whittaker pairs for the virasoro algebra and the gaiotto bonelli maruyoshi tanzini states whittaker modules for two families of whittaker pairs related to the subalgebras of the virasoro algebra generated by lr l2r and l1 ln are analyzed the structure theorems for the corresponding universal whittaker modules are proved and some of their consequences are derived all the gaiotto e print arxiv 0908 0307 and the bonelli maruyoshi tanzini j high energy phys 1202 031 2012 10 1007 jhep02 2012 031 states in an arbitrary virasoro algebra verma module are explicitly constructed

superconvergence and a posteriori error estimates of splitting positive definite mixed finite element methods for elliptic optimal control problems in this paper we investigate superconvergence and a posteriori error estimates of splitting positive definite mixed finite element methods for elliptic optimal control problems the presented scheme is independent symmetric and positive definite for the state variables and the adjoint state variables moreover the matching relation i e lbb condition between the mixed element spaces v h and wh is not necessary thus we can choose the approximation spaces more flexibly in order to derive the superconvergence we will use classical mixed finite element spaces the state and co state are approximated by the lowest order raviart thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions at first we derive some superconvergence properties for the control variable the state variables and the adjoint state variables then using a recovery operator we obtain a superconvergence result for the control variable next combining energy approach with postprocessing method we derive a posteriori error estimates for optimal control problems we will show that the method does not involve the jump residuals which make the analysis simpler finally a numerical example is given to demonstrate the theoretical results on superconvergence

whittaker modules over virasoro like algebra in this paper we study whittaker modules over virasoro like algebra relative to some total order we determine all whittaker vectors and the irreducibilities of the universal whittaker modules for the reducible ones we determine their unique maximal submodules and the corresponding irreducible quotient modules are just those modules constructed by batra et al j algebra 322 12 4163 4180 2009 using their results we can deduce more properties on the maximal submodules and irreducible modules

approximation of sparse controls in semilinear equations by piecewise linear functions semilinear elliptic optimal control problems involving the l 1 norm of the control in the objective are considered a priori finite element error estimates for piecewise linear discretizations for the control and the state are proved these are obtained by a new technique based on an appropriate discretization of the objective function numerical experiments confirm the convergence rates

whittaker vectors of the virasoro algebra in terms of jack symmetric polynomial abstract we give an explicit formula of whittaker vector for virasoro algebra in terms of the jack symmetric functions our fundamental tools are the feigin fuchs bosonization and the split expression of the calogero sutherland model given by awata matsuo odake and shiraishi

a class of algebras similar to the enveloping algebra of sl 2 fix f e c x define r c a b h subject to the relations ha ah a hb bh b ab ba f h we study these algebras for different f and in particular show how they are similar to and different from u sl 2 the enveloping algebra of sl 2 c there is a notion of highest weight modules and a category a for such r for each n 0 if f x x 1 n l xn 1 then r has precisely n simple modules in each finite dimension and every finite dimensional r module is semisimple

a new family of modules over the virasoro algebra abstract in this paper we constructed a new family of virasoro modules h parameterized by complex numbers 0 c and a polynomial h t they are a special type of modules on which the non central cartan part acts freely of infinite rank these modules are natural generalizations of the modules defined and studied in 5 11 and 19 we determine the sufficient and necessary conditions for them to be irreducible when they are reducible we also determine all their maximal submodules and corresponding simple quotients explicitly for some special cases we can determine all submodules

a priori and a posteriori error estimates of h 1 galerkin mixed finite element methods for elliptic optimal control problems in this paper we investigate numerical approximations of h 1 galerkin mixed finite element methods for elliptic optimal control problems the presented scheme is independent symmetric and positive definite for the state variables and the adjoint state variables moreover the matching relation i e lbb condition between the mixed element spaces v h and w h is not necessary thus we can choose the approximation spaces more flexibly the state and co state are approximated by the lowest order raviart thomas mixed finite element spaces and the standard finite element spaces the control variable is approximated by piecewise constant functions we derive a priori and a posteriori error estimates for the control variable the state variables and the adjoint state variables finally some numerical examples are given to demonstrate the theoretical results about a priori error estimates

