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Abstract: In 1.9 of the paper [A. Hahn, A Hermitian Morita theorem for algebras with anti-structure, J. Algebra 93 (1985) 215–235], should be replaced by . This leads to minor changes in the rest of the paper where the ring should be replaced by its opposite and vice versa. [Copyright &y& Elsevier]

Abstract: Quasimodules for vertex algebras are generalizations of modules for vertex algebras. These new objects arise from a generalization of locality for fields. Quasimodules tie together module theory and twisted module theory, and both twisted and untwisted modules feature Poincaré–Birkhoff–Witt-like spanning sets. This paper generalizes these spanning set results to quasimodules for certain Möbius vertex algebras. In particular this paper presents two spanning sets, one featuring a difference-zero ordering restriction on modes and another featuring a difference-one ordering restriction. [Copyright &y& Elsevier]

Abstract: This paper describes an algorithm which produces all ideals compatible with a given surjective Frobenius near-splitting. [Copyright &y& Elsevier]

Abstract: This paper concerns systems with small coherence parameter. Simple greedy-type algorithms perform well on these systems, which are also useful in the construction of compressed sensing matrices. We discuss the following problems for both and . How large can a dictionary be, if we prescribe the coherence parameter? How small could the resulting coherence parameter be, if we impose a size on the dictionary? How could we construct such a system? Several fundamental results from different areas of mathematics shed light on these important problems with far-reaching implications in approximation theory. [Copyright &y& Elsevier]

Abstract: In this paper we present a new primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only full Nesterov–Todd step. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, , which is as good as the linear analogue. [Copyright &y& Elsevier]

Abstract: In this paper, we show that minimization problems involving sublinear regularizing terms are ill-posed, in general, although numerical experiments in image processing give very good results. The energies studied here are inspired by image restoration and image decomposition. Rewriting the nonconvex sublinear regularizing terms as weighted total variations, we give a new approach to perform minimization via the well-known Chambolle''s algorithm. The approach developed here provides an alternative to the well-known half-quadratic minimization one. [Copyright &y& Elsevier]

Abstract: In this paper we consider partial actions of groups on algebras and partial skew group rings. After some general results we prove two versions of Maschke''s theorem and then we study von Neumann regularity, the prime radical and the Jacobson radical of partial skew group rings. In this way we extend many results which are known for skew group rings. [Copyright &y& Elsevier]

Abstract: In a variety of dynamical systems, formations of motion patterns occur. Observing colonies of animals, for instance, for the scientist it is not only of interest which kinds of formations these animals show, but also how they altogether move around. In order to analyse motion patterns for the purpose of making predictions, to describe the behaviour of systems, or to index databases of moving objects, methods are required for dealing with them. This becomes increasingly important since a number of technologies have been devised which allow objects precisely to get traced. However, the indeterminacy of spatial information in real world environments also requires techniques to approximate reasoning, for example, in order to compensate for small and unimportant distinctions which are due to noisy measurements. As a consequence, precise as well as coarse motion patterns have to be dealt with. A set of 16 atomic motion patterns is proposed. On the one hand, a relation algebra is defined on them. On the other hand, these 16 relations form the basis of a visual language using which motion patterns can easily be dealt with in a diagrammatic way. The relations are coarse but crisp and they allow imprecise knowledge about motion patterns to be dealt with, while their diagrammatic realisation also allow precise patterns to get handled. While almost all approaches consider motion patterns along arbitrary time intervals, this paper in particular focuses on short-term motion patterns as we permanently observe them in our everyday life. The bottom line of the current work, however, is yet more general. While it has been widely argued that it makes sense to use both sentential and diagrammatic representations in order to represent different things in the same system adequately (and hence differently), we argue that it makes even sense to represent the same things differently in order to grasp different aspects of one and the same object of interest from different viewpoints. We demonstrate this by providing both a sentential and a diagrammatic representation for the purpose of grasping different aspects of motion patterns. It shows that both representations complement each other. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a generalization for the class of laura algebras, called almost laura. We show that this new class of algebras retains most of the essential features of laura algebras, especially concerning the important role played by the non-semiregular components in their Auslander–Reiten quivers. Also, we study more intensively the left supported almost laura algebras, showing that these are characterized by the presence of a generalized standard, convex and faithful component. Finally, we prove that almost laura algebras behave well with respect to full subcategories, split-by-nilpotent extensions and skew group algebras. [Copyright &y& Elsevier]

