A quasi-linear fuzzy measure of multi-attributes

Evaluations of multi-attributes using fuzzy measures and fuzzy integrals have been recently found to be useful in the classification processes of complex systems. However, one of the existing problems in using the aggregation operation of fuzzy integral is the identification of fuzzy measures or the “fuzzy densities” in terms of the g_λ-measure. This paper presents a new methodology to assess the weights of each individual attribute and the combinatorial subsets of these attributes. The measures of multi-attributes are considered herein as the regionalized variables in space Rⁿ, whose spatial values are characterized by the membership function of a fuzzy set. The present algorithm is based on the concept of the theory of regionalized variables which provides a mathematical framework for estimating the unknown values of the variables whose magnitudes are dependent on the spatial continuity expressed by a semi-variogram, and the optimal estimation of kriging method. This is a quasi-linear approach as the estimation is based on a linear-unbiased estimator, but the combined evidences do not hold additivity due to the basic assumption and formulation.     

Reflected BSDEs with nonpositive jumps,and controller-and-stopper games

We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution are proved by a double penalization approach under regularity assumptions on the obstacle. In a suitable regime switching diffusion framework, we show the connection between our class of BSDEs and fully nonlinear variational inequalities. Our BSDE representation provides in particular a Feynman–Kac type formula for PDEs associated to general zero-sum stochastic differential controller-and-stopper games, where control affects both drift and diffusion term, and the diffusion coefficient can be degenerate. Moreover, we state a dual game formula of this BSDE minimal solution involving equivalent change of probability measures, and discount processes. This gives in particular a new representation for zero-sum stochastic differential controller-and-stopper games.     

Preduals of semigroup algebras

For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C ₀(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak^*-continuous. Given a discrete semigroup S, the convolution algebra ℓ ¹(S) also carries a coproduct. In this paper we examine preduals for ℓ ¹(S) making both the product and the coproduct weak^*-continuous. Under certain conditions on S, we show that ℓ ¹(S) has a unique such predual. Such S include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on ℓ ¹(S) when S is either ℤ₊×ℤ or (ℕ,⋅).     

Products of conjugacy classes in finite and algebraic simple groups

We prove the Arad–Herzog conjecture for various families of finite simple groups — if A$A$ and B$B$ are nontrivial conjugacy classes, then AB$AB$ is not a conjugacy class. We also prove that if G$G$ is a finite simple group of Lie type and A$A$ and B$B$ are nontrivial conjugacy classes, either both semisimple or both unipotent, then AB$AB$ is not a conjugacy class. We also prove a strong version of the Arad–Herzog conjecture for simple algebraic groups and in particular show that almost always the product of two conjugacy classes in a simple algebraic group consists of infinitely many conjugacy classes. As a consequence we obtain a complete classification of pairs of centralizers in a simple algebraic group which have dense product. A special case of this has been used by Prasad to prove a uniqueness result for Tits systems in quasi-reductive groups. Our final result is a generalization of the Baer–Suzuki theorem for p$p$-elements with p≥5$p\ge 5$.     

Torsion Abelian afi-Groups

This paper is devoted to the study of Abelian afi-groups. A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. We will call an Abelian group an afi-group if all of its absolute ideals are fully invariant subgroups. In this paper, we will describe afi-groups in the class of fully transitive torsion groups (in particular, separable torsion groups) and divisible torsion groups.     

Existence,blow‐up,and exponential decay estimates for a system of semilinear wave equations associated with the helicalflows of Maxwell fluid

The paper is devoted to the study of a system of semilinear wave equations associated with the helical flows of Maxwell fluid. First, based on Faedo–Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we establish two local existence theorems of weak solutions. Next, we prove that any weak solutions with negative initial energy will blow up in finite time. Finally, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions via the construction of a suitable Lyapunov functional. Copyright © 2015 John Wiley & Sons, Ltd.     

A hybrid stochastic optimization framework for composite nonconvex optimization

Mathematical Programming - We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea...     

Development of new ethanologenic Escherichia coli strains for fermentation of lignocellulosic biomass

Two new ethanologenic strains (FBR4 and FBR5) of Escherichia coli were constructed and used to ferment corn fiber hydrolysate. The strains carry the plasmid pLO1297, which contains the genes from Zymomonas mobilis necessary for efficiently converting pyruvate into ethanol. Both strains selectively maintained the plasmid when grown anaerobically. Each culture was serially transferred 10 times in anaerobic culture with sugar-limited medium containing xylose, but noselective antibiotic. An average of 93 and 95% of the FBR4 and FBR5 cells, respectively, maintained pLO1297 in anaerobic culture. The fermentation performances of the repeatedly transferred cultures were compared with those of cultures freshly revived from stock in pH-controlled batch fermentations with 10% (w/v) xylose. Fermentation results were similar for all the cultures. Fermentations were completed within 60 h and ethanol yields were 86–92% of theoretical. Maximal ethanol concentrations were 3.9–4.2% (w/v). The strains were also tested for their ability to ferment corn fiber hydrolysate, which contained 8.5% (w/v) total sugars (2.0% arabinose, 2.8% glucose, and 3.7% xylose). E. coli FBR5 produced more ethanol than FBR4 from the corn fiber hydrolysate. E. coli FBR5 fermented all but 0.4% (w/v) of the available sugar, whereas strain FBR4 left 1.6% unconsumed. The fermentation with FBR5 was completed within 55 h and yielded 0.46 g of ethanol/g of available sugar, 90% of the maximum obtainable. Author to whom all correspondence and reprint requests should be addressed. Names are necessary to report factually on available data. However, the USDA neither guarantees nor warrants the standard of the product, and the use of the name by USDA im plies no approval of the product to the exclusion of others that may also be suitable.     

A new efficient algorithm based on DC programming and DCA for clustering

In this paper, a version of K-median problem, one of the most popular and best studied clustering measures, is discussed. The model using squared Euclidean distances terms to which the K-means algorithm has been successfully applied is considered. A fast and robust algorithm based on DC (Difference of Convex functions) programming and DC Algorithms (DCA) is investigated. Preliminary numerical solutions on real-world databases show the efficiency and the superiority of the appropriate DCA with respect to the standard K-means algorithm.