关键词： MODULES (Algebra)   ALGORITHMS   EXPANSION (Mathematics)   ALGEBRAIC numbers   CONTINUED fractions  

摘要： The simplex-module algorithm for expansion of algebraic numbers α = (α₁ α_d) in multidimensional continued fractions is suggested. The method is based on minimal rational simplices s, where α ∈ s, and Pisot matrices P_α, for which α̂ = (α₁,.. , α_d, 1) is an eigenvector. A multidimensional generalization of the Lagrange theorem is proved. © 2017, Springer Science+Business Media, LLC.

关键词： 排课   数学模型   算法   教务管理系统  

摘要： 智能排课作为教务管理系统中的一个重要组成部分,其对于高中院校的管理工作有着非常重要的意义.本文就以教务管理系统中排课的数学模型以及算法进行了分析研究.

关键词： Zeros of polynomials over noncommutative R-4 algebras   Isolated   Spherical   Hyperbolic   Unexpected zeros  

摘要： This paper will contain an extension of Niven's algorithm of 1941, which in its original form is designed for finding zeros of unilateral polynomials p over quaternions H . The extensions will cover the algebra H-coq of coquaternions, the algebra H-nec of nectarines and the algebra H-coq of conectarines. These are nondivision algebras in R-4 . In addition, it is also shown that in all algebras the most difficult part of Niven's algorithm can easily be solved by inserting the roots of the companion polynomial c of p, with the result, that all zeros of all unilateral polynomials over all noncommutative R-4 algebras can be found. In addition, for all four algebras the maximal number of zeros can be given. For the three nondivision algebras besides the known types of zeros: isolated, spherical, hyperbolic, a new type of zero will appear, which will be called unexpected zero of p.

关键词： Stream ciphers   Fast algebraic attacks   Time complexity   Algebraic immunity  

摘要： Although several methods for estimating the resistance of a random Boolean function against (fast) algebraic attacks were proposed, these methods are usually infeasible in practice for relatively large number of input variables n (for instance n >= 30) due to increased computational complexity. An efficient estimation of the resistance of Boolean functions, with relatively large number of inputs n, against (fast) algebraic attacks appears to be a rather difficult task. In this paper, the concept of partial linear relations decomposition is introduced, which decomposes any given nonlinear Boolean function into many linear (affine) subfunctions by using the disjoint sets of input variables. Based on this result, a general probabilistic decomposition algorithm for nonlinear Boolean functions is presented which gives a new framework for estimating the resistance of Boolean function against (fast) algebraic attacks. It is shown that our new probabilistic method gives very tight estimates (lower and upper bound) and it only requires about O(n(2)2(n)) operations for a random Boolean function with n variables, thus having much less time complexity than previously known algorithms. (C) 2017 Elsevier Inc. All rights reserved.

关键词： DISTRIBUTED algorithms   STOCHASTIC convergence   EXPONENTIAL functions   LINEAR algebras   LINEAR equations  

摘要： In a recent paper, a distributed algorithm was proposed for solving linear algebraic equations of the form Ax = b assuming that the equation has at least one solution. The equation is presumed to be solved by m agents assuming that each agent knows a subset of the rows of the matrix [A b], the current estimates of the equation's solution generated by each of its neighbors, and nothing more. Neighbor relationships are represented by a time-dependent directed graph N(t) whose vertices correspond to agents and whose arcs characterize neighbor relationships. Sufficient conditions on N(t) were derived under which the algorithm can cause all agents' estimates to converge exponentially fast to the same solution to Ax = b. These conditions were also shown to be necessary for exponential convergence, provided the data about [A b] available to the agents is "non-redundant". The aim of this paper is to relax this "non-redundant" assumption. This is accomplished by establishing exponential convergence under conditions which are the weakest possible for the problem at hand;the conditions are based on a new notion of graph connectivity. An improved bound on the convergence rate is also derived. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Automatic Differentiation   Numerical Methods   MATLAB   Algorithmic differentiation   scientific computation   applied mathematics   chain rule   forward mode   overloading   source transformation  

摘要： A toolbox called ADiGator is described for algorithmically differentiating mathematical functions in MATLAB. ADiGator performs source transformation via operator overloading using forward mode algorithmic differentiation and produces a file that can be evaluated to obtain the derivative of the original function at a numeric value of the input. A convenient by-product of the file generation is the sparsity pattern of the derivative function. Moreover, because both the input and output to the algorithm are source codes, the algorithm may be applied recursively to generate derivatives of any order. A key component of the algorithm is its ability to statically exploit derivative sparsity at the MATLAB operation level to improve runtime performance. The algorithm is applied to four different classes of example problems and is shown to produce runtime efficient derivative code. Due to the static nature of the approach, the algorithm is well suited and intended for use with problems requiring many repeated derivative computations.

关键词： Eryngium billardieri   Supercritical fluid extraction   Experimental optimization   Mathematical modeling   Simulated annealing (SA) algorithm  

摘要： This article presents experimental results and mathematical modeling predictions of the extraction of essential oil from Eryngium billardieri, for the first time, using supercritical carbon dioxide (SC-CO2) method. Design of experiments and experimental optimization were carried out with a response surface methodology (RSM) to investigate the effects of different operating parameters including pressure (100-300 bar), temperature (308-328 K), particle size (0.45-1.05 mm) and extraction time (30-150 min). The maximum extraction yield was found to be 0.8522% w/w at the optimum conditions 300 bar, 308 K, 0.75 mm and 130 min. Moreover, in order to describe the kinetic behavior of extraction process, a mathematical model based on the Brunauer-Emmett-Teller (BET) theory of adsorption with three adjustable parameters was developed for correlating experimental data. Model parameters have been optimized by applying simulated annealing (SA) algorithm. The obtained results from model predictions were consistent with experimental data in the different extraction conditions.

关键词： Biclustering   Fuzzy mathematics   Multi-objective optimization   Mean square residue  

摘要： Biclustering algorithm is to cluster in the horizontal and vertical directions simultaneously in matrix. This algorithm identifies a set of sub-matrix by adopting a greedy iterative strategy, which employs the mean squared residue to measure the element consistency of a sub-matrix. Biclustering algorithm is widely applied in large and complex data. However, different versions of biclustering algorithm always have the problem that with the increasing of data size, more irrelevant rows or columns are involved in clustering which results in the poor performance of clustering. Therefore, this paper proposes a new algorithm, which combines fuzzy member matrix and comprehensive evaluation in fuzzy mathematics with multi-objective optimization algorithm to improve the performance of biclustering algorithm. In order to validate the effectiveness of the new algorithm, the performance the new algorithm and other three mainstream algorithms are compared on three gene/protein expression datasets. The results show the new algorithm has better element consistency, and sub-matrix capacity than other algorithms. (C) 2017 Elsevier B.V. All rights reserved.