mean square dissipative methods for stochastic age dependent capital system with fractional brownian motion and jumps abstract in this paper we analyze mean square dissipativity of numerical methods applied to a class of stochastic age dependent vintage capital system with fractional brownian motion fbm and poisson jumps some sufficient conditions are obtained for ensuring the underlying systems are mean square dissipative it is shown that the mean square dissipativity is preserved by the compensated split step backward euler method and compensated backward euler method without any restriction on stepsize while the split step backward euler method and backward euler method could reproduce mean square dissipativity under a stepsize constraint those results indicate that compensated numerical methods achieve superiority over non compensated numerical methods in terms of mean square dissipativity a numerical example is provided to illustrate the theoretical results

artin groups of spherical type up to isomorphism we prove that two artin groups of spherical type are isomorphic if and only if their defining coxeter graphs are the same

banach strong novikov conjecture for polynomially contractible groups abstract we prove the banach strong novikov conjecture for groups having polynomially bounded higher order combinatorial functions this includes all automatic groups

numerical methods for singular nonlinear volterra type equations with two point boundary conditions abstract the purpose of this article is to generalize the work in a paper by shaw and garey 1 to include equations with weakly singular kernels an example to illustrate the methods is given in section 4

k π 1 and word problems for infinite type artin tits groups and applications to virtual braid groups let be a coxeter graph let w s be its associated coxeter system and let a be its associated artin tits system we regard w as a reflection group acting on a real vector space v let i be the tits cone and let e be the complement in i iv of the reflecting hyperplanes recall that salvetti charney and davis have constructed a simplicial complex having the same homotopy type as e we observe that if t subset s then t naturally embeds into we prove that this embedding admits a retraction pi t omega gamma to omega gamma t and we deduce several topological and combinatorial results on parabolic subgroups of a from a family mathcal s of subsets of s having certain properties we construct a cube complex we show that has the same homotopy type as the universal cover of e and we prove that is cat 0 if and only if mathcal s is a flag complex we say that x subset s is free of infinity if x has no edge labeled by we show that if e gamma x is aspherical and a x has a solution to the word problem for all x subset s free of infinity then e is aspherical and a has a solution to the word problem we apply these results to the virtual braid group vb n in particular we give a solution to the word problem in vb n and we prove that the virtual cohomological dimension of vb n is n 1

small cancellation theory and automatic groups part ii the main results obtained in part i can be rephrased in the language of root systems and euclidean planar tessellations as saying that finite a1 x a1 and a 2 piecewise euclidean abbreviated pe complexes of non positive curvature have automatic fundamental groups a 2 dimensional complex is a a 1 a1 respectively a2 pe complex if every 2 cell can be identified with a unit square resp equilateral triangle in the euclidean plane in such a way that the induced metrics agree on intersections such a complex has non positive curvature if the link of each vertex contains no circuits without backtracking of length less than 2 n here we prove using similar techniques that finite 2 complexes modelled on the other two root systems b 2 and g2 corresponding to tessellations by 45 right angle triangles and by 30 60 right angle triangles also have automatic fundamental groups theorems 2 3 and 3 2 to be precise

garside families and garside germs garside families have recently emerged as a relevant context for extending results involving garside monoids and groups which themselves extend the classical theory of generalized braid groups here we establish various characterizations of garside families that is equivalently various criteria for establishing the existence of normal decompositions of a certain type

a note on words in braid monoids abstract the purpose of this note is to give a self contained apart from simple facts about coxeter groups and we hope a bit shorter and more understandable account of some results of c1 c2 on normal forms of braids which are themselves based on the papers d1 t in particular a motivation was to give a proof of proposition 5 1 that we use in b m some proofs and results from section 2 onwards seem to be new i thank several people for improvements from earlier versions of the manuscript m geck for pointing out some errors f digne for pointing out that some results don t need the braid group to be of finite type and j y hee for suggesting and providing further improvements in that direction

braid pictures for artin groups we define the braid groups of a two dimensional orbifold and introduce conventions for drawing braid pictures we use these to realize the artin groups associated to the spherical coxeter diagrams a n b n c n and d n and the affine diagrams a n b n c n and d n as subgroups of the braid groups of various simple orbifolds the cases d n b n c n and d n are new in each case the artin group is a normal subgroup with abelian quotient in all cases except a n the quotient is finite we also illustrate the value of our braid calculus by giving a picture proof of the basic properties of the garside element of an artin group of type d n

artin groups of large type are shortlex automatic with regular geodesics we prove that any artin group of large type is shortlex automatic with respect to its standard generating set and that the set of all geodesic words over the same generating set satisfies the falsification by fellow traveller property fftp and hence is regular

an isoperimetric inequality for artin groups of finite type we show that artin groups of finite type satisfy a quadratic isoperimetric inequality moreover we describe an explicit algorithm to solve the word problem in quadratic time

thick metric spaces relative hyperbolicity and quasi isometric rigidity we study the geometry of non relatively hyperbolic groups generalizing a result of schwartz any quasi isometric image of a non relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup this implies that a group being relatively hyperbolic with non relatively hyperbolic peripheral subgroups is a quasi isometry invariant as an application artin groups are relatively hyperbolic if and only if freely decomposable we also introduce a new quasi isometry invariant of metric spaces called metrically thick which is sufficient for a metric space to be non hyperbolic relative to any non trivial collection of subsets thick finitely generated groups include mapping class groups of most surfaces outer automorphism groups of most free groups certain artin groups and others non uniform lattices in higher rank semisimple lie groups are thick and hence non relatively hyperbolic in contrast with rank one which provided the motivating examples of relatively hyperbolic groups mapping class groups are the first examples of non relatively hyperbolic groups having cut points in any asymptotic cone resolving several questions of drutu and sapir about the structure of relatively hyperbolic groups outside of group theory teichmuller spaces for surfaces of sufficiently large complexity are thick with respect to the weil peterson metric in contrast with brock farb s hyperbolicity result in low complexity