Abstract: The gap function of an infinite word over the binary alphabet gives the distances between consecutive 1''s in this word. In this paper we study infinite binary words whose gap function is injective or “almost injective.” A method for computing the subword complexity of such words is given. A necessary and sufficient condition for a function to be the subword complexity function of a binary word whose gap function is increasing is obtained. [Copyright &y& Elsevier]

Abstract: In [B. De Bruyn, P. Vandecasteele, Valuations and hyperplanes of dual polar spaces, J. Combin. Theory Ser. A 112 (2005) 194–211], we introduced the class of the SDPS-valuations of dual polar spaces. We showed that these valuations and all their extensions give rise to hyperplanes of dual polar spaces. We call these hyperplanes SDPS-hyperplanes. In the present paper, we show that a hyperplane of a thick dual polar space is an SDPS-hyperplane if and only if every hex not contained in intersects in either a singular hyperplane or the extension of an ovoid. [Copyright &y& Elsevier]

Abstract: Consider the class of exp–log constants, which is constructed from the integers using the field operations, exponentiation and logarithm. Let be such an exp–log constant and let be its size as an expression. Witness conjectures attempt to give bounds for the number of decimal digits which need to be evaluated in order to test whether equals zero. For this purpose, it is convenient to assume that exponentials are only applied to arguments with absolute values bounded by 1. In that context, several witness conjectures have appeared in the literature and the strongest one states that it is possible to choose . In this paper we give a counterexample to this conjecture. We also extend it so as to cover similar, polynomial witness conjectures. [Copyright &y& Elsevier]

Abstract: In this article, we generalize a localization theorem of Lovász and Simonovits [Random walks in a convex body and an improved volume algorithm, Random Struct. Algorithms 4–4 (1993) 359–412] which is an important tool to prove dimension-free functional inequalities for log-concave measures. In a previous paper [Fradelizi and Guédon, The extreme points of subsets of -concave probabilities and a geometric localization theorem, Discrete Comput. Geom. 31 (2004) 327–335], we proved that the localization may be deduced from a suitable application of Krein–Milman''s theorem to a subset of log-concave probabilities satisfying one linear constraint and from the determination of the extreme points of its convex hull. Here, we generalize this result to more constraints, give some necessary conditions satisfied by such extreme points and explain how it may be understood as a generalized localization theorem. Finally, using this new localization theorem, we solve an open question on the comparison of the volume of sections of non-symmetric convex bodies in by hyperplanes. A surprising feature of the result is that the extremal case in this geometric inequality is reached by an unusual convex set that we manage to identify. [Copyright &y& Elsevier]

Abstract: Algebraic function fields of positive characteristic are non-perfect fields, and many standard algorithms for solving some fundamental problems in commutative algebra simply do not work over these fields. This paper presents practical algorithms for the first time for (1) computing the primary decomposition of ideals of polynomial rings defined over such fields and (2) factoring arbitrary multivariate polynomials over such fields. Difficulties involving inseparability and the situation where the transcendence degree is greater than one are completely overcome, while the algorithms avoid explicit construction of any extension of the input base field. As a corollary, the problem of computing the primary decomposition of a positive-dimensional ideal over a finite field is also solved. The algorithms perform very effectively in an implementation within the Magma Computer Algebra System, and an analysis of their practical performance is given. [Copyright &y& Elsevier]

Abstract: In this paper, we present different results related to bezoutian and residue theory. We consider, in particular, the problem of computing the structure of the quotient ring by an affine complete intersection, and an algorithm to obtain it, as conjectured in [Cardinal, J.-P., 1993. Dualité et algorithmes itératifs pour la résolution de systèmes polynomiaux. Ph.D. Thesis, Univ. de Rennes]. We analyze it in detail and prove the validity of the conjecture, for a modification of the initial method. Direct applications of the results in effective algebraic geometry are given. [Copyright &y& Elsevier]