Journal of Applied and Industrial Mathematics最新文献

Additive differentials of the function( (x oplus y) lll r ) whose probability is( 0 ) are considered, where( x, y in mathbb {Z}_2^{n} ) and( 1 leq r < n ). They are called impossible differentials and are interesting in the context ofdifferential cryptanalysis of ciphers whose schemes consist of additions modulo( 2^n ), bitwise XORs (( oplus )), and bit rotations (( lll r )). The number of all such differentials is calculated for all possible( r ) and( n ). It is also shown that this number is greater than( frac {38}{245} 8^n ). Moreover, the estimate is asymptotically tight for( r, n-r to infty ). For any fixed( n ) the number of all impossible differentials decreases as( r ) goes from( 1 ) to( lceil n/2 rceil ) (to( lceil n/2 rceil + 1 ) in the case of( n in {4, 5, 6, 8, 10, 12} )) and then increases monotonically as( r ) goes to( n-1 ). A simplified description of all impossible differentials is obtained up toknown symmetries.

A new threshold stability problem in the context of facility location and discriminatorypricing is considered. In the statement of facility location and pricing problem, the companydecides to open facilities and assign prices to each customer at each facility. The implementationof discriminatory pricing leads to a scenario where each customer is compelled to expend themaximum amount of their available financial resources, thereby ensuring the maximum revenuefor the company. In the threshold stability problem, the available financial resources or budget ofeach consumer is a parameter with a known expected value. The objective is to maximize thedeviation of the parameters from the expected value, provided that the company’s income remainsabove a given threshold.

An algorithm based on variable neighborhood descent (VND) is proposed to solvethe threshold stability problem. Numerical investigation of the algorithm is carried out on knowninstances and randomly generated ones. Various ways of constructing the starting facility locationand different criteria for comparing the location vectors are analyzed.

We prove that the complexity of a universal depth-( n ) parallel prefix circuit on( 2^n ) inputs with fanout bounded by( 2 ) is at least( 0.75(n-1)2^{n} ). We also propose a number of simple constructions and upper complexitybounds on fanout-( 2 ) prefix circuits of depth( n+k ).

Word-representable graphs are vital in the Combinatorics of Words and Graph Theory.We define one such graph, the( ell )-Rauzy graph, and study its structural properties for a few infinite words. The( ell )-Rauzy graph of order( k ) for an infinite word( w ) is a directed graph in which each vertex is a subword of length( k ) of( w ), where any two vertices( u,v ) form an arc( uv ) iff the prefix of( v ) of length( ell ) is the same as the suffix of( u ) of length( ell ) and the concatenated word formed by the arc( uv ) of length( 2k-ell ) is a subword of( w ). As main results, we show that the( ell )-Rauzy graph of order( k ) for the infinite Fibonacci word( f ) is strongly connected, and we explicitly find the graph structure of the( ell )-Rauzy graph of order( k ) for an infinite periodic word, by knowing the locations of subwords of( f ) and infinite periodic words. As locating the subwords in an infinite word isnot easy, we show that the( ell )-Rauzy graph of order( k ) for an Arnoux-Rauzy word is strongly connected using a different approach.( ell )

In the cluster editing problem, one has to partition the set of vertices of a graph intopairwise disjoint subsets (called clusters) minimizing the number of edges between clusters and thenumber of missing edges within clusters. We consider a version of the problem in which clustersizes are bounded from above by a positive integer( s ). This problem is NP-hard for any fixed( s geqslant 3 ). We propose polynomial-time approximation algorithms for this version ofthe problem. Their performance guarantees equal( 5/3 ) for the case( s = 3 ) and( 2 ) for( s = 4 ). We also show that the cluster editing problem is APX-hard for the case of( s = 3 ).

We consider a two-bar charts packing problem in which it is necessary to pack bar chartsconsisting of two bars in a unit-height strip of minimum length. Each bar has a height of at most1 and unit length. The problem under consideration is NP-hard and generalizes the bin packingproblem and two-dimensional vector packing problem. This paper proves updated accuracyestimates and time complexity for several previously developed polynomial approximationalgorithms for the two-bar charts packing problem and particular cases of the problem. We showthe attainability of the estimates. Furthermore, we consider a problem of packing an unlimitednumber of bar charts belonging to( k ) different types and propose a polynomial algorithm to solve the problem incase( k = text {const} ).

The paper is devoted to the study of the qualitative behavior of solutions for theKelvin–Voigt model taking into account memory along fluid motion trajectories. Namely, basedon the theory of attractors of noninvariant trajectory spaces, for the model under consideration inthe nonautonomous case the existence of a uniform trajectory and a uniform global attractor isproved under certain conditions on the coefficients.

We present a method for calculating the signed distance field to three-dimensionalgeometric models by representing them as a result of Boolean operations on elementary objects foreach of which the signed distance is known. Two versions of the algorithm are proposed. The firstis a simplified version for quick calculation of the rough distance approximation (with an exactzero isosurface and correct separation of domains inside and outside the model). The secondversion includes calculation of the distance to the intersection contours between elements, allowingthe distance to be reconstructed with a greater accuracy without considerable additionalcomputational costs. Both methods are much faster than the computation of distance based onthe triangulation of the surfaces. The proposed approach also allows for interactively changingrelative positions and orientation of the geometry parts; this makes it possible to performcalculations with moving boundaries. The approach has been tested in fluid dynamics simulationwith an interphase boundary and adaptive multilevel grid refinement in Basilisk open source code for simulation ofmultiphase flows.

More precise definitions of concepts and constructs used in biomedical sciences areproposed to analyze the joint action of factors using isobolograms. Formal definitions of conceptsof zero interaction, scale-equivalent dose–response functions, and zero-interaction manifold aregiven. A general construction is proposed that formalizes the conditions of applicability and thebasic methods for analyzing the combined action using isoboles. Equations of zero-interactionmanifolds are derived both in the case of scale-equivalent and arbitrary dose–response functions.

The resource-constrained project scheduling problem (briefly RCPSP) is a generalscheduling problem that includes precedence and resource constraints. Activities preemptions arenot allowed. Resources are renewable and there is a unique way to perform the activities. Theproblem with renewable resources is NP-hard in the strong sense. We propose a new deterministicgreedy algorithm. It is based on heuristics that use information obtained from a relaxing problem.The algorithm is tested with standard data sets given by Kolisch library PSPLIB for j60, j90, andj120 and found to be performing well.