the ubiquitous kronecker product abstract the kronecker product has a rich and very pleasing algebra that supports a wide range of fast elegant and practical algorithms several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role to play in the future first the application areas where kronecker products abound are all thriving these include signal processing image processing semidefinite programming and quantum computing second sparse factorizations and kronecker products are proving to be a very effective way to look at fast linear transforms researchers have taken the kronecker methodology as developed for the fast fourier transform and used it to build exciting alternatives third as computers get more powerful researchers are more willing to entertain problems of high dimension and this leads to kronecker products whenever low dimension techniques are tensored together

nonlinear age dependent diffusive equations a bifurcation approach the main goal of this paper is the study of the existence and uniqueness of positive solutions of some nonlinear age dependent diffusive models arising from dynamic populations we use a bifurcation method for which it has been necessary to study in detail the linear and eigenvalue problems associated to the nonlinear problem in an appropriate space

nilpotency almost nonnegative curvature and the gradient flow on alexandrov spaces we show that almost nonnegatively curved m manifolds are up to finite cover nilpotent spaces in the sense of homotopy theory and have c m nilpotent fundamental groups we also show that up to a finite cover almost nonnegatively curved manifolds are fiber bundles with simply connected fibers over nilmanifolds

global structure of the periodic positive solutions for a general class of periodic parabolic logistic equations with indefinite weights abstract this paper classifies all admissible global bifurcation diagrams of periodic positive solutions for a general class of generalized periodic parabolic problems in the presence of indefinite weights and non classical mixed boundary conditions

the long time behavior of 3 dimensional ricci flow on certain topologies de gruyter 2017 in this paper we analyze the long time behavior of 3 dimensional ricci flow with surgery we prove that under the topological condition that the initial manifold only has non aspherical or hyperbolic components in its geometric decomposition there are only finitely many surgeries and the curvature is bounded by ct 1 for large t this proves a conjecture of perelman for this class of initial topologies the proof of this fact illustrates the fundamental ideas that are used in the subsequent papers of the author

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

geometric structures gromov norm and kodaira dimensions abstract we define the kodaira dimension for 3 dimensional manifolds through thurston s eight geometries along with a classification in terms of this kodaira dimension we show this is compatible with other existing kodaira dimensions and the partial order defined by non zero degree maps for higher dimensions we explore the relations of geometric structures and mapping orders with various kodaira dimensions and other invariants especially we show that a closed geometric 4 manifold has nonvanishing gromov norm if and only if it has geometry h 2 h 2 h 2 c or h 4

hard and soft packing radius theorems singular spaces are playing an increasingly important role in riemannian geometry in particular this is true of the so called alexandrov spaces i e finite hausdorff dimensional complete inner metric spaces with a lower curvature bound in the local triangle comparison sense interest in alexandrov spaces is largely explained by the fact that the natural process of taking gromov hausdorff limits is closed in alexandrov geometry but not in riemannian geometry this simple observation has become a powerful tool in riemannian geometry see for example fy gp2 or gpw and pe in this paper we use a new means to obtain results in riemannian geometry by studying alexandrov spaces the operation of forming spherical suspensions of positively curved spaces an operation which is also closed in alexandrov geometry but not in riemannian geometry will be applied to prove a differentiable sphere theorem which is unlike all previous solutions to the following basic problem

collapsing manifolds obtained by kummer type constructions we construct f structures on a bott manifold and on some other manifolds obtained by kummer type constructions we also prove that if m e x where e is a fiber bundle with structure group g and a fiber admitting a g invariant metric of non negative sectional curvature and x admits an f structure with one trivial covering then one can construct on m a sequence of metrics with sectional curvature uniformly bounded from below and volume tending to zero i e vol k m 0 as a corollary we prove that all the elements in the spin cobordism ring can be represented by manifolds m with vol k m 0

collapsing with a lower bound on the curvature operator cheeger and gromov showed that f structures are related to collapse with a double sided curvature bound we define fibered f structures and extend some of the cheeger gromov results to the setting of collapse with a lower bound on the curvature operator

