local well posedness for a lotka volterra system in besov spaces this paper is devoted to study local existence uniqueness and continuous dependence upon the initial data of mild solutions for a diffusive non autonomous lotka volterra system initial data are taken in the besov space b p q n

complexity and multiple complexes in this chapter we introduce the notion of the complexity of a module and explore some related ideas complexity was first defined by jon alperin in the late 1970 s and it helped to motivate much of the development of the homological properties of modules in fact the complexity of a finitely generated kg module m is a rather crude invariant in that it only measures the polynomial rate of growth of a minimal projective resolution of the module the original theorem of alperin and evens which extended quillen s dimension theorem to modules was proved only in terms of complexity later it was extended to support varieties as well the theorem computes the complexity of a kg module m as the maximum of the complexities of the restrictions of m to the elementary abelian subgroups of the group g

one fixed point actions on spheres ii the object of this paper is to treat the following old question of montgomery and samelson m s and some of its consequences which groups act smoothly on a closed homotopy sphere with exactly one fixed point and what are the isotropy representations of g which occur on the tangent space at the fixed point the first and only previously existing example of such an action was given by e stein for the group sl 2 z st a related question was solved by oliver o which groups act smoothly on a disk without fixed points a group which acts on a sphere with one fixed point acts on a disk without fixed points in p the author announced

fixed set systems of equivariant infinite loop spaces we develop machinery enabling us to show that suitable g spaces including the equivariant version of bf are equivariant infinite loop spaces this involves a recognition principle for systems of spaces which behave for mally like the system of fixed sets of a g space that is we give a necessary and sufficient condition for such a system to be equivalent to the fixed set system of an equivariant infinite loop space the advantage of using the language of fixed set systems is that one can frequently replace the system of fixed sets of an ac tual g space by an equivalent formal system which is considerably simpler and which admits the requisite geometry necessary for delooping we also apply this machinery to construct equivariant eilenberg mac lane spaces corresponding to mackey functors

the structure of some equivariant thom spectra we show that the equivariant thom spectra moz2 and moz2 do not split as wedges of equivariant eilenberg mac lane spectra as they do nonequivariantly this is done by finding two stage postnikov towers giving these spectra and determining the nontrivial k invariants we also consider the question in what sense is the spectrum moz2 representing unoriented bordism unique

integral deligne cohomology for real varieties we develop an integral version of deligne cohomology for smooth proper real varieties for this purpose the role played by singular cohomology in the complex case has to be replaced by the ordinary bigraded gal mathbb c mathbb r equivariant cohomology of lewis et al bull am math soc n s 4 2 208 212 1981 the equivariant counterpart of singular cohomology the theory is aimed at giving more precise information about the 2 primary components of regulators we establish basic properties and give a geometric interpretation for the groups in dimension 2 in weights 1 and 2

lie algebras and higher torsion in p groups abstract the primary aim of this paper is to study exceptional torsion in the integral cohomology of a family of p groups associated to p adic lie algebras a spectral sequence e r g is defined for any lie algebra g which models the bockstein spectral sequence of the corresponding group in characteristic p this spectral sequence is then studied for complex semisimple lie algebras like sl n c and the results there are transferred to the corresponding p group via the intermediary arithmetic lie algebra defined over z the results obtained this way for a fixed lie algebra scheme like sl n hold in a range in the corresponding bockstein spectral sequence for all but finitely many primes depending on the chosen range over c it is shown that e 1 g h g u g h bg where u g is the filtered dual of the universal enveloping algebra of g equipped with the dual adjoint action and bg is the free loop space of the classifying space of an associated compact connected real form lie group g to g when passing to characteristic p in the corresponding bockstein spectral sequence a char 0 to char p phase transition is observed for example it is shown that the algebra e 1 sl 2 f p requires at least 17 generators unlike its characteristic zero counterpart which only requires two

symplectic diffeomorphisms and the flux homomorphism let x be a connected smooth manifold without boundary we will write difff ox for the group of all compactly supported diffeomorphisms of x which preserve the symplectic form o2 topologized as usual as the direct limit of the subgroups diff x of all diffeomorphisms with support in the fixed compact set k let diff oox be its identity component the flux is locally a homomorphism from a neighbourhood of the identity in diffo ox to h x r see calabi 6 it gives rise to a global homomorphism s o from the universal cover of difffo0x to hi x f and hence to a homomorphism