product integration for weakly singular integral equations in this note we discuss the numerical solution of the second kind fredholm integral equation y t f t lambda int limits omega psi alpha t s g t s y s ds t in bar omega 1 where lambda in not subset backslash 0 the functions f g are given and continuous denotes the euclidean norm and 0 m is a given function on 0 which satisfies psi alpha j r leqq c j left begin array 20 c r a m j j geqq 0 m alpha 0 left begin array 20 c ln r j 0 r j j 0 end array right alpha m end array right with cj not depending on r here is the closure of a bounded domain m

algorithms and geometry for graph products of groups recent work of gromov epstein cannon thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups see 16 17 and 14 many of these structures are preserved by taking graph products the graph product of groups not to be confused with the fundamental group of a graph of groups is a product mixing direct and free products whether the product between two groups in the graph product is free or direct is determined by a simplicial graph given a simplicial graph we say that two vertices are adjacent if they are joined by a single edge

conjugacy problem for braid groups and garside groups abstract we present a new algorithm to solve the conjugacy problem in artin braid groups which is faster than the one presented by birman ko and lee adv math 139 1998 322 353 this algorithm can be applied not only to braid groups but to all garside groups which include finite type artin groups and torus knot groups among others

symmetrical subgroups of artin groups we show that the subgroup fixed by a group of symmetries of an artin system a s is itself an artin group under the hypothesis that the deligne complex associated to a admits a suitable cat 0 metric such a metric is known to exist for all artin groups of type fc which include all the finite type artin groups as well as many infinite types we also recover the previously known analogous result for an arbitrary coxeter system w s

the cyclic sliding operation in garside groups we present a new operation to be performed on elements in a garside group called cyclic sliding which is introduced to replace the well known cycling and decycling operations cyclic sliding appears to be a more natural choice simplifying the algorithms concerning conjugacy in garside groups and having nicer theoretical properties we show in particular that if a super summit element has conjugates which are rigid that is which have a certain particularly simple structure then the optimal way of obtaining such a rigid conjugate through conjugation by positive elements is given by iterated cyclic sliding

a stochastic sirs epidemic model with infectious force under intervention strategies abstract in this paper we extend a classical sirs epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation sde one through introducing random fluctuations the value of our study lies in two aspects mathematically by using the markov semigroups theory we prove that the reproduction number r 0 s can be used to govern the stochastic dynamics of sde model if r 0 s 1 under mild extra conditions the sde system has a disease free absorbing set which means the extinction of disease with probability one if r 0 s 1 under mild extra conditions it has an endemic stationary distribution which leads to the stochastical persistence of the disease epidemiologically we find that random fluctuations can suppress disease outbreak which can provide us some useful control strategies to regulate disease dynamics

metric systolicity and two dimensional artin groups we introduce the notion of metrically systolic simplicial complexes we study geometric and large scale properties of such complexes and of groups acting on them geometrically we show that all two dimensional artin groups act geometrically on metrically systolic complexes as direct corollaries we obtain new results on two dimensional artin groups and all their finitely presented subgroups we prove that the conjugacy problem is solvable and that the dehn function is quadratic we also show several large scale features of finitely presented subgroups of two dimensional artin groups lying background for further studies concerning their quasi isometric rigidity

gaussian groups and garside groups two generalisations of artin groups it is known that a number of algebraic properties of the braid groups extend to arbitrary finite coxeter type artin groups here we show how to extend the results to more general groups that we call garside groups define a gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths and where left and right lowest common multiples exist a garside monoid is a gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition a gaussian group is the group of fractions of a gaussian monoid and a garside group is the group of fractions of a garside monoid braid groups and more generally finite coxeter type artin groups are garside groups we determine algorithmic criteria in terms of presentations for recognizing gaussian and garside monoids and groups and exhibit infinite families of such groups we describe simple algorithms that solve the word problem in a gaussian group show that these algorithms have a quadratic complexity if the group is a garside group and prove that garside groups have quadratic isoperimetric inequalities we construct normal forms for gaussian groups and prove that in the case of a garside group the language of normal forms is regular symmetric and geodesic has the 5 fellow traveller property and has the uniqueness property this shows in particular that garside groups are geodesically fully biautomatic finally we consider an automorphism of a finite coxeter type artin group derived from an automorphism of its defining coxeter graph and prove that the subgroup of elements fixed by this automorphism is also a finite coxeter type artin group that can be explicitly determined 1991 mathematics subject classification primary 20f05 20f36 secondary 20b40 20m05

algorithmic recognition of quasipositive braids of algebraic length two abstract we give an algorithm to decide if a given braid is a product of two factors which are conjugates of given powers of standard generators of the braid group the same problem is solved in a certain class of garside groups including artin tits groups of spherical type the solution is based on the garside theory and especially on the theory of cyclic sliding developed by gebhardt and gonzalez meneses we show that if a braid is of the required form then any cycling orbit in its sliding circuit set in the dual garside structure contains an element for which this fact is immediately seen from the left normal form

product integration methods for second kind abel integral equations the construction and convergence of high order product integration methods for the second kind abel equation are discussed and the results of de hoog and weiss are generalised backward difference methods are introduced and numerical results are presented which verify the theoretical rates of convergence