error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems abstract in this paper we investigate error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems the gradient for our method belongs to the square integrable space instead of the classical h div space the state and co state are approximated by the p 0 2 p 1 velocity pressure pair and the control variable is approximated by piecewise constant functions first we derive a priori error estimates in h 1 norm for the state and the co state scalar functions a priori error estimates in l 2 2 norm for the state and the co state vector functions and a priori error estimates in l 2 norm for the control function then using postprocessing projection operator we derive a superconvergence result for the control variable next we get a priori error estimates in l 2 norm for the state and the co state scalar functions finally a numerical example is given to demonstrate the theoretical results

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

a finite element method for elliptic optimal control problem on a non convex polygon with corner singularities abstract in this paper we study a finite element method overcoming corner singularities for elliptic optimal control problem posed on a polygon based on a corner singularity decomposition of singular solution for the associated elliptic system we derive an extraction formula for coefficients of singular parts called stress intensity factors and introduce a finite element discretization for regular parts of the solution pair furthermore we analyze the finite element solutions in l 2 and h 1 norms by numerical experiments we confirm the efficiency and reliability of the proposed method

whittaker modules for uq sl2 abstract we define and study the class of whittaker modules for the quantum enveloping algebra u q sl 2 of sl 2 one of our main results describes an arbitrary whittaker module as a quotient of u q sl 2 from this description we determine precise criteria for when a whittaker module is simple as well as a decomposition of an arbitrary whittaker module into indecomposable submodules we also prove that the annihilator ann u q sl 2 v of a whittaker module v is generated by its intersection with the center of u q sl 2 this is the analogue of a classical result in the lie algebra setting due to kostant

new elliptic projections and a priori error estimates of h1 galerkin mixed finite element methods for optimal control problems governed by parabolic integro differential equations in this paper we discuss a priori error estimates of h1 galerkin mixed finite element methods for optimal control problems governed by parabolic integro differential equations the state variables and co state variables are approximated by the lowest order raviart thomas mixed finite element and linear finite element and the control variable is approximated by piecewise constant functions both semidiscrete and fully discrete schemes are considered based on some new elliptic projections we derive a priori error estimates for the control variable the state variables and the adjoint state variables the related a priori error estimates for the new projections error are also established a numerical example is given to demonstrate the theoretical results

a class of simple weight modules over the twisted heisenberg virasoro algebra a class of weight modules m v a over the twisted heisenberg virasoro h are constructed which includes modules of intermediate series where v is an hr d module and a is a complex number we give the necessary and sufficient conditions under which these modules are simple and also determine all the equivalent simple modules in this class moreover we show that simple modules in this class are new finally we construct a class of new simple non weight h modules

simple restricted modules for neveu schwarz algebra abstract in this paper we give a construction of simple modules generalizing both highest weight and whittaker modules for the neveu schwarz algebra in the spirit of the work of mazorchuk and zhao on simple virasoro modules we establish a 1 1 correspondence between simple restricted neveu schwarz modules and simple modules of a family of finite dimensional solvable lie superalgebras associated to the neveu schwarz algebra moreover for two of these superalgebras all simple modules are classified

on the diffusive nature of entropy flow in infinite systems remarks to a paper by guo papanicolau varadhan the hydrodynamic behaviour of interacting diffusion processes is investigated by means of entropy free energy arguments the methods of 13 are simplified and extended to infinite systems including a case of anharmonic oscillators in a degenerate thermal noise following 14 15 and 3 5 we derive a priori bounds for the rate of entropy production in finite volumes as the size of the whole system is infinitely extended the flow of entropy through the boundary is controlled in much the same way as energy flow in diffusive systems 4

regular nilpotent elements and quantum groups we suggest new realizations of quantum groups uq corresponding to complex simple lie algebras and of affine quantum groups these new realizations are labeled by coxeter elements of the corresponding weyl group and have the following key feature the natural counterparts of the subalgebras u where is a maximal nilpotent subalgebra possess non singular characters

asymptotic equivalence of fluctuation fields for reversible exclusion processes with speed change on considere des processus d exclusion reversibles stationnaires avec changement de vitesse et on etudie la forme asymptotique des champs de fluctuation

