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Probabilistic construction of small strongly sum-free sets via large Sidon sets

Andreas Schoen, Tomasz Srivastav, Anand Baltz (2000)

Colloquium Mathematicae

We give simple randomized algorithms leading to new upper bounds for combinatorial problems of Choi and Erdős: For an arbitrary additive group G let P n ( G ) denote the set of all subsets S of G with n elements having the property that 0 is not in S+S. Call a subset A of G admissible with respect to a set S from P n ( G ) if the sum of each pair of distinct elements of A lies outside S. Suppose first that S is a subset of the positive integers in the interval [2n,4n). Denote by f(S) the number of elements in a...

Program Algebra over an Algebra

Grzegorz Bancerek (2012)

Formalized Mathematics

We introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The execution of a program is changing state according to successor function using supporting terms.

Progress in developing Poisson-Boltzmann equation solvers

Chuan Li, Lin Li, Marharyta Petukh, Emil Alexov (2013)

Molecular Based Mathematical Biology

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided...

Quantized cooperative output regulation of continuous-time multi-agent systems over switching graph

Ji Ma, Bo Yang, Jiayu Qiu, Ziqin Chen, Wenfeng Hu (2024)

Kybernetika

This paper investigates the problem of quantized cooperative output regulation of linear multi-agent systems with switching graphs. A novel dynamic encoding-decoding scheme with a finite communication bandwidth is designed. Leveraging this scheme, a distributed protocol is proposed, ensuring asymptotic convergence of the tracking error under both bounded and unbounded link failure durations. Compared with the existing quantized control work of MASs, the semi-global assumption of initial conditions...

Quasi-hierarchical evolution algorithm for flow assignment in survivable connection-oriented networks

Michal Przewozniczek, Krzysztof Walkowiak (2006)

International Journal of Applied Mathematics and Computer Science

The main objective of this paper is to develop an effective evolutionary algorithm (EA) for the path-assignment problem in survivable connection-oriented networks. We assume a single-link failure scenario, which is the most common and frequently reported failure event. Since the network flow is modeled as a non-bifurcated multicommodity flow, the discussed optimization problem is NP-complete. Thus, we develop an effective heuristic algorithm based on an evolutionary algorithm. The main novelty of...

Real and complex pseudozero sets for polynomials with applications

Stef Graillat, Philippe Langlois (2007)

RAIRO - Theoretical Informatics and Applications

Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero...

Relaxed algorithms for p -adic numbers

Jérémy Berthomieu, Joris van der Hoeven, Grégoire Lecerf (2011)

Journal de Théorie des Nombres de Bordeaux

Current implementations of p -adic numbers usually rely on so called zealous algorithms, which compute with truncated p -adic expansions at a precision that can be specified by the user. In combination with Newton-Hensel type lifting techniques, zealous algorithms can be made very efficient from an asymptotic point of view.In the similar context of formal power series, another so called lazy technique is also frequently implemented. In this context, a power series is essentially a stream of coefficients,...

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