group actions and group extensions in this paper we study finite group extensions represented by special cohomology classes as an application we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces in particular we prove that if z p acts freely on s then r k

pin 2 equivariant seiberg witten floer homology and the triangulation conjecture we define pin 2 equivariant seiberg witten floer homology for rational homology 3 spheres equipped with a spin structure the analogue of froyshov s correction term in this setting is an integer valued invariant of homology cobordism whose mod 2 reduction is the rokhlin invariant as an application we show that there are no homology 3 spheres y of rokhlin invariant one such that y y bounds an acyclic smooth 4 manifold by previous work of galewski stern and matumoto this implies the existence of non triangulable high dimensional manifolds

free actions on products of spheres the rational case let x s x x s be a product of spheres of total dimension n nl n2 nk a fundamental unanswered question is the determination of which finite groups can act freely on x and what actions on the cohomology so arise in particular it is conjectured that if an elementary abelian group acts freely then its rank is less than or equal to k great progress has been made recently on this question by carlsson ec adem browder a b and hoffman hi in the case where all the spheres have the same dimension in this paper we completely solve the rational analogue of the above question given an action of a finite group g on the rational cohomology ring h x we give necessary and sufficient conditions for g to act freely on a closed manifold y having the rational homotopy type of x so that the g action induces the specified action on h y q h x q in particular the necessary conditions give new obstructions for g to act freely on x with a specified representation in h x q our method includes a general discussion as to when a space with finite fundamental group has the rational homotopy type of a closed manifold we now give our necessary and sufficient conditions a for all geg for all ni even g esn s nj for some nonzero rational number b for all g g e 1 i t r g h x q hi x q 0 c i for n even some n i odd the equivariant intersection form on h 2 x q is hyperbolic ii for all ni even no further condition iii for n odd z 89 q ea o g w cl g w

topological rigidity of hamiltonian loops and quantum homology this paper studies the question of when a loop t 0 t 1 in the group symp m of symplectomorphisms of a symplectic manifold m is isotopic to a loop that is generated by a time dependent hamiltonian function loops with this property are said to be hamiltonian our main result is that hamiltonian loops are rigid in the following sense if is hamiltonian with respect to and if is a small perturbation of that preserves another symplectic form then is hamiltonian with respect to this allows us to get some new information on the structure of the flux group i e the image of 1 symp m under the flux homomorphism we give a complete proof of our result for some manifolds and sketch the proof in general the argument uses methods developed by seidel for studying properties of hamiltonian loops via the quantum homology of m

global existence versus blow up in a high dimensional keller segel equation with degenerate diffusion and nonlocal aggregation abstract in this paper we study the degenerate keller segel equation with nonlocal aggregation u t u m u b u in r d r where m 1 d 3 and b u 2 u with 2 d by analyzing the interaction between the degenerate diffusion and the nonlocal aggregation we determine the conditions for initial data under which weak solutions globally exist or blow up in finite time with m 1 d d d furthermore a sharper criterion is given for global existence and finite time blow up of weak solutions with m in the subrange 2 d 2 d d d 1 d d

well posedness of the cauchy problem for the fractional power dissipative equations abstract this paper studies the cauchy problem for the nonlinear fractional power dissipative equation u t u f u for initial data in the lebesgue space l r r n with either r r d n b 2 d or the homogeneous besov space b p r n with 2 d b n p and 1 p where 0 f u f u or q d f u with q d being a homogeneous pseudo differential operator of order d 0 2 and f u is a function of u which behaves like u b u with b 0

equivariant gysin maps and pulling back fixed points we develop a new approach to the pulling back fixed points theorem of w browder and use it in order to prove various generalizations of this result

