sampling and reconstruction of signals in a reproducing kernel subspace of lp rd in this paper we consider sampling and reconstruction of signals in a reproducing kernel subspace of lp rd 1 p associated with an idempotent integral operator whose kernel has certain off diagonal decay and regularity the space of p integrable non uniform splines and the shift invariant spaces generated by finitely many localized functions are our model examples of such reproducing kernel subspaces of lp rd we show that a signal in such reproducing kernel subspaces can be reconstructed in a stable way from its samples taken on a relatively separated set with sufficiently small gap we also study the exponential convergence consistency and the asymptotic pointwise error estimate of the iterative approximation projection algorithm and the iterative frame algorithm for reconstructing a signal in those reproducing kernel spaces from its samples with sufficiently small gap

existence of bubbling solutions for chern simons model on a torus we study the existence of bubbling solutions for the the following chern simons higgs equation delta u frac1 varepsilon 2 rm e u 1 rm e u 4 pi sum i 1 2k delta p i quad text in omega where is a torus if k 1 for any critical point q of the associated sum of the green functions we introduce a quantity d q see 1 11 below we show that for any non degenerate critical point q with d q 0 the above problem has a solution ue satisfying that e 0 ue blows up at q the calculations in this paper also show that if a sequence of solutions ue blows up at q as e 0 then q must be a critical point of the associated sum of the green functions and d q leqq 0 so the condition d q 0 is almost necessary to obtain our result we also construct solutions with k bubbles for k geqq 2

the relativistic non abelian chern simons equations we study ther xr system of nonlinear elliptic equations delta u a lambda sum limits b 1 r k ab e u b lambda sum limits b 1 r sum limits c 1 r e u b k ab e u c k bc 4 pi sum limits j 1 n a delta p aj a 1 2 r x r 2 where 0 is a constant parameter k kab is the cartan matrix of a semi simple lie algebra and p is the dirac measure concentrated atp r 2 this system of equations arises in the relativistic non abelian chern simons theory and may be viewed as a nonintegrable deformation of the integrable toda system we establish the existence of a class of solutions known as topological multivortices the crucial step in our method is the use of the decomposition theorem of cholesky for positive definite matrices so that a variational principle can be formulated

the random generation of directed animals abstract in this paper we propose an algorithm to randomly generate a directed animal directed animals are well known combinatorial objects and have been widely used for modelling the physical phenomenon of percolation the algorithm consists of three steps and we prove that each of them is performed in linear time finally we report the results of our experiments made by means of appropriate computer programs in order to give empirical evidence that our algorithm really works

perturbation of regular sampling in shift invariant spaces for frames perturbation theorems for regular sampling in shift invariant spaces are derived using a generalized perturbation theorem for frames in a hilbert space which generalizes the irregular sampling theorem established by chen using this generalized irregular sampling theorem estimates for the maximum perturbation are obtained some typical examples illustrate the result

wiener s lemma for infinite matrices in this paper we introduce a class of infinite matrices related to the beurling algebra of periodic functions and we show that it is an inverse closed subalgebra of mathcal b ell q w the algebra of all bounded linear operators on the weighted sequence space ell q w for any 1 q and any discrete muckenhoupt aq weight w

on the entire radial solutions of the chern simons su 3 system in this paper we study the entire radial solutions of the self dual equations arising from the relativistic su 3 chern simons model proposed by kao and lee phys rev d 50 6626 6632 1994 and dunne phys lett b 345 452 457 1995 nuclear phys b 433 333 348 1995 understanding the structure of entire radial solutions is one of the fundamental issues for the system of nonlinear equations in this paper we prove that any entire radial solutions must be one of topological non topological and mixed type solutions and completely classify the asymptotic behaviors at infinity of these solutions even for radial solutions this classification has remained an open problem for many years as an application of this classification we prove that the two components u and v have intersection at most finite times

new type of nontopological bubbling solutions in the su 3 chern simons model in r2 abstract we are concerned with su 3 chern simons model in r 2 nontopological solutions were shown to exist in 10 in a radially symmetric situation also in 10 there constructed a sequence of partially bubbling solutions of which one component only bubbles we here construct a sequence of radial nontopological bubbling solutions of another type explicitly one component of these bubbling solutions locally converges to a nice function but both components blow up partially in different regions at infinity at the same time this type of bubbling solutions not only is a new phenomenon to this type of systems but also shows a more complicated pattern of the nontopological solution structure than the abelian chern simons higgs equation proposed by 13 15

asymptotic behavior of condensate solutions in the chern simons higgs theory we study the asymptotic behavior of condensate solutions in the chern simons higgs model as the chern simons coupling parameter tends to zero using the variational method we prove that there exist condensate solutions which show concentration phenomena

