Search

In this paper, we prove that for a linearly ordered skewfield the groups of quotients of the semigroup Gn(픻) coincides with the group GLn(픻) for n ≥ 3. [ABSTRACT FROM AUTHOR]

Let F be a function on pairs of vertices. An F-labeling scheme is composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute F( u, v) for any two vertices u and v directly from their labels. As applications for labeling schemes concern mainly large and dynamically changing networks, it is of interest to study distributed dynamic labeling schemes. This paper investigates labeling schemes for dynamic trees. We consider two dynamic tree models, namely, the leaf-dynamic tree model in which at each step a leaf can be added to or removed from the tree and the leaf-increasing tree model in which the only topological event that may occur is that a leaf joins the tree. A general method for constructing labeling schemes for dynamic trees (under the above mentioned dynamic tree models) was previously developed in Korman et al. (Theory Comput Syst 37:49–75, 2004). This method is based on extending an existing static tree labeling scheme to the dynamic setting. This approach fits many natural functions on trees, such as distance, separation level, ancestry relation, routing (in both the adversary and the designer port models), nearest common ancestor etc.. Their resulting dynamic schemes incur overheads (over the static scheme) on the label size and on the communication complexity. In particular, all their schemes yield a multiplicative overhead factor of Ω(log n) on the label sizes of the static schemes. Following (Korman et al., Theory Comput Syst 37:49–75, 2004), we develop a different general method for extending static labeling schemes to the dynamic tree settings. Our method fits the same class of tree functions. In contrast to the above paper, our trade-off is designed to minimize the label size, sometimes at the expense of communication. Informally, for any function k( n) and any static F-labeling scheme on trees, we present an F-labeling scheme on dynamic trees incurring multiplicative overhead factors (over the static scheme) of $$O(\log_{k(n)} n)$$ on the label size and $$O(k(n)\log_{k(n)} n)$$ on the amortized message complexity. In particular, by setting $$k(n) = n^{\epsilon}$$ for any $$0 < \epsilon < 1$$ , we obtain dynamic labeling schemes with asymptotically optimal label sizes and sublinear amortized message complexity for the ancestry relation, the id-based and label-based nearest common ancestor relation and the routing function. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a weak convergence algorithm, called the linesearch algorithm, for solving a split equilibrium problem and nonexpansive mapping (SEPNM) in real Hilbert spaces, in which the first bifunction is pseudomonotone with respect to its solution set, the second bifunction is monotone, and fixed point mappings are nonexpansive. In this algorithm, we combine the extragradient method incorporated with the Armijo linesearch rule for solving equilibrium problems and the Mann method for finding a fixed point of an nonexpansive mapping. We then combine the proposed algorithm with hybrid cutting technique to get a strong convergence algorithm for SEPNM. Special cases of these algorithms are also given. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to study the proximal split feasibility problems. For solving the problems, we present new self-adaptive algorithms with the regularization technique. By using these algorithms, we give some strong convergence theorems for the proximal split feasibility problems. [ABSTRACT FROM AUTHOR]

A discrete element code with impact model has been developed and calibrated to simulate the dynamic behavior of rock materials, with special regard to rock fragmentation upon impact during rock-fall analysis. The paper summarizes the discrete element code, the calibration algorithms developed to identify the model microparameters, and the impact model. Experimental work on drop tests is then used to validate the code on modeling impact fragmentation. It has been found that the developed discrete element code and impact model can reasonably simulate rock fragmentation in drop tests. The use of the discrete element code and impact model can provide good reference results in evaluating impact fragmentation in rock-fall analysis. [ABSTRACT FROM AUTHOR]

Two-way finite automata with quantum and classical states (2QCFA) were introduced by Ambainis and Watrous, and two-way two-tape deterministic finite automata (2TFA) were introduced by Rabin and Scott. In this paper we study 2TFA and propose a new computing model called two-way two-tape finite automata with quantum and classical states (2TQCFA). First, we give efficient 2TFA algorithms for identifying languages which can be recognized by 2QCFA. Second, we give efficient 2TQCFA algorithms to recognize several languages whose status vis-a-vis 2QCFA have been posed as open questions, such as $L_{\mathit{square}}=\{a^{n}b^{n^{2}}\mid n\in \mathbf{N}\}$. Third, we show that $\{a^{n}b^{n^{k}}\mid n\in \mathbf{N}\}$ can be recognized by ( k+1)- tape deterministic finite automata (( k+1)TFA). Finally, we introduce k- tape automata with quantum and classical states ( kTQCFA) and prove that $\{a^{n}b^{n^{k}}\mid n\in \mathbf{N}\}$ can be recognized by kTQCFA. [ABSTRACT FROM AUTHOR]