moduli spaces of curves and representation theory we establish a canonical isomorphism between the second cohomology of the lie algebra of regular differential operators on x of degree 1 and the second singular cohomology of the moduli space hat f g 1 of quintuples c p z l wherec is a smooth genusg riemann surface p a point onc z a local parameter atp l a degreeg 1 line bundle onc and a class of local trivializations ofl atp which differ by a non zero factor the construction uses an interplay between various infinite dimensional manifolds based on the topological spaceh of germs of holomorphic functions in a neighborhood of 0 in x and related topological spaces the basic tool is a canonical map from hat f g 1 to the infinite dimensional grassmannian of subspaces ofh which is the orbit of the subspaceh of holomorphic functions on x vanishing at under the group auth as an application we give a lie algebraic proof of the mumford formula n 6n2 6n 1 1 where n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg whose fiber overc is the space of differentials of degreen onc

on the hydrodynamic limit of a ginzburg landau lattice model the law of large numbers in arbitrary dimensions a lattice system of interacting diffusion processes is investigated the evolution is attractive and time reversible the spin satisfies a conservation law it is shown that the rescaled spin field converges in probability to the corresponding solution to a nonlinear diffusion equation

nonlinear diffusion limit for a system with nearest neighbor interactions we consider a system of interacting diffusions the variables are to be thought of as charges at sites indexed by a periodic one dimensional lattice the diffusion preserves the total charge and the interaction is of nearest neighbor type with the appropriate scaling of lattice spacing and time a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density

whittaker modules for heisenberg algebras and imaginary whittaker modules for affine lie algebras abstract we classify the irreducible whittaker modules for finite and infinite dimensional heisenberg algebras and for the lie algebra obtained by adjoining a degree derivation to an infinite dimensional heisenberg algebra we use these modules to construct a new class of modules for non twisted affine lie algebras which we call imaginary whittaker modules we show that the imaginary whittaker modules of non zero level are irreducible

error estimates of mixed methods for optimal control problems governed by parabolic equations in this paper we investigate the error estimates for the solutions of parabolic optimal control problem by mixed finite element methods the state and co state are approximated by the lowest order raviart thomas mixed finite element spaces and the control is approximated by piecewise constant functions the convergence for the states co states and the control is demonstrated copyright 2008 john wiley sons ltd

robust error estimates for the finite element approximation of elliptic optimal control problems in this paper we consider the finite element approximation of an elliptic optimal control problem based on an assumption on the adjoint state of the continuous problem with a small parameter which represents a regularization of the bang bang type control problem we derive robust a priori error estimates for optimal control and state and a posteriori error estimate is also presented numerical experiments confirm our theoretical results

new simple modules for the heisenberg virasoro algebra abstract we construct a large class of simple modules for the heisenberg virasoro algebra these modules are determined by the simple modules over the finite dimensional quotient algebras of certain natural subalgebras the known simple modules such as the highest weight modules and whittaker modules are included in particular we recover one of the main results of billig 2003 in 3 and reobtain the simplicity of the verma modules in a special case of arbarello et al 1988 in 1 we also characterize a large subclass of these modules as simple modules with locally finite actions of elements in certain positive part

the gradient condition for one dimensional symmetric exclusion processes for every gibbs measure on the one dimensional lattice z with translation invariant potential of finite range an exchange rate for one dimensional lattice gas which satisfy both the detailed balance condition relative to the gibbs measure and the gradient condition is constructed

l infty estimates for approximated optimal control problems an optimal control problem for a two dimensional elliptic equation is investigated with pointwise control constraints this paper is concerned with discretization of the control by piecewise linear functions the state and the adjoint state are discretized by linear finite elements approximation of order h in the l infty norm is proved in the main result

whittaker modules for the schrodinger witt algebra in this paper whittaker modules for the schrodinger witt algebra sv are defined the whittaker vectors and the irreducibility of the whittaker modules are studied sv has a triangular decomposition according to its cartan subalgebra h sv sv h sv for any lie algebra homomorphism sv c we can define whittaker modules of type when is nonsingular the whittaker vectors the irreducibility and the classification of whittaker modules are completely determined when is singular by constructing some special whittaker vectors we find that the whittaker modules are all reducible moreover we get some more precise results for special