global well posedness and asymptotic behavior in besov morrey spaces for chemotaxis navier stokes fluids in this work we consider the keller segel system coupled with navier stokes equations in rn for n 2 we prove the global well posedness with small initial data in besov morrey spaces our initial data class extends previous ones found in the literature such as that obtained by kozono miura and sugiyama j funct anal 270 5 1663 1683 2016 it allows us to consider initial cell density and fluid velocity concentrated on smooth curves or at points depending on the spatial dimension self similar solutions are obtained depending on the homogeneity of the initial data and considering the case of a chemical attractant without the degradation rate moreover we analyze the asymptotic stability of solutions at infinity and obtain a class of asymptotically self similar ones in this work we consider the keller segel system coupled with navier stokes equations in rn for n 2 we prove the global well posedness with small initial data in besov morrey spaces our initial data class extends previous ones found in the literature such as that obtained by kozono miura and sugiyama j funct anal 270 5 1663 1683 2016 it allows us to consider initial cell density and fluid velocity concentrated on smooth curves or at points depending on the spatial dimension self similar solutions are obtained depending on the homogeneity of the initial data and considering the case of a chemical attractant without the degradation rate moreover we analyze the asymptotic stability of solutions at infinity and obtain a class of asymptotically self similar ones

realizability of branched coverings of surfaces absrract a branched covering m n of degree d between closed surfaces determines a collection 6d of partitions of d its branch data corresponding to the set of branch points the collection of partitions must satisfy certain obvious conditions implied by the riemann hurwitz formula this paper investigates the extent to which any such finite collection 6d of partitions of d can be realized as the branch data of a suitable branched covering if n is not the 2 sphere such data can always be realized if 6d contains sufficiently many elements compared to d then it can be realized and whenever d is nonprime examples are constructed of nonrealizable data

equivariant cohomology and sheaves abstract ro g graded equivariant cohomology was originally defined by using equivariant spectra in this paper we construct a sheaf version of ro g graded equivariant cohomology theory by introducing a complex of presheaves we obtain an isomorphism theorem of two different cohomology theories we further apply the results to the study of real algebraic varieties

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

symmetrization techniques on unbounded domains application to a chemotaxis system on rn the authors study the parabolic elliptic system on rn u t u u v 0 v v u u 0 u0 a version of the mathematical model of chemotaxis proposed by keller and segel a differential inequality for the quantity s0u t d where u is the decreasing rearrangement of the solution u t with respect to the spatial variable is obtained as a consequence they obtain e g lp bounds of the solution u v on r2 and global in time existence of solutions under the condition r2u0 8 then the solution u v blows up in a finite time compared to the previous work of diaz diaz and nagai adv math sci appl 5 1995 no 2 659 680 mr1361010 96j 35246 where this problem has been considered on bounded domains of rn there are some additional technical difficulties connected with the regularity of the derivative u t

global strong solution to the semi linear keller segel system of parabolic parabolic type with small data in scale invariant spaces abstract we shall show existence of global strong solution to the semi linear keller segel system in r n n 3 of parabolic parabolic type with small initial data u 0 h n r 2 r r n and v 0 h n r r r n for max 1 n 4 r n 2 our method is based on the perturbation of linealization together with the l p l q estimates of the heat semigroup and the fractional powers of the laplace operator as a by product of our method we shall prove the decay property of solutions as the time goes to infinity

global solutions for some nonlinear parabolic equations with nonmonotonic peturbations publisher summary this chapter discusses the existence uniqueness and decay property of the solutions of two problems it also presents the sobolev s lemma and gagliardo nirenberg inequality

vector bundles over classifying spaces of compact lie groups the completion theorem of atiyah and segal as says that the complex k theory group k bg of the classifying space of any compact lie group g is isomorphic to r g the representation ring completed with respect to its augmentation ideal however the group k bg bg z bu does not directly contain information about vector bundles over the infinite dimensional complex bg itself the purpose of this paper is to compare the grothendieck group of vector bundles over bg which we denote k bg with both k bg and r g the main result is an algebraic description of k bg in terms of the representation rings of certain subgroups of g as one consequence we show that of the natural maps

on the lusternik schnirelmann category of symplectic manifolds and the arnold conjecture in arn appendix 9 arnold proposed a beautiful conjecture concerning the relation between the number of fixed points of certain i e exact or hamiltonian selfdiffeomorphisms of a closed symplectic manifold m and the minimum number of critical points of any smooth c function on m the first author succeeded in proving this form of the arnold conjecture r2 under the hypothesis that and c1 vanish on all spherical homology classes and that there is equality between the lusternik schnirelmann category of m and the dimension of m in this paper we use a fundamental property of category weight to show that for any closed symplectic manifold whose symplectic form vanishes on the image of the hurewicz map the required equality holds thus we show that the original form of the arnold conjecture holds for all symplectic manifolds having 2 m 0 c1 2 m