We consider a class of discrete dynamical models allowing a quantum description. Our approach to quantization consists in the introduction of a gauge connection with values in an n-dimensional unitary representation of some group (of internal symmetries) Γ; elements of the connection are interpreted as amplitudes of quantum transitions. The standard quantization is a special case of this construction: Feynman’s path amplitude e i ∫ Ldt can be interpreted as a parallel transport with values in the (1-dimensional) fundamental representation of the group Γ= U(1). If we take a finite group as the quantizing group Γ, all our manipulations – in contrast to the standard quantization – remain within the framework of constructive discrete mathematics, requiring no more than the ring of algebraic integers. On the other hand, the standard quantization can be approximated by taking 1-dimensional representations of sufficiently large finite groups. The models considered in this paper are defined on regular graphs with transitive groups of automorphisms (space symmetries). The vertices of the graphs take values in finite sets of local states. The evolution of the models proceeds in discrete time steps. We assume that one-time-step quantum transitions are allowed only within neighborhoods of the graph vertices. Simple illustrations are given. An essential part of our study was carried out with the help of a program in C implementing computer algebra and computational group theory algorithms that we develop now. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

The disassembly line is the best choice for automated disassembly of disposal products. Therefore, disassembly line should be designed and balanced so that it can work as efficiently as possible. In this paper, a mathematical model for the multi-objective disassembly line balancing problem is formalized firstly. Then, a novel multi-objective ant colony optimization (MOACO) algorithm is proposed for solving this multi-objective optimization problem. Taking into account the problem constraints, a solution construction mechanism based on the method of tasks assignment is utilized in the algorithm. Additionally, niche technology is used to embed in the updating operation to search the Pareto optimal solutions. Moreover, in order to find the Pareto optimal set, the MOACO algorithm uses the concept of Pareto dominance to dynamically filter the obtained non-dominated solution set. To validate the performance of algorithm, the proposed algorithm is measured over published results obtained from single-objective optimization approaches and compared with multi-objective ACO algorithm based on uniform design. The experimental results show that the proposed MOACO is well suited to multi-objective optimization in disassembly line balancing. [ABSTRACT FROM AUTHOR]

Abstract  The paper presents the novel adaptive splitting and selection algorithm (AdaSS) used for learning compound pattern recognition system. Splitting a feature space into its constituents and selection of the best area classifier from the pool of available recognizers for each region are key processes of the proposed model. Both take place simultaneously as part of a compound optimization process aimed at maximizing system performance. Evolutionary algorithms are used to find out the optimal solution. The results of experiments for algorithm evaluation purposes prove the quality of the proposed approach. [ABSTRACT FROM AUTHOR]

Motivated by an important problem of load balancing in parallel computing, this paper examines a modified algorithm to enhance Q-learning methods, especially in asynchronous recursive procedures for self-adaptive load distribution at runtime. Unlike the existing projection method that utilizes a fixed region, our algorithm employs a sequence of growing truncation bounds to ensure the boundedness of the iterates. Convergence and rates of convergence of the proposed algorithm are established. This class of algorithms has broad applications in signal processing, learning, financial engineering, and other related fields. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold. [ABSTRACT FROM AUTHOR]

Deterministic global optimization algorithms frequently rely on the convex underestimation of nonconvex functions. In this paper we describe the structure of the polyhedral convex envelopes of edge-concave functions over polyhedral domains using geometric arguments. An algorithm for computing the facets of the convex envelope over hyperrectangles in R3 is described. Sufficient conditions are described under which the convex envelope of a sum of edge-concave functions may be shown to be equivalent to the sum of the convex envelopes of these functions. [ABSTRACT FROM AUTHOR]

We consider asynchronous consensus in the shared-memory setting. We present the first efficient low-contention consensus algorithm for the weak-adversary-scheduler model. The algorithm achieves consensus intotal workand(hot-spot) contention, both expected and with high probability. The algorithm assumes thevalue-oblivious scheduler, which is defined in the paper. Previous efficient consensus algorithms for weak adversaries suffer frommemory contention. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to develop a new generalized form of the fractional kinetic equation involving a generalized k-Mittag-Leffler function Ek,ζ,ηγ,ρ(⋅). The solutions of fractional kinetic equations are discussed in terms of the Mittag-Leffler function. Further, numerical values of the results and their graphical interpretation is interpreted to study the behavior of these solutions. The results established here are quite general in nature and capable of yielding both known and new results. [ABSTRACT FROM AUTHOR]