dirichlet form approach to infinite dimensional wiener processes with singular interactions we construct infinite dimensional wiener processes with interactions by constructing specific quasi regular dirichlet forms our assumptions are very mild accordingly our results can be applied to singular interactions such as hard core potentials lennard jones type potentials and dyson s model we construct nonequilibrium dynamics

symmetry reductions and exact solutions of the 2 1 dimensional jaulent miodek equation by applying the direct symmetry method we obtain the symmetry reductions group invariant solutions and some new exact solutions of the 2 1 dimensional jaulent miodek equation which include jacobi elliptic function solutions airy function solutions trigonometric function solutions hyperbolic function solutions and so on

regularity of invariant measures on finite and infinite dimensional spaces and applications abstract in this paper we prove new results on the regularity i e smoothness of measures solving the equation l 0 for operators of type l b on finite and infinite dimensional state spaces e in particular we settle a conjecture of i shigekawa in the situation where h is the gross laplacian e h is an abstract wiener space and b id e v where v takes values in the cameron martin space h using gross logarithmic sobolev inequality in an essential way we show that is always absolutely continuous w r t the gaussian measure and that the square root of the density is in the malliavin test function space of order 1 in l 2 furthermore we discuss applications to infinite dimensional stochastic differential equations and prove some new existence results for l 0 these include results on the inverse problem i e we give conditions ensuring that b is the vector logarithmic derivative of a measure we also prove necessary and sufficient conditions for to be symmetrizing i e l is symmetric on l 2 finally a substantial part of this work is devoted to the uniqueness of symmetrizing measures for l we characterize the cases where we have uniqueness by the irreducibility of the associated classical dirichlet forms

painleve equations nonlinear special functions the six painleve equations pi pvi were first discovered about a hundred years ago by painleve and his colleagues in an investigation of nonlinear second order ordinary differential equations recently there has been considerable interest in the painleve equations primarily due to the fact that they arise as reductions of the soliton equations which are solvable by inverse scattering consequently the painleve equations can be regarded as completely integrable equations and possess solutions which can be expressed in terms of solutions of linear integral equations despite being nonlinear equations although first discovered from strictly mathematical considerations the painleve equations have arisen in a variety of important physical applications including statistical mechanics plasma physics nonlinear waves quantum gravity quantum field theory general relativity nonlinear optics and fibre optics the painleve equations may be thought of a nonlinear analogues of the classical special functions they possess hierarchies of rational solutions and one parameter families of solutions expressible in terms of the classical special functions for special values of the parameters further the painleve equations admit symmetries under affine weyl groups which are related to the associated backlund transformations in this paper i discuss some of the remarkable properties which the painleve equations possess including connection formulae backlund transformations associated discrete equations and hierarchies of exact solutions in particular the second painleve equation pii is used to illustrate these properties and some of the applications of pii are also discussed

uniqueness of diffusion generators for two types of particle systems with singular interactions abstract for two types of stochastic particle systems in r d we show non explosion in finite time by proving that their respective generators are l1 unique where is their respective invariant in these cases even symmetrizing measure we also prove the much harder l2 uniqueness in both models

ergodicity ofl2 semigroups and extremality of gibbs states we extend the classical results of holley stroock on the characterization of extreme gibbs states for the ising model in terms of the irreducibility resp ergodicity of the corresponding glauber dynamics to the case of lattice systems with unbounded linear spin spaces we first develop a general framework to discuss questions of this type using classical dirichlet forms on infinite dimensional state spaces and their associated diffusions we then describe concrete applications to lattice models with polynomial interactions i e the discretep d models of euclidean quantum field theory in addition we prove the equivalence of extremality and shift ergodicity for tempered gibbs states of these models and also discuss this question in the general framework

strong solutions of stochastic equations with singular time dependent drift we prove existence and uniqueness of strong solutions to stochastic equations in domains with unit diffusion and singular time dependent drift b up to an explosion time we only assume local l q l p integrability of b in g with d p 2 q 1 we also prove strong feller properties in this case if b is the gradient in x of a nonnegative function blowing up as g x g we prove that the conditions 2d t k 2d t ke 0 2 imply that the explosion time is infinite and the distributions of the solution have sub gaussian tails

generalized design of low complexity block diagonalization type precoding algorithms for multiuser mimo systems block diagonalization bd based precoding techniques are well known linear transmit strategies for multiuser mimo mu mimo systems by employing bd type precoding algorithms at the transmit side the mu mimo broadcast channel is decomposed into multiple independent parallel single user mimo su mimo channels and achieves the maximum diversity order at high data rates the main computational complexity of bd type precoding algorithms comes from two singular value decomposition svd operations which depend on the number of users and the dimensions of each user s channel matrix in this work low complexity precoding algorithms are proposed to reduce the computational complexity and improve the performance of bd type precoding algorithms we devise a strategy based on a common channel inversion technique qr decompositions and lattice reductions to decouple the mu mimo channel into equivalent su mimo channels analytical and simulation results show that the proposed precoding algorithms can achieve a comparable sum rate performance as bd type precoding algorithms substantial bit error rate ber performance gains and a simplified receiver structure while requiring a much lower complexity

