the wasserstein distance and approximation theorems by an extension of the idea of the multivariate quantile transform we obtain an explicit formula for the wasserstein distance between multivariate distributions in certain cases for the general case we use a modification of the definition of the wasserstein distance and determine optimal markov constructions we give some applications to the problem of approximation of stochastic processes by simpler ones as e g weakly dependent processes by independent sequences and finally determine the optimal martingale approximation to a given sequence of random variables the doob decomposition gives only the one step optimal approximation

q epsilon tensor for quantum and braided spaces the machinery of braided geometry introduced previously is used now to construct the e totally antisymmetric tensor on a general braided vector space determined by r matrices this includes natural q euclidean and q minkowski spaces the formalism is completely covariant under the corresponding quantum group such as soq 4 or soq 1 3 the hodge operator and differentials are also constructed in this approach

the monge ampere equation and its link to optimal transportation we survey old and new regularity theory for the monge ampere equation show its connection to optimal transportation and describe the regularity properties of a general class of monge ampere type equations arising in that context

multi to one dimensional optimal transport we consider the monge kantorovich problem of transporting a probability density on m to another on the line so as to optimize a given cost function we introduce a nestedness criterion relating the cost to the densities under which it becomes possible to solve this problem uniquely by constructing an optimal map one level set at a time this map is continuous if the target density has connected support we use level set dynamics to develop and quantify a local regularity theory for this map and the kantorovich potentials solving the dual linear program we identify obstructions to global regularity through examples more specifically fix probability densities f and g on open sets x m and y n with m n 1 consider transporting f onto g so as to minimize the cost s x y we give a nondegeneracy condition on s c1 1 that ensures the set of x paired with g a e y y lie in a codimension n submanifold of x specializing to the case m n 1 we discover a nestedness criterion relating s to f g that allows us to construct a unique optimal solution in the form of a map f x y when s c2 w3 1 and g and f are bounded the kantorovich dual potentials u satisfy cloc1 1 y and the normal velocity v of f 1 y with respect to changes in y is given by v x syy dxsy x f x positivity of v locally implies a lipschitz bound on f moreover c2 if f 1 y intersects x c1 transversally on subsets where this nondegeneracy positivity and transversality can be quantified for each integer r 1 the norms of u cr 1 1 and f cr 1 are controlled by these bounds g log f x cr 1 1 x w2 1 s cr 1 1 and the smallness of f 1 y we give examples showing regularity extends from x to part of x but not from y to y we also show that when s remains nested for all f g the problem in m reduces to a supermodular problem in 2017 wiley periodicals inc

on the monotonicity of optimal transportation plans abstract we obtain analytical properties of the maps that give optimal transportation plans for the l 2 wasserstein distance we take advantage of the monotonicity of such optimal transportation plans to discuss their measurability and continuity as a main result of independent interest we obtain the a e continuity of monotone in the sense of zarantonello operators

quantum spinors and spin groups from quantum clifford algebras a general construction of multiparametric quantum spinors and corresponding quantum groups associated to pseudo euclidean spaces is presented and their homomorphism to the respective groups is discussed this construction is based on a quantum clifford algebra and is described in detail for involutive pure twists intertwining braids for general braid operators that admit abstract volume elements a procedure is also given for deriving quantum analogues of these groups

computing the numerical radius abstract a simple algorithm is presented for computing the numerical radius of a complex matrix it is based on the power method for finding the maximum modulus eigenvalue of a hermitian matrix

multiplicativity factors for seminorms ii let s be a seminorm on an algebra a in this paper we study multiplicativity and quadrativity factors for s i e constants 0 and 0 for which s xy s x s y and s x2 s x 2 for all x y a we begin by investigating quadrativity factors in terms of the kernel of s we then turn to the question under what conditions does s have multiplicativity factors if it has quadrativity factors we show that if a is commutative then quadrativity factors imply multiplicativity factors we further show that in the noncommutative case there exist both proper seminorms and norms that have quadrativity factors but no multiplicativity factors

isoq 3 and isoq 2 1 we prove the embedding of isoq 3 isu qex 2 and isoq 2 1 islqex 2 r as algebras and give a hilbert space representation of isu qex 2