cohomology of metacyclic groups group n by a finite cyclic group k using homological perturbation theory we introduce the beginning of a free resolution of the integers z over the group ring zg of g in such a way that the resolution reflects the structure of g as an extension of n by k and we use this resolution to compute the additive structure of the integral cohomology of g in many cases we proceed by first establishing a number of special cases thereafter constructing suitable cohomology classes thereby obtaining a lower bound then computing characteristic classes introduced in an earlier paper and finally exploiting these classes obtaining upper bounds for the cohomology via the integral cohomology spectral sequence of the extension e the calculation is then completed by comparing the two bounds

the equivariant hurewicz map let g be a compact lie group y be a based g space and v be a g representation if v g y is the equivariant homotopy group of y in dimension v and h v g y fis the equivariant ordinary homology group of y with burnside ring coefficients in dimension v then there is an equivariant hurewicz map h v g y h v g y one should not expect this map to be an isomorphism since h v g y must be a module over the burnside ring but v g y need not be however here it is shown that under the obvious connectivity conditions on y this map induces an isomorphism between h v g y and an algebraically defined modification of v g y

hecke algebras and cohomotopical mackey functors in this paper we define the concept of the cohomotopical mackey functor which is more general than the usual cohomological mackey functor and show that hecke algebra techniques are applicable to cohomotopical mackey functors our theory is valid for any possibly infinite discrete group some applications to topology are also given

the optimal temporal decay estimates for the fractional power dissipative equation in negative besov spaces in this paper we first generalize a new energy approach developed by guo and wang commun partial differ equations 37 2165 2208 2012 in the framework of homogeneous besov spaces for proving the optimal temporal decay rates of solutions to the fractional power dissipative equation then we apply this approach to the critical and supercritical surface quasi geostrophic equation and the critical keller segel system we show that certain weighted negative besov norm of solutions is preserved along time evolution and obtain the optimal temporal decay rates of the spatial derivatives of solutions by the fourier splitting approach and the interpolation techniques

topological complexity of symplectic manifolds open access via springer compact agreement the authors wish to thank ay se borat michael farber jarek kedra and john oprea for helpful comments regarding an earlier draft of this paper

reliability analysis of uncertain weighted k out of n systems the uncertain variable is used to model a quantity under human uncertainty and the weighted k out of n system is used to model a system of n components which functions if and only if the total weights of functioning components is greater than k considering the human uncertainty in operating the system this paper introduces the uncertain variable to the weighted k out of n system and proposes a concept of uncertain weighted k out of n system some formulas are derived to calculate the reliability index of such a system as a generalization this paper also studies an uncertain weighted k out of n system whose weights are estimated by experts and modeled by uncertain variables instead of crisp numbers in addition this paper analyzes the importance measure of the components in the uncertain weighted k out of n systems

non hamiltonian actions with isolated fixed points we construct a non hamiltonian symplectic circle action on a closed connected six dimensional symplectic manifold with exactly 32 fixed points

system failure engineering and fuzzy methodology an introductory overview abstract system failure engineering may encompass reliability safety security maintainability risk and quality control in this paper we pay a unified view i e a failure oriented view to system failure engineering the notion of failure can be represented in terms of fuzzy sets and widely interpreted we then discuss various application aspects of fuzzy methodology in system failure engineering which include fuzzy methodology in fault diagnosis in probist systems in structural reliability in software reliability in human reliability in safety engineering in security engineering in risk engineering and in quality control as well as profust posbist and posfust reliability theories engineering case studies and mathematical problems raised by applications of fuzzy methodology in system failure engineering are also addressed in this paper