analysis and geometry on configuration spaces the gibbsian case using a natural riemannian geometry like structure on the configuration space over rd we prove that for a large class of potentials the corresponding canonical gibbs measures on 1 can be completely characterized by an integration by parts formula that is if is the gradient of the riemannian structure on one can define a corresponding divergence div such that the canonical gibbs measures are exactly those measures for which and div are dual operators onl2 one consequence is that for such the corresponding dirichlet forms e are defined in addition each of them is shown to be associated with a conservative diffusion process on with invariant measure the corresponding generators are extensions of the operator div the diffusions can be characterized in terms of a martingale problem and they can be considered as a brownian motion on perturbed by a singular drift another main result of this paper is the following if is a canonical gibbs measure then it is extreme or a pure phase if and only if the corresponding weak sobolev spacew1 2 on is irreducible as a consequence we prove that for extreme canonical gibbs measures the above mentioned diffusions are time ergodic in particular this holds for tempered grand canonical gibbs measures ruelle measures provided that the activity constant is small enough we also include a complete discussion of the free case i e 0 where the underlying space rdis even replaced by a riemannian manifoldx

hidden symmetries and exact solutions of integro differential jaulent miodek evolution equation use of the adjoint method to obtain optimal lie vectors a reduction of the jm equation to ordinary differential equations and detection of lie symmetries test if these symmetries are hidden analysis and plot of results comparison with previous work in the field analytical solutions of a 2 1 dimensional nonlinear model using the jaulent miodek hierarchy are investigated following a similarity reduction procedure for this adjoint lie matrices are first evaluated and an extensive list of optimal lie vectors is obtained the systematic reduction of jaulent miodek evolution equation to lower number of variables leads to hidden symmetries and new solutions

construction of infinite dimensional interacting diffusion processes through dirichlet forms by the theory of quasi regular dirichletforms and the associated special standard processes the existence of symmetric diffusion processes taking values in the space of non negative integer valued radon measures on mbox boldmath r nu and having gibbs invariant measures associated with some given pair potentials is considered the existence of such diffusions can be shown for a wide class of potentials involving some singular ones also as a consequence of an application of stochastic calculus a representation for the diffusion by means of a stochastic differential equation is derived

lattice reduction based approximate map detection with bit wise combining and integer perturbed list generation for iterative detection and decoding idd in multiple input multiple output mimo systems the log likelihood ratio llr of each coded bit can be found by an optimal bit wise maximum a posteriori probability map detector however since this map detector requires a prohibitively high computational complexity low complexity suboptimal detectors are desirable in this paper lattice reduction lr based mimo detection is investigated to derive a low complexity detector that can achieve near map performance for idd in order to approximate llr values incorporating the extrinsic information provided by a soft input soft output siso decoder bit wise lr based minimum mean square error mmse filters are derived furthermore in order to minimize the performance degradation due to quantization or rounding errors in the lr based detection a low complexity integer perturbed list generation method is proposed where no tree search is used by taking advantage of a near orthogonal channel basis obtained by lr through a complexity analysis and simulations it is shown that the proposed approach achieves near optimal performance while the complexity is comparable with that of the mmse soft cancellation method which is known to be computationally efficient as a bit wise detector a parallel implementation of the proposed method would be straightforward which lowers the detection delay

fuzzy topology on fuzzy sets fuzzy semicontinuity and fuzzy semiseparation axioms the concept of a fuzzy topology on a fuzzy set was introduced in fuzzy set syst 45 1992 103 the aim of this paper is to introduce fuzzy semicontinuity and fuzzy semiseparation axioms in this new situation and validity of some characterization of these concepts have been examined also we define a fuzzy generalized semiopen set and introduce fuzzy separation axioms by using this concept fuzzy semiconnected and fuzzy semicompact spaces are introduced and some of their properties are discussed

a simple direct method to find equivalence transformations of a generalized nonlinear schrodinger equation and a generalized kdv equation a simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations by using the direct method we obtain the continuous equivalence transformations of a class of nonlinear schroequations with variable coefficients and a family of nonlinear kdv equations with variable coefficients for the nonlinear schrodinger equations with variable coefficients the equivalence transformations obtained by the direct method coincide in nature with those obtained via the infinitesimal lie criterion but our computation is much simpler