a priori and a posteriori error estimates of h 1 galerkin mixed finite element methods for optimal control problems governed by pseudo hyperbolic integro differential equations abstract in this paper we investigate a priori and a posteriori error estimates of h1 galerkin mixed finite element methods for optimal control problems governed by pseudo hyperbolic integro differential equations the state variables and co state variables are approximated by the lowest order raviart thomas mixed finite element and linear finite element and the control variable is approximated by piecewise constant functions based on two new elliptic projections we derive a priori error estimates both for the control variable the state variable and the co state variable the related a priori error estimates for the new projections error are also established moreover a posteriori error estimates for all variables are derived via energy method such a posteriori error estimates which are apparently not available in the literature are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem

quasi whittaker modules for the schrodinger algebra abstract in this paper we construct a class of new modules for the schrodinger algebra s called quasi whittaker modules different from 30 the quasi whittaker module is not induced by the borel subalgebra of the schrodinger algebra related with the triangular decomposition but by its heisenberg subalgebra h we prove that a simple s module v is a quasi whittaker module if and only if v is a locally finite h module furthermore we classify simple quasi whittaker modules by central character of u s and their quasi whittaker functions finally we characterize arbitrary quasi whittaker modules

nonlinear fluctuations of weakly asymmetric interacting particle systems we introduce what we call the second order boltzmann gibbs principle which allows one to replace local functionals of a conservative one dimensional stochastic process by a possibly nonlinear function of the conserved quantity this replacement opens the way to obtain nonlinear stochastic evolutions as the limit of the fluctuations of the conserved quantity around stationary states as an application of this second order boltzmann gibbs principle we introduce the notion of energy solutions of the kpz and stochastic burgers equations under minimal assumptions we prove that the density fluctuations of one dimensional stationary weakly asymmetric conservative particle systems are sequentially compact and that any limit point is given by energy solutions of the stochastic burgers equation we also show that the fluctuations of the height function associated to these models are given by energy solutions of the kpz equation in this sense unfortunately we lack a uniqueness result for these energy solutions we conjecture these solutions to be unique and we show some regularity results for energy solutions of the kpz burgers equation supporting this conjecture

optimal control of the stokes equations a priori error analysis for finite element discretization with postprocessing an optimal control problem for 2d and 3d stokes equations is investigated with pointwise control constraints this paper is concerned with the discretization of the control by piecewise constant functions the state and the adjoint state are discretized by finite element schemes in the paper a postprocessing strategy is suggested which allows for significant improvement of the accuracy

adaptive finite elements for elliptic optimization problems with control constraints in this paper we develop a posteriori error estimates for finite element discretization of elliptic optimization problems with pointwise inequality constraints on the control variable we derive error estimators for assessing the discretization error with respect to the cost functional as well as with respect to a given quantity of interest these error estimators provide quantitative information about the discretization error and guide an adaptive mesh refinement algorithm allowing for substantial saving in degrees of freedom the behavior of the method is demonstrated on numerical examples

decay of correlations under dobrushin s uniqueness condition and its applications an estimate on the correlation of functionals of gibbs fields satisfying dobrushin s uniqueness condition is given as a consequence a result of gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole dobrushin uniqueness region applications to the central limit theorem and the second derivative of the pressure are also given

a c0 interior penalty method for the dirichlet control problem governed by biharmonic operator an energy space based dirichlet boundary control problem governed by biharmonic equation is investigated and subsequently a c0 interior penalty method is proposed and analyzed an abstract a priori error estimate is derived under the minimal regularity conditions the abstract error estimate guarantees optimal order of convergence whenever the solution is sufficiently regular further an optimal order l2 norm error estimate is derived numerical experiments illustrate the theoretical findings

whittaker modules for the twisted heisenberg virasoro algebra we define whittaker modules for the twisted heisenberg virasoro algebra and obtain several results from the classical setting including a classification of simple whittaker modules by central characters