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

quantum deformation of lorentz group a one parameter quantum deformations l 2 ofsl 2 is introduced and investigated an analog of the iwasawa decomposition is proved the compact part of this decomposition coincides withs u 2 whereas the solvable part is identified as a pontryagin dual ofs u 2 it shows thats l 2 is the result of the dual version of drinfeld s double group construction applied tos u 2 the same construction applied to any compact quantum groupgc is discussed in detail in particular the explicit formulae for the haar measures on the pontryagin dualgd ofgc and on the double groupg are given we show that there exists remarkable 1 1 correspondence between representations ofg and bicovariant bimodules tensor bundles overgc the theory of smooth representations ofs l 2 is the same as that ofsl 2 clebsh gordon coefficients are however modified the corresponding tame bicovariant bimodules ons u 2 are classified an application to 4d differential calculus is presented the nonsmooth case is also discussed

notes on the wasserstein metric in hilbert spaces let x y be a pair of hilbert valued random variables for which the wasserstein distance between the marginal distributions is reached we prove that the mapping omega rightarrow x omega y omega is increasing in a certain sense moreover if y satisfies a nondegeneration condition we can take x t y with t monotone in the sense of zarantarello we apply these results to obtain a proof of the central limit theorem clt in hilbert spaces which does not make use of the clt for real valued random variables

noncommutative fields and actions of twisted poincare algebra within the context of the twisted poincare algebra there exists no noncommutative analog of the minkowski space interpreted as the homogeneous space of the poincare group quotiented by the lorentz group the usual definition of commutative classical fields as sections of associated vector bundles on the homogeneous space does not generalize to the noncommutative setting and the twisted poincare algebra does not act on noncommutative fields in a canonical way we make a tentative proposal for the definition of noncommutative classical fields of any spin over the moyal space which has the desired representation theoretical properties we also suggest a way to search for noncommutative minkowski spaces suitable for studying noncommutative field theory with deformed poincare symmetries

on eigenvalues and boundary curvature of the numerical range abstract let a be an n n matrix by donoghue s theorem all corner points of its numerical range w a belong to the spectrum a it is therefore natural to expect that more generally the distance from a point p on the boundary w a of w a to a should be in some sense bounded by the radius of curvature of w a at p we establish some quantitative results in this direction

operator norms multiplicativity factors and c numerical radii abstract let v be a normed vector space over c let b v denote the algebra of linear bounded operators on v and let n be an arbitrary seminorm or norm on b v in this paper we discuss multiplicativity factors for n i e constants 0 for which n n is submultiplicative we find that while in the finite dimensional case nontrivial indefinite seminorms have no multiplicativity factors and norms do have multiplicativity factors in the infinite dimensional case n may or may not have such factors our results are then applied in order to compute multiplicativity factors for certain generalizations of the classical numerical radius called c numerical radii this is done with the help of a combinatorial inequality which seems to be of independent interest

quantum instantons with classical moduli spaces we introduce a quantum minkowski space time based on the quantum group su 2 q extended by a degree operator and formulate a quantum version of the anti self dual yang mills equation we construct solutions of the quantum equations using the classical adhm linear data and conjecture that up to gauge transformations our construction yields all the solutions we also find a deformation of penrose s twistor diagram giving a correspondence between the quantum minkowski space time and the classical projective space p 3

complex symmetric matrices with strongly stable iterates we study complex valued symmetric matrices a simple expression for the spectral norm of such matrices is obtained by utilizing a unitarily congruent invariant form consequently we provide a sharp criterion for identifying those symmetric matrices whose spectral norm does not exceed one such strongly stable matrices are usually sought in connection with convergent difference approximations to partial differential equations as an example we apply the derived criterion to conclude the strong stability of a lax wendroff scheme

from semidiscrete to fully discrete stability of runge kutta schemes by the energy method the integration of semidiscrete approximations for time dependent problems is encountered in a variety of applications the runge kutta rk methods are widely used to integrate the ode systems which arise in this context resulting in large ode systems called methods of lines these methods of lines are governed by possibly ill conditioned systems with a growing dimension consequently the naive spectral stability analysis based on scalar eigenvalues arguments may be misleading instead we present here a stability analysis of rk methods for well posed semidiscrete approximations based on a general energy method we review the stability question for such rk approximations and highlight its intricate dependence on the growing dimension of the problem in particular we prove the strong stability of general fully discrete rk methods governed by coercive approximations we conclude with two nontrivial examples which demonstrate the versatility of our approach in the context of general systems of convection diffusion equations with variable coefficients a straightforward implementation of our results verify the strong stability of rk methods for local finite difference schemes as well as global spectral approximations since our approach is based on the energy method which is carried in the physical space and since it avoids the von neumann analysis which is carried in the dual fourier space we are able to easily adapt additional extensions due to nonperiodic boundary conditions general geometries etc

multiplicativity factors for c numerical radii abstract for matrices a c c n x n the c numerical radius of a is the nonnegative quantity r c a max tr cu au uunitary this generalizes the classical numerical radius r a it is known that r c constitutes a norm on c n x n if and only if c is nonscalar and tr c 0