lie poisson structure on some poisson lie groups poisson lie groups appeared in the work of drinfel d see e g drl dr2 as classical objects corresponding to quantum groups going in the other direction we may say that a poisson lie group is a group of symmetries of a phase space that are allowed to twist in a certain sense the symplectic or poisson structure the poisson structure on the group controls this twisting in a precise way quantizing both the phase space and the symmetries one may obtain a quantum group acting on a quantum phase space in recent work lu and ratiu lr used so called standard poisson structures on a compact semisimple lie group k and on its poisson dual k in order to give a new proof of the nonlinear convexity theorem of kostant ko their method is analogous to the famous symplectic proof of the linear convexity theorem given by atiyah a and guillemin and stemnberg gs the nonlinear convexity theorem like the linear one follows from a very general result on convexity of the image of the momentum map a gs however in lr it is applied not to a coadjoint orbit in t but to a symplectic leaf in k the main result of this paper is that the standard poisson structure on the poisson dual k to a compact semisimple poisson lie group k is actually isomorphic to the linear one on t this theorem seems to be related to some facts in the theory of quantum groups namely for generic q the universal enveloping algebra u t and its quantum deformation uq t are isomorphic as algebras though not as coalgebras of course since the quantum version is not cocommutative in particular there is a bijective correspondence between their representations a direct connection between our work and its quantum analogues though is still to be found the present work supplies a positive answer to question 5 1 in lr and strongly depends on that paper to simplify reading we keep the notations of lr wherever possible on one hand but give all necessary definitions on the other our work is also related to du in which the nonlinear convexity theorem is reduced to the linear one by a deformation argument not unlike the one that we use in 5 the paper is organized as follows in 2 we define poisson lie groups discuss

global well posedness for nonlocal fractional keller segel systems in critical besov spaces abstract in this paper we study keller segel systems with fractional diffusion and a nonlocal term we establish the global existence uniqueness and stability of solutions for systems with small initial data in critical besov spaces our main tools are the l p l q estimates for e t 2 in besov spaces and the perturbation of linearization

shapes of free resolutions over a local ring we classify the possible shapes of minimal free resolutions over a regular local ring this illustrates the existence of free resolutions whose betti numbers behave in surprisingly pathological ways we also give an asymptotic characterization of the possible shapes of minimal free resolutions over hypersurface rings our key new technique uses asymptotic arguments to study formal mathbb q betti sequences

fuzzy universal generating functions for multi state system reliability assessment the paper considers a multi state system mss where performance rates or and corresponding state probabilities are presented as fuzzy values in many real world msss it is difficult to estimate precise values of performance rates and their probabilities because of two main reasons the first reason is inaccuracy and insufficiency of data the second one is based on the fact that msss are often used as the approximation for continuous state systems in order to simplify computational burden to overcome these deficiencies performance rates levels or and corresponding probabilities are considered as fuzzy values in this paper the fuzzy universal generating function fugf is developed to extend the universal generating function with crisp sets the composition operators are extended for fugfs and introduced in more general forms based on this a special technique for reliability assessment of such msss is developed illustrative examples are presented to demonstrate the technique

pulling back fixed points if x y are g spaces spaces on which a compact lie group g acts and f x y is a g map then the image of a fixed point in x is fixed in i1 when does the inverse image of a fixed point contain a fixed point in particular if x y are g manifolds and f has degree prime to gi order of g in unpublished work of the author1 this is shown for elementary abelian p groups with x y more general spaces n near manifolds in this paper we show that this is true for abelian p groups g acting smoothly on x with p odd or with p 2 with an additional complex hypothesis we give a counterexample for nonabelian g the method is to prove a generalization of a theorem of bredon 1973 for 7lip actions which says that maps of degree prime to p induce injections on the mod p cohomology of the fixed set we generalize this theorem to abelian p groups where the action on x is smooth and p 4 2 or other hypothesis this seems to be new even in the case of elementary abelian p groups of rank 1 we actually prove a stronger theorem for a generalization of the notion of degree which may be non zero for maps between manifolds of different dimension the proof involves complex linear equivariant k theory in an essential way which requires smoothness and p 2 or a complexity hypothesis on x in order to produce the appropriate complex linear bundles among the corollaries we show that an abelian p group p odd cannot act smoothly on a closed manifold with exactly one isolated fixed point generalizing an old result of atiyah and bott 1964 for g z p this was found independently by ewing and stong 1986 by a different argument i am indebted to ib madsen for his comments in particular for discussions on equivariant k theory thanks are due also to michael davis for carefully reading the manuscript and pointing out several difficulties i also wish to thank the referee for his comments

stable maps into free g spaces in this paper we introduce a systematic method for calculating the group of stable equivariant maps x y g 3 18 into a g free space or spectrum y in fact the method applies without restriction on x whenever g is a p group and y is p complete and satisfies standard finiteness assumptions the method is an adams spectral sequence based on a new equivariant coho mology theory c x which we introduce in 1 this spectral sequence is quite calculable and provides a natural generalisation of the classical adams spectral sequence based on ordinary modp cohomology it also geometrically realises certain inverse limits of nonequivariant adams spectral sequences which have been useful in the study of the segal conjecture 19 5 21 9