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

a characterization of first order phase transitions for superstable interactions in classical statistical mechanics we give bounds on finite volume expectations for a set of boundary conditions containing the support of any tempered gibbs state and prove a theorem connecting the behavior of gibbs states to the differentiability of the pressure for continuum statistical mechanical systems with long range superstable potentials convergence of grand canonical gibbs states is also studied

integer programming with a fixed number of variables it is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable the proof depends on methods from geometry of numbers

symmetry and similarity solutions of variable coefficients generalized zakharov kuznetsov equation abstract in this paper we propose a compatibility method of finding symmetry and similarity reduction of partial differential equations being a simple example the 2 1 dimensional variable coefficients zakharov kuznetsov equation is considered as a result we derive the symmetries and corresponding reductions of the zakharov kuznetsov equation at the same time some new similarity solutions are obtained the method can also be applied to other nonlinear evolution equations in mathematical physics

explicit solutions of the bogoyavlensky konoplechenko equation by means of the generalized direct method a relationship is constructed between the new solutions and the old ones of the bogoyavlensky konoplechenko equation based on the relationship a new solution is obtained by using a given solution of the equation the symmetry is also obtained for the bk equation then we get the reductions using the symmetry and give some exact solutions of the bk equation

quasi periodic solutions for some 2 1 dimensional integrable models generated by the jaulent miodek hierarchy some 2 1 dimensional integrable models including the modified kadomtsev petviashvili equation generated by the jaulent miodek hierarchy are investigated with the help of the jaulent miodek eigenvalue problem these 2 1 dimensional integrable models are separated into compatible hamiltonian systems of ordinary differential equations using the generating function flow method the involutivity and the functional independence of the integrals are proved the abel jacobi coordinates are introduced from which the quasi periodic solutions for these 2 1 dimensional integrable models are derived by resorting to the riemann theta functions pacs number 0230j

boosted kz and lll algorithms there exist two issues among popular lattice reduction algorithms that should cause our concern the first one is korkine zolotarev kz and lenstra lenstra lovasz lll algorithms may increase the lengths of basis vectors the other is kz reduction suffers worse performance than minkowski reduction in terms of providing short basis vectors despite its superior theoretical upper bounds to address these limitations we improve the size reduction steps in kz and lll to set up two new efficient algorithms referred to as boosted kz and lll for solving the shortest basis problem with exponential and polynomial complexity respectively both of them offer better actual performance than their classic counterparts and the performance bounds for kz are also improved we apply them to designing integer forcing if linear receivers for multi input multioutput communications our simulations confirm their rate and complexity advantages

reduced and fixed complexity variants of the lll algorithm for communications the lenstra lenstra lovasz lll algorithm is a popular lattice reduction algorithm in communications in this paper variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed specifically the use of effective lll reduction for lattice decoding is presented where size reduction is only performed for pairs of consecutive basis vectors its average complexity measured by the number of floating point operations and averaged over i i d standard normal lattice bases is shown to be o n 3 log n where n is the lattice dimension this average complexity is an order lower than previously thought to address the issue of variable complexity of the lll algorithm two fixed complexity approximations are proposed one is fixed complexity effective lll for which the first vector of the basis is proven to be bounded in length the other is fixed complexity lll with deep insertion which is shown to be closely related to the well known v blast algorithm such fixed complexity structures are much desirable in hardware implementation since they allow straightforward constant throughput implementation

fixed complexity lll algorithm a common technique to perform lattice basis reduction is the lenstra lenstra lovasz lll algorithm an implementation of this algorithm in real time systems suffers from the problem of variable run time and complexity this correspondence proposes a modification of the lll algorithm the signal flow is altered to follow a deterministic structure which promises to obtain an easier implementation as well as a fixed execution time known in advance in the case of a maximum number of iterations as it is likely in real time systems our modification clearly outperforms the original lll algorithm as far as the quality of the reduced lattice basis is concerned

similarity reduction and explicit solutions for the variable coefficient coupled burger s equations abstract by means of the compatibility method the symmetry and the optimal system of the variable coefficient coupled burger s equations are obtained in addition six types of similarity reduction and a lot of explicit solutions to this equations are presented

ergodicity for the stochastic dynamics of quasi invariant measures with applications to gibbs states the convex set maof quasi invariant measures on a locally convex spaceewith given shift radon nikodym derivatives i e cocycles a atk k k0 t ris analyzed the extreme points of maare characterized and proved to be non empty a specification of lattice type is constructed so that macoincides with the set of the corresponding gibbs states as a consequence via a well known method due to dynkin and follmer a unique representation of an arbitrary element in main terms of extreme ones is derived furthermore the corresponding classical dirichlet forms e d e and their associated semigroups t t t 0onl2 e are discussed under a mild positivity condition it is shown that mais extreme if and only if e d e is irreducible or equivalently t t t 0is ergodic this implies time ergodicity of associated diffusions applications to gibbs states of classical and quantum lattice models as well as those occuring in euclidean quantum field theory are presented in particular it is proved that the stochastic quantization of a guerra rosen simon gibbs state on d r2 ininfinite volumewith polynomial interaction is ergodic if the gibbs state is extreme i e is a pure phase which solves a long standing open problem

lattice reduction aided broadcast precoding a precoding scheme for multiuser broadcast communications is described which fills the gap between the low complexity tomlinson harashima precoding and the sphere decoder based system of peel et al simulation results show that replacing the closest point search with the babai approximation the full diversity order supported by the channel is available to each user as in the system of peel et al and unlike tomlinson harashima precoding which suffers some diversity penalty the complexity of the scheme is similar to that of tomlinson harashima precoding