chemins de schroder et hierarchies aleatoires abstract un chemin de schroder est un chemin positif du plan z 2 commencant et terminant sur l axe des abscisses en effectuant des pas nord est sud est ou deux pas est consecutifs nous donnons dans cet article un algorithme de complexite moyenne o n en espace et en temps qui engendre de facon aleatoire et uniforme un chemin de schroder de longueur 2n si l on considere uniquement les chemins de schroder n ayant aucun pas horizontal sur l axe des abscisses on obtient un ensemble de chemins enumeres par les petits nombre de schroder nous donnons une bijection entre ces chemins et des arbres ordonnes enracines appeles arbres de schroder ou hierarchies ordonnees dont les noeuds internes ont au moins deux fils nous deduisons de cette bijection un algorithme lineaire de generation aleatoire et uniforme de hierarchies ordonnees selon le nombre de feuilles

the existence of chern simons vortices a new type of vortices called chern simons vortices is considered and the existence is established

uniform generation of a motzkin word abstract we present a simple and efficient algorithm which builds randomly and uniformly a motzkin word of size n the average complexity of this algorithm is o n the basic idea is to choose a slightly enlarged probability space where uniformity can be achieved and then to filter out the desired words without destorying uniformity

perturbed sampling formulas and local reconstruction in shift invariant spaces abstract let v be a closed subspace of l 2 r generated from the integer shifts of a continuous function with a certain decay at infinity and a non vanishing property for the function n z n e i n on in this paper we determine a positive number so that the set n n n z is a set of stable sampling for the space v for any selection of the elements n within the ranges we demonstrate the resulting sampling formula called perturbation formula for functions f v and also we establish a finite reconstruction formula approximating f on bounded intervals we compute the corresponding error and we provide estimates for the jitter error as well

bubbling solutions for relativistic abelian chern simons model on a torus we prove the existence of bubbling solutions for the following chern simons higgs equation delta u frac 1 varepsilon 2 e u 1 e u 4 pi sum j 1 n delta p j quad rm in omega where is a torus we show that if n 4 and p 1 p j j 2 n then for small e 0 the above problem has a solution u e and as e 0 u e blows up at the vertex point p 1 and satisfies frac 1 varepsilon 2 e u 1 e u to 4 pi n delta p 1 this is the first result for the existence of a solution which blows up at a vertex point

uniqueness of the topological multivortex solution in the self dual chern simons theory we establish a uniqueness result for the topological multivortex solution to the self dual equations of the abelian relativistic self dual chern simons higgs model we prove that the topological multivortex solution is unique if the chern simons coupling parameter 0 is sufficiently small we also establish a uniqueness result for 0 sufficiently large

self dual symmetric nontopological solutions in the su 3 model in mathbb r 2 in this paper we study non topological solutions u 1 u 2 to the su 3 chern simons system satisfying the asymptotic behavior u k x 2 alpha k ln x o 1 for some alpha k 1 k 1 2 we show that solutions remain uniformly bounded as long as 1 2 lies in s n see sect 1 and then we prove the existence of non topological solutions for any alpha 1 alpha 2 in s n for this purpose we have to study the phenomena of partial blowup at infinity and show that s n is the optimal range of 1 2 such that the partial blowup could occur if 1 2 is on some part of partial s n

the existence of non topological multivortex solutions in the relativistic self dual chern simons theory we construct a general type of multivortex solutions of the self duality equations the bogomol nyi equations of 2 1 dimensional relativistic chern simons model with the non topological boundary condition near infinity for such construction we use a perturbation argument around the explicit solutions of the liouville equation

symmetry and inverse closedness of matrix algebras and functional calculus for infinite matrices we investigate the symbolic calculus for a large class of matrix algebras that are defined by the off diagonal decay of infinite matrices applications are given to the symmetry of some highly non commutative banach algebras to the analysis of twisted convolution and to the theory of localized frames

a calculus for the random generation of labelled combinatorial structures a systematic approach to the random generation of labelled combinatorial objects is presented it applies to structures that are decomposable i e formally specifiable by grammars involving set sequence and cycle constructions a general strategy is developed for solving the random generation problem with two closely related types of methods for structures of size n the boustrophedonic algorithms exhibit a worst case behaviour of the form o n log n the sequential algorithms have worst case o n2 while offering good potential for optimizations in the average case the complexity model is in terms of arithmetic operations and both methods appeal to precomputed numerical table of linear size that can be computed in time o n2 a companion calculus permits systematically to compute the average case cost of the sequential generation algorithm associated to a given specification using optimizations dictated by the cost calculus several random generation algorithms of the sequential type are developed most of them have expected complexity 1 2n log n and are thus only slightly superlinear the approach is exemplified by the random generation of a number of classical combinatorial structures including cayley trees hierarchies the cycle decomposition of permutations binary trees functional graphs surjections and set partitions

on sampling in shift invariant spaces a necessary and sufficient condition for sampling in the general framework of shift invariant spaces is derived then this result is applied respectively to the regular sampling and the perturbation of regular sampling in shift invariant spaces a simple necessary and sufficient condition for regular sampling in shift invariant spaces is attained furthermore an improved estimate for the perturbation is derived for the perturbation of regular sampling in shift invariant spaces the derived estimate is easy to calculate and shown to be optimal in some shift invariant spaces the algorithm to calculate the reconstruction frame is also presented