well posedness of the cauchy problem for the fractional power dissipative equation in critical besov spaces abstract in this paper we study the cauchy problem for the semilinear fractional power dissipative equation u t u f u for the initial data u 0 in critical besov spaces b 2 r with n 2 2 d b where 0 f u p d u b 1 with p d being a homogeneous pseudo differential operator of order d 0 2 and b 0 being an integer making use of some estimates of the corresponding linear equation in the frame of mixed time space spaces the so called mono norm method which is different from the kato s double norm method fourier localization technique and littlewood paley theory we get the well posedness result in the case n 2

bigraded equivariant cohomology of real quadrics we give a complete description of the bigraded bredon co homology ring of smooth projective real quadrics with coefficients in the constant mackey functor z these invariants are closely related to the integral motivic cohomology ring which is not known for these va rieties some of the results and techniques introduced can be applied to other geometrically cellular real varieties

a transfer homomorphism for compact lie group actions here a space is perfectly normal if it is normal and every open subspace is a countable union of closed subspaces transfer maps for actions of finite groups were defined by floyd 10 and used in particular for studying orbit spaces for actions on contractible spaces when g is a compact lie group acting freely on x then n x h x g is a fiber bundle with fiber g h and the transfer constructed by becker and gottlieb 1 applies in this case so our goal here is to generalize both of these constructions one obvious consequence of the above theorem is that

global and exploding solutions for nonlocal quadratic evolution problems nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered the inertial type nonlinearity is quadratic and nonlocal while the diffusive term also nonlocal is anomalous and fractal i e represented by a fractional power of the laplacian conditions for global in time existence versus finite time blow up are studied self similar solutions are constructed for certain homogeneous initial data

global existence and decay properties for a degenerate keller segel model with a power factor in drift term abstract the following degenerate parabolic system modelling chemotaxis is considered ks u t u m u q 1 v x r n t 0 v t v v u x r n t 0 u x 0 u 0 x v x 0 v 0 x x r n where m 1 q 2 0 or 1 and n 1 the aim of this paper is to prove the existence of a time global weak solution u v of ks with the l 0 l r n bound such a global bound is obtained in the case of i m q 2 n for large initial data and ii 1 m q 2 n for small initial data in the case of ii the decay properties of the solution u v are also discussed

equivariant fixed point index and fixed point transfer in nonzero dimensions dold s fixed point index and fixed point transfer are generalized for certain coincidence situations namely maps which change the equivariant di mension those invariants change the dimension correspondingly a formula for the index of a situation over a space with trivial group action is exhibited for the transfer a generalization of dold s lefschetz hopf trace formula is proved

repairable consecutive k out of n f system with fuzzy states in this paper we study a repairable consecutive k out of n f system with fuzzy states the maintenance of the system is carried out by r repairmen or repair facilities the system is either circular or linear it is assumed that the working time and the repair time of each component in the system are both exponentially distributed and every component after repair is as same as new each component is classified as either a key component or an ordinary one according to its priority role to the system s repair when the system displays a gradual degradation of its performance its reliability is then analyzed in terms of fuzzy failure and success states the difference between fuzzy reliability theory and the conventional reliability theory is highlighted

fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context abstract conventional reliability theory is based on the binary state assumption and the probability assumption namely 1 the systems are precisely defined as functioning or failed 2 the system behavior is fully characterized in the context of probability measures however the probability assumption is no longer reasonable in the case of small size of samples since the term probability stems from the sample generality in this way possibility measures should be used to characterize the sample particularity in this paper the binary state assumption is reserved and the possibility assumption is taken in place of the probability assumption thus a concept of fuzzy reliability i e posbist reliability is introduced and a theory of fuzzy reliability i e posbist reliability theory is established various conclusions which are contrary to statements in conventional reliability theory i e probist reliability theory are then drawn

