Combined m-consecutive and k-out-of-n sliding window systems

This paper proposes a new model that generalizes the linear multi-state sliding window system. In this model the system consists of n linearly ordered multi-state elements. Each element can have different states: from complete failure up to perfect functioning. A performance rate is associated with each state. The system fails if at least one of the following two conditions is met: (1) there exist at least m consecutive overlapping groups of r adjacent elements having the cumulative performance lower than V; (2) there exist at least k arbitrarily located groups of r adjacent elements having the cumulative performance lower than W. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of evaluating system reliability and elements’ reliability importance indices are presented. Optimal sequencing of system elements is demonstrated.     

Additivity for derivator K-theory

We prove the additivity theorem for the K-theory of triangulated derivators. This solves one of the conjectures made by Maltsiniotis in [G. Maltsiniotis, La K-théorie d'un dérivateur triangulé, in: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman (Eds.), Categories in Algebra, Geometry and Physics, Conference and Workshop in honor of Ross Street's 60th Birthday, in: Contemp. Math., vol. 431, Amer. Math. Soc., 2007, pp. 341-368]. We also review some basic definitions and results in the theory of derivators in the sense of Grothendieck.     

K-theory of equivariant quantization

Using an equivariant version of Connes? Thom isomorphism, we prove that equivariant K-theory is invariant under strict deformation quantization for a compact Lie group action.     

K-Harmonic means data clustering with tabu-search method

Clustering is a popular data analysis and data mining technique. Since clustering problem have NP-complete nature, the larger the size of the problem, the harder to find the optimal solution and furthermore, the longer to reach a reasonable results. A popular technique for clustering is based on K-means such that the data is partitioned into K clusters. In this method, the number of clusters is predefined and the technique is highly dependent on the initial identification of elements that represent the clusters well. A large area of research in clustering has focused on improving the clustering process such that the clusters are not dependent on the initial identification of cluster representation. Another problem about clustering is local minimum problem. Although studies like K-Harmonic means clustering solves the initialization problem trapping to the local minima is still a problem of clustering. In this paper we develop a new algorithm for solving this problem based on a tabu search technique—Tabu K-Harmonic means (TabuKHM). The experiment results on the Iris and the other well known data, illustrate the robustness of the TabuKHM clustering algorithm.     

Tight sets and m-ovoids of finite polar spaces

An intriguing set of points of a generalised quadrangle was introduced in [J. Bamberg, M. Law, T. Penttila, Tight sets and m-ovoids of generalised quadrangles, Combinatorica, in press] as a unification of the pre-existing notions of tight set and m-ovoid. It was shown in [J. Bamberg, M. Law, T. Penttila, Tight sets and m-ovoids of generalised quadrangles, Combinatorica, in press] that every intriguing set of points in a finite generalised quadrangle is a tight set or an m-ovoid (for some m). Moreover, it was shown that an m-ovoid and an i-tight set of a common generalised quadrangle intersect in mi points. These results yielded new proofs of old results, and in this paper, we study the natural analogue of intriguing sets in finite polar spaces of higher rank. In particular, we use the techniques developed in this paper to give an alternative proof of a result of Thas [J.A. Thas, Ovoids and spreads of finite classical polar spaces, Geom. Dedicata 10 (1-4) (1981) 135-143] that there are no ovoids of H(2r,q²), Q⁻(2r+1,q), and W(2r−1,q) for r>2. We also strengthen a result of Drudge on the non-existence of tight sets in W(2r−1,q), H(2r+1,q²), and Q⁺(2r+1,q), and we give a new proof of a result of De Winter, Luyckx, and Thas [S. De Winter, J.A. Thas, SPG-reguli satisfying the polar property and a new semipartial geometry, Des. Codes Cryptogr. 32 (1-3) (2004) 153-166; D. Luyckx, m-Systems of finite classical polar spaces, PhD thesis, The University of Ghent, 2002] that an m-system of W(4m+3,q) or Q⁻(4m+3,q) is a pseudo-ovoid of the ambient projective space.     