signed real measure of regular languages for discrete event automata this paper presents the concept and formulation of a signed real measure of regular languages for analysis of discrete event supervisory control systems the measure is constructed based upon the principles of language theory and real analysis for quantitative evaluation and comparison of the controlled behaviour for discrete event automata the marked i e accepted states of finite state automata are classified in different categories such that the event strings terminating at good and bad marked states have positive and negative measures respectively in this setting a controlled language attempts to disable as many bad strings as possible and as few good strings as possible different supervisors may achieve this goal in different ways and generate a partially ordered set of controlled languages the language measure creates a total ordering on the performance of the controlled languages which provides a precise quantitative comparison of the controlled plant behaviour under different supervisors

analytical approach to evaluate language measure parameters for discrete event supervisory control the discrete event dynamic behaviour of physical plants is usually represented by regular languages that can be realized as deterministic finite state automata dfsa the concept and construction of signed real measure of regular languages have been recently developed in literature the language measure is assigned two parameters namely a state transition cost matrix and a state cost vector this article formulates an analytical approach to determine the language measure parameters the proposed approach is based on the theory of markov stochastic processes the dfsa of the discrete event dynamic behaviour is first transformed into a markov chain therefore an event cost is calculated by the occurrence probability of this event in a given state of a discrete time markov chain the determination of the state cost vector is based on the underlying continuous time markov chain to evaluate the steady state state probabilities kronecker algebra is used to facilitate the description of large systems while

maximum and antimaximum principles for some nonlocal diffusion operators abstract in this work we consider the maximum and antimaximum principles for the nonlocal dirichlet problem j u u u h r n j x y u y d y u x u x h x 0 in a bounded domain with u x 0 in r n the kernel j in the convolution is assumed to be a continuous compactly supported nonnegative function with unit integral we prove that for 1 the solution verifies u 0 in if h l 2 h 0 while for 1 and close to 1 the solution verifies u 0 in provided h x x d x 0 h l this last assumption is also shown to be optimal the neumann version of the problem is also analyzed

resident invader dynamics in infinite dimensional systems abstract motivated by evolutionary biology we study general infinite dimensional dynamical systems involving two species the resident and the invader sufficient conditions for competition exclusion phenomena are given when the two species play similar but distinct strategies those conditions are based on invasibility criteria for instance evolutionarily stable strategies in the framework of adaptive dynamics these types of questions were first proposed and studied by s geritz et al 20 and s geritz 19 for a class of ordinary differential equations we extend and generalize previous work in two directions firstly we consider analytic semiflows in infinite dimensional spaces secondly we devise an argument based on hadamard s graph transform method that does not depend on the monotonicity of the two species system our results are applicable to a wide class of reaction diffusion models as well as models with nonlocal diffusion operators

morse novikov cohomology of almost nonnegatively curved manifolds abstract let m n be a closed manifold of almost nonnegative sectional curvature and nonzero first de rham cohomology group using a topological argument we show that the morse novikov cohomology group h p m n vanishes for any p and h d r 1 m n 0 based on a new integral formula we also show that a similar result holds for a closed manifold of almost nonnegative ricci curvature under the additional assumption that its curvature operator is uniformly bounded from below

signed real measure of regular languages for discrete event supervisory control this paper reviews expands and clarifies the underlying concepts of a signed real measure of regular languages which has been used as a novel tool for synthesis of discrete event supervisory control systems the language measure is constructed upon the principles of automata theory and real analysis it allows total ordering of a set of partially ordered sublanguages of a regular language for quantitative evaluation of the supervised behaviour of deterministic finite state automata dfsa under different supervisors in the setting of the language measure a supervisor s performance is superior if the supervised plant is more likely to terminate at a good marked state and or less likely to terminate at a bad marked state the computational complexity of the language measure algorithm is polynomial in the number of dfsa states

volume collapsed three manifolds with a lower curvature bound in this paper we determine the topology of three dimensional complete orientable riemannian manifolds with a uniform lower bound of sectional curvature whose volume is sufficiently small

stability and stabilizability of discrete event dynamic systems a finite state automaton is adopted as a model for discrete event dynamic systems deds stabdity is defined as wslting a given set e mtinitely often stabilizability is defined as choosing state feedback such that the closed loop system is stable these notions are proposed as properties of resiliency or error recovery an important ingredient in stability is shown to be a notion of transition function invariance relations between our notions of stability and invariance and the notions of safety fairness hvelock deadlock etc in computer science literature are pointed out connections are established between our notions of invariance and the classical notions of a invariance and a 11 invariance of linear systems polynomial algorithms for testing stability and stabilizabdity and for constructing a stabilizing control law are also presented