a general formal approach for fuzzy reliability analysis in the possibility context abstract in this paper we focus on the fuzzy reliability analysis in the posbist reliability theory in accordance with this theory the system failure state is defined precisely and the system failure and repair behaviour is fully characterized in the context of possibility measures to formalize the reliability analysis in the posbist theory we propose a general approach on the basis of a system of functional equations the solution of the system allows us to obtain fuzzy reliability characteristics of the arbitrary repairable and unrepairable systems to illustrate the construction and application of the system of functional equations various examples are given

cuplength estimates on lagrangian intersections on demontre l estimation suivante sur des intersections lagrangiennes si l est une sous variete lagrangienne de p avec 2 p l 0 et l est obtenue a partir de l par un diffeomorphisme exact de p alors le nombre d elements de l l est superieure ou egale a la longueur de calotte de p

global existence and decay properties of solutions for some degenerate quasilinear parabolic systems modelling chemotaxis abstract the following degenerate parabolic system modelling chemotaxis is considered ks u t u m u v x r n t 0 v t v v u x r n t 0 u x 0 u 0 x v x 0 v 0 x x r n where 0 or 1 we show here that the system of ks with m 1 has a time global weak solution u v with a uniform bound in time when u 0 v 0 is a nonnegative function and in l 1 l r n l 1 h 1 w 1 r n u 0 m h 1 r n the decay properties of the solution with small initial data are also discussed

strichartz type estimates for fractional heat equations abstract we obtain strichartz estimates for the fractional heat equations by using both the abstract strichartz estimates of keel tao and the hardy littlewood sobolev inequality we also prove an endpoint homogeneous strichartz estimate via replacing l x r n by bmo x r n and a parabolic homogeneous strichartz estimate meanwhile we generalize the strichartz estimates by replacing the lebesgue spaces with either besov spaces or sobolev spaces moreover we establish the strichartz estimates for the fractional heat equations with a time dependent potential of an appropriate integrability as an application we prove the global existence and uniqueness of regular solutions in spatial variables for the generalized navier stokes system with l r r n data

the stable free rank of symmetry of products of spheres a well known conjecture in the theory of transformation groups states that if p is a prime and p r acts freely on a product of k spheres then r k we prove this assertion if p is large compared to the dimension of the product of spheres the argument builds on tame homotopy theory for non simply connected spaces

cohomologically symplectic spaces toral actions and the gottlieb group aspects of symplectic geometry are explored from a homotopical viewpoint in particular the question of whether or not a given toral action is hamiltonian is shown to be independent of geometry rather a new homotopical obstruction is described which detects when an action is hamiltonian this new entity the ae invariant allows many results of symplectic geometry to be generalized to manifolds which are only cohomologically symplectic in the sense that there is a degree 2 cohomology class which cups to a top class furthermore new results in symplectic geometry also arise from this homotopical approach

preventing blow up in a chemotaxis model abstract this paper deals with a chemotactic model of keller segel type the main feature of the keller segel model is the possibility of blow up of solutions in a finite time to eliminate the possibility of blow up a modified version of keller segel model is introduced the blow up control relies on the presence of a pressure function which increases faster than a logarithm for high enough cells densities for such a pressure function the solutions cannot blow up in a finite time some other conditions are introduced to ensure the global boundedness

on fundamental groups of symplectically aspherical manifolds a smooth manifold m is called symplectically aspherical if it admits a symplectic form with 2 m 0 it is easy to see that unlike in the case of closed symplectic manifolds not every finitely presented group can be realized as the fundamental group of a closed symplectically aspherical manifold the goal of the paper is to study the fundamental groups of closed symplectically aspherical manifolds motivated by some results of gompf we introduce two classes of fundamental groups 1 m of symplectically aspherical manifolds m the first one consists of fundamental groups of such m with 2 m 0 while the second with 2 m 0 relations between these classes are discussed we show that several important classes of groups can be realized in both classes while some groups can be realized in the first class but not in the second one also we notice that there are some interesting dimensional phenomena in the realization problem the above results are framed by a general study of symplectically aspherical manifolds for example we find some conditions which imply that the gompf sum of symplectically aspherical manifolds is symplectically aspherical or that a total space of a bundle is symplectically aspherical

on the nonexistence of elements of kervaire invariant one we show that the kervaire invariant one elements j 2j 1 2s exist only for j 6 by browder s theorem this means that smooth framed manifolds of kervaire invariant one exist only in dimensions 2 6 14 30 62 and possibly 126 except for dimension 126 this resolves a longstanding problem in algebraic topology