Probability of Color Singlet String States in e + e- → qq + ng at Large Nc Limit

We use the method of color effective Hamiltonian to calculate the probability of color singlet string states at the large N_c limit. We show that a qq + ng system produced from e + e^- annihilation is definitely in color singlet string states when N_c → ∞, i.e., color,singlet string states account for 100% of all possible color singlet states. This justifies the approximation that the hadronization mechanism of each color-neutral flow piece connecting two color-adjacent partons is assumed to be the same as an independent qq singlet system.     

Complexity properties of recursively enumerable sets andbsQ-completeness

The notions of boundedly strongly effectively speedable set and boundedly effectively speedable set are introduced. It is proved that the notions of boundedly strongly effectively speedable set, boundedly effectively speedable set, creative set, andbsQ-complete recursively enumerable set are equivalent. Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 554–559, October, 2000.     

MEASURES AND THEIR DIMENSION SPECTRUMS FOR COOKIE-CUTTER SETS IN R~d

0. IntroductionMany theoretical physicists and mathematicians have studied the Hausdorff dimensions,measures and multifractal decompositions of fractals and obtained a lot of satisfactory results. Particularlyl there hajs given thorough and detailed study for self-similar fractals(of. e.g. [1--7]). mom the dynamical system point of view self-similar sets are regarded asthe attractors of iterated function systems consisting of self-similar cofltraction mappings.However, the researches for measu…     

Contraction behaviour of iteration–discretization based on gradient type projections

There is a wide range of iterative methods in infinite dimensional spaces to treat variational equations or variational inequalities. As a rule, computational handling of problems in infinite dimensional spaces requires some discretization. Any useful discretization of the original problem leads to families of problems over finite dimensional spaces. Thus, two infinite techniques, namely discretization and iteration are embedded into each other. In the present paper, the behaviour of truncated iterative methods is studied, where at each discretization level only a finite number of steps is performed. In our study no accuracy dependent a posteriori stopping criterion is used. From an algorithmic point of view, the considered methods are of iteration–discretization type. The major aim here is to provide the convergence analysis for the introduced abstract iteration–discretization methods. A special emphasis is given on algorithms for the treatment of variational inequalities with strongly monotone operators over fixed point sets of quasi-nonexpansive mappings.     

Solving Matrix Games with I-fuzzy Payoffs: Pareto-optimal Security Strategies Approach

A recent research work of Clemente et al. [12] on Pareto-optimal security strategies (POSS) in matrix games with fuzzy payoffs is extended to I-fuzzy scenario. Besides, the membership and the non-membership functions of the I-fuzzy values for both players are obtained by employing the technique of multiobjective optimization. The presented approach provides an efficient solution to a class of I-fuzzy matrix games with piecewise linear membership and non-membership functions. This class also includes I-fuzzy matrix games with triangular and trapezoidal I-fuzzy numbers as special cases. Further, POSS approach also provides an approximate solution to I-fuzzy matrix games with payoffs as general I-fuzzy numbers.     

Online streaming feature selection using rough sets

Feature Selection (FS) is an important pre-processing step in data mining and classification tasks. The aim of FS is to select a small subset of most important and discriminative features. All the traditional feature selection methods assume that the entire input feature set is available from the beginning. However, online streaming features (OSF) are an integral part of many real-world applications. In OSF, the number of training examples is fixed while the number of features grows with time as new features stream in. A critical challenge for online streaming feature selection (OSFS) is the unavailability of the entire feature set before learning starts. Several efforts have been made to address the OSFS problem, however they all need some prior knowledge about the entire feature space to select informative features. In this paper, the OSFS problem is considered from the rough sets (RS) perspective and a new OSFS algorithm, called OS-NRRSAR-SA, is proposed. The main motivation for this consideration is that RS-based data mining does not require any domain knowledge other than the given dataset. The proposed algorithm uses the classical significance analysis concepts in RS theory to control the unknown feature space in OSFS problems. This algorithm is evaluated extensively on several high-dimensional datasets in terms of compactness, classification accuracy, run-time, and robustness against noises. Experimental results demonstrate that the algorithm achieves better results than existing OSFS algorithms, in every way.     

Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices,II

Recent results of several authors have led to constructions of parallelotopes which are bounded remainder sets for totally irrational toral rotations. In this brief note we explain, in retrospect, how some of these results can easily be obtained from a geometric argument which was previously employed by Duneau and Oguey in the study of deformation properties of mathematical models for quasicrystals.