Comparison between algebraic and topological K-theory of locally convex algebras

This paper is concerned with the algebraic K-theory of locally convex C-algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological K-theory agree on the completed projective tensor product , and that the obstruction for the comparison map to be an isomorphism is (absolute) algebraic cyclic homology. We prove the existence of an exact sequence (Theorem 6.2.1)We show that cyclic homology vanishes in the case when J is the ideal of compact operators and L is a Fréchet algebra whose topology is generated by a countable family of sub-multiplicative seminorms and admits an approximate right or left unit which is totally bounded with respect to that family (Theorem 8.3.3). This proves the generalized version of Karoubi's conjecture due to Mariusz Wodzicki and announced in his paper [M. Wodzicki, Algebraic K-theory and functional analysis, in: First European Congress of Mathematics, Vol. II, Paris, 1992, in: Progr. Math., vol. 120, Birkhäuser, Basel, 1994, pp. 485-496].We also consider stabilization with respect to a wider class of operator ideals, called sub-harmonic. Every Fréchet ideal is sub-harmonic, but not conversely; for example the Schatten ideal Lp is sub-harmonic for all p>0 but is Fréchet only if p?1. We prove a variant of the exact sequence above which essentially says that if A is a C-algebra and J is sub-harmonic, then the obstruction for the periodicity of K_∗(AC_⊗J) is again cyclic homology (Theorem 7.1.1). This generalizes to all algebras a result of Wodzicki for H-unital algebras announced in [M. Wodzicki, Algebraic K-theory and functional analysis, in: First European Congress of Mathematics, Vol. II, Paris, 1992, in: Progr. Math., vol. 120, Birkhäuser, Basel, 1994, pp. 485-496].The main technical tools we use are the diffeotopy invariance theorem of Cuntz and the second author (which we generalize in Theorem 6.1.6), and the excision theorem for infinitesimal K-theory, due to the first author.     

A Note on Varieties of Groupoids Arising from m-Cycle Systems

Decompositions of the complete graph with n vertices K _n into edge disjoint cycles of length m whose union is K _n are commonly called m-cycle systems. Any m-cycle system gives rise to a groupoid defined on the vertex set of K _n via a well known construction. Here, it is shown that the groupoids arising from all m-cycle systems are precisely the finite members of a variety (of groupoids) for m = 3 and 5 only.     

On distorted probabilities and m-separable fuzzy measures

Fuzzy measures are used in conjunction with fuzzy integrals for aggregation. Their role in the aggregation is to permit the user to express the importance of the information sources (either criteria or experts). Due to the fact that fuzzy measures are set functions, the definition of such measures requires the definition of 2ⁿ parameters, where n is the number of information sources. To make the definition easier, several families of fuzzy measures have been defined in the literature.In this paper m-separable fuzzy measures are introduced. We present some results on this type of measures and we relate them to some of the previous existing ones. We study generating functions for m-separable fuzzy measures and some properties related to these generating functions.     

Soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m, n) equations

We consider the nonlinear dispersive K(m,n) equation with the generalized evolution term and derive analytical expressions for some conserved quantities. By using a solitary wave ansatz in the form of sech^p function, we obtain exact bright soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m,n) equations with the generalized evolution terms. The results are then generalized to multi-dimensional K(m,n) equations in the presence of the generalized evolution term. An extended form of the K(m,n) equation with perturbation term is investigated. Exact bright soliton solution for the proposed K(m,n) equation having higher-order nonlinear term is determined. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients.     

Uniqueness properties of m-subharmonic functions in Cegrell classes

Let u,v$u,v$ be m-subharmonic functions defined on a domain Ω   in Cⁿ${\mathbb{C}}^n$. We are interested in giving sufficient conditions on u,v$u,v$ such that u=v$u=v$ on the whole domain Ω. Some applications to weak convergence of sequence of m-subharmonic functions are also discussed.     

Noncommutative localisation in algebraic K-theory II

In [Amnon Neeman, Andrew Ranicki, Noncommutative localisation in algebraic K-theory I, Geom. Topol. 8 (2004) 1385-1425] we proved a localisation theorem in the algebraic K-theory of noncommutative rings. The main purpose of the current article is to express the general theorem of the previous paper in a more user-friendly fashion, in a way more suitable for applications. In the process we compare our result to the existing theorems in the literature, showing how the previous paper improves all the existing results.It should be pointed out that there have been two very interesting recent preprints on related topics. The reader is referred to the beautiful papers of Krause [Henning Krause, Cohomological quotients and smashing localizations, http://wwwmath.upb.de/~hkrause/publications.html. [8]] and Dwyer [William G. Dwyer, Noncommutative localization in homotopy theory, preprint, http://www.nd.edu/~wgd/. [4]]. Krause studies the lifting of chain complexes and the relation with the telescope conjecture, and Dwyer generalises to the homotopy theoretic framework.     