margulis lemma for compact lie groups we improve margulis lemma for a compact connected lie group g there is a neighborhood u of the identity such that for any finite subgroup gamma subset g u cap gamma generates an abelian group we show that for each n there exists an integer w n 0 such that if h is a closed subgroup of a compact connected lie group g of dimension n then the quotient group h h0 has an abelian subgroup of index le w n where h0 is the identity component of h as an application we show that the fundamental group of the homogeneous space g h has an abelian subgroup of index le w n we show this same property for the fundamental groups of almost non negatively curved n manifolds whose universal coverings are not collapsed

correction of a technical point and some remarks about the paper appeared in arch ration mech anal 195 2010 no 3 1025 1058

evaluation of language measure parameters for discrete event manufacturing systems with multiproduct machines the concept of language measure provides a mathematical framework for quantitative analysis and synthesis of discrete event supervisory control systems the language measure is assigned two parameters namely the state transition cost matrix and the state cost vector in a recent paper khatab and nourelfath 2006 an analytical approach has been formulated to evaluate the language measure parameters for discrete event manufacturing systems composed of several monoproduct machines i e each machine is able to perform only one kind of product this paper generalizes these results to the multiproduct case i e to the case where each machine in the manufacturing system is able to perform different kinds of products the proposed approach is based on the theory of markov stochastic processes and kronecker algebra the main advantage of the proposed approach is that the mathematical expressions of the system language measure parameters are derived from data of individual elementary machines without generat

principal eigenvalue and maximum principle for cooperative periodic parabolic systems abstract this paper classifies the set of supersolutions of a general class of periodic parabolic problems in the presence of a positive supersolution from this result we characterize the positivity of the underlying resolvent operator through the positivity of the associated principal eigenvalue and the existence of a positive strict supersolution lastly this scalar characterization is used to characterize the strong maximum principle for a class of periodic parabolic systems of cooperative type under arbitrary boundary conditions of mixed type

metrics of positive ricci curvature on quotient spaces one of the classical problems in differential geometry is the investigation of closed manifolds which admit riemannian metrics with given lower bounds for the sectional or the ricci curvature and the study of relations between the existence of such metrics and the topology and geometry of the underlying manifold despite many efforts during the past decades this problem is still far from being understood for example so far the only obstructions to the existence of a metric with positive ricci curvature come from the obstructions to the existence of metrics with positive scalar curvature li hi ro schy ta and the bonnet myers theorem which implies that the fundamental group of a closed manifold with positive ricci curvature must be finite fruitful constructions of metrics with positive ricci curvature on closed manifolds have so far been established by techniques that include deformation of metrics au eh we kahler geometry yau1 yau2 bundles and warping po na bb gpt special kinds of surgery sy wr metrical glueing gz2 and sasakian geometry bgn particularly large classes of examples of manifolds with positive ricci curvature are given by all compact homogeneous spaces with finite fundamental group na and all closed cohomogeneity one manifolds with finite fundamental group gz2 in this article we present several new classes of manifolds which admit metrics of positive or nonnegative ricci curvature the idea is to consider quotients of manifolds m g of positive or nonnegative ricci curvature by a free isometric action while taking such a quotient non decreases the sectional curvature it may well happen in general that the ricci curvature of the quotient is inferior to the one of m our first results however state that the quotient of m does admit metrics of positive ricci curvature if m belongs to one of the aforementioned classes of homogeneous spaces or spaces with a cohomogeneity one action more precisely we prove

renormalized measure of regular languages this paper modifies the signed real measure of regular languages which has been reported in recent literature for analysis and synthesis of discrete event supervisory control laws a new concept of renormalized measure is introduced to eliminate a user selectable parameter in the present version of the language measure the concept of measure renormalization is illustrated by an example

a singular semilinear problem with dependence on the gradient abstract in the present paper we study the problem of finding classical and weak solutions for a semilinear elliptic equation involving a singular term and a nonlinearity depending on the gradient the approach we follow based on a suitable combination of sub supersolutions techniques and fixed point theory is not quite the same in the two cases and requires different kind of assumptions