overlap with arXiv:math/040140

Application of the Homotopy Analysis Method for Solving the Systems of Linear and Nonlinear Integral Equations

In this paper we indicate some applications of homotopy analysis method for solving the systems of linear and nonlinear integral equations. The method is based on the concept of creating function series. If the series converges, its sum is the solution of this system of equations. The paper presents conditions to ensure the convergence of this series and estimation of the error of approximate solution obtained when the partial sum of the series is used. Application of the method will be illustrated by examples

TOROIDAL VARIETIES AND THE WEAK FACTORIZATION THEOREM

We develop the theory of stratified toroidal varieties, which gives, together with theory of birational cobordisms [71], a proof of the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field K of characteristic zero is a composite of blow ups and blow downs with smooth centers

Oriented Metric-Affine Plane --- Part I

this paper. Let V be an Abelian non empty loop structure and let v, w be elements of the carrier of V . Let us note that the functor v + w is commutative. We follow the rules: V denotes a real linear space, u, u 1 , u 2 , v, v 1 , v 2 , w, w 1 , x, y denote vectors of V , and n denotes a real number. Let us consider V , x, y and let us consider u. The functor a

Functional framework for representing and transforming quantum channels

Abstract We develop a framework which aims to simplify the analysis of quantum states and quantum operations by harnessing the potential of function programming paradigm. We show that the introduced framework allows a seamless manipulation of quantum channels, in particular to convert between different representations of quantum channels, and thus that the use of functional programming concepts facilitates the manipulation of abstract objects used in the language of quantum theory. For the purpose of our presentation we will use Mathematica computer algebra system. This choice is motivated twofold. First, it offers a rich programming language based on the functional paradigm. Second, this programming language is combined with powerful symbolic and numeric manipulation capabilities

Partial Functions from a Domain to a Domain

this paper

The Problem of Distribution of Park-and-Ride Car Parks in Warsaw

[[abstract]]The development of cities and agglomerations brings new problems to be solved. One of them is the excessive road traffic and the related air pollution. Heavy traffic causes ongestions and thus increases the pollution level, because one of the most significant sources of air pollution are car exhaust gases. It is known that the public transport produces less pollution per one passenger then the private one. On the basis of this fact the idea of the Park-and-Ride (P&R or P+R) was developed, where commuters travel to the borders of the city by their cars and from there they continue their trip by public transportation. In this work, we will concentrate on finding the best localizations for P&R points. Our approach is composed of two steps. In the first step, a number of communication hubs is selected where P&R can be located (feasibility analysis). In the second ste a subset of hubs is chosen to actually have P&R points built (commuters’ convenience analysis). We solve the P&R location problem on the first step using some aspects of the Hub and Spoke method by applying a specialized evolutionary algorithm. As the problem of the second step is rather small, we propose to have it solved by experts

Functions and Finite Sequences of Real Numbers

this paper