On the Isomorphism Conjecture in algebraic K-theory

The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RΓ, where Γ is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed Riemannian manifolds with strictly negative sectional curvature and arbitrary coefficient rings R. If R is regular this leads to a concrete calculation of low dimensional K-theory groups of RΓ in terms of the K-theory of R and the homology of the group.     

Existence theorems for m-accretive operators in Banach spaces

In 1985, the second author proved a surjective result for m-accretive and ?-expansive mappings for uniformly smooth Banach spaces. However, in this case, we have been able to remove the uniform smoothness of the Banach space, without any additional assumption.     

Polynomial sequential continuity on C(K,E) spaces

We show that, for bounded sequences in C(K,E), the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence. We introduce several conditions on E under which different versions of the result are true when K is a scattered compact space. These conditions are related with some others appeared in the literature and they seem to be of independent interest.     

Note on K-analyticity and normality in function spaces

We prove that whenever X is zero-dimensional metrizable with σ-compact set of accumulation points and K   is compact metrizable, the function space K^X$K^X$ endowed with the compact-open topology is a compact-covering image of the product of the irrationals and the Cantor cube. In particular, for any metrizable E  , the iterated function space E^(KX)$E^{(K^X)}$ is perfectly normal and paracompact. However, there is a closed subgroup G   of {0,1}^X${\{0,1\}}^X$ with X   as above whose space of characters G^∧$G^{\wedge }$ is not normal.     

On global attractor for nonlinear parabolic equations of m-Laplacian type

Existence and some regularity results of global attractor in Lq, q?1, for m-Laplacian type quasilinear parabolic equation with a perturbation like a(x)(α|u|u−β|u|u)+f(x) with α>β?0, a(x)?0 are proved. For the proofs Moser's technique is used extensively.     

Finding the K shortest hyperpaths using reoptimization

We present some reoptimization techniques for computing (shortest) hyperpath weights in a directed hypergraph. These techniques are exploited to improve the worst-case computational complexity (as well as the practical performance) of an algorithm finding the K shortest hyperpaths in acyclic hypergraphs.     

Positive solution for m-point boundary value problems

In this paper, we investigate an m-point boundary value problem with sign changing nonlinearity. The existence of an interval of parameters which ensures the problem has at least one positive solution is determined by constructing available operator and combining the method of lower solution with the method of topology degree. Moreover, the associated Green's function for the above problem is also given.     

Enumerating K best paths in length order in DAGs

We address the problem of finding the K best paths connecting a given pair of nodes in a directed acyclic graph (DAG) with arbitrary lengths. One of the main results in this paper is the proof that a tree representing the kth shortest path is obtained by an arc exchange in one of the previous (k − 1) trees (each of which contains a previous best path). An O(m + K(n + log K)) time and O(K + m) space algorithm is designed to explicitly determine the K shortest paths in a DAG with n nodes and m arcs. The algorithm runs in O(m + Kn) time using O(K + m) space in DAGs with integer length arcs. Empirical results confirming the superior performance of the algorithm to others found in the literature for randomly generated graphs are reported.     

Chern character for twisted K-theory of orbifolds

For an orbifold X and α∈H³(X,Z), we introduce the twisted cohomology and prove that the non-commutative Chern character of Connes-Karoubi establishes an isomorphism between the twisted K-groups and the twisted cohomology . This theorem, on the one hand, generalizes a classical result of Baum-Connes, Brylinski-Nistor, and others, that if X is an orbifold then the Chern character establishes an isomorphism between the K-groups of X tensored with C, and the compactly-supported cohomology of the inertia orbifold. On the other hand, it also generalizes a recent result of Adem-Ruan regarding the Chern character isomorphism of twisted orbifold K-theory when the orbifold is a global quotient by a finite group and the twist is a special torsion class, as well as Mathai-Stevenson's theorem regarding the Chern character isomorphism of twisted K-theory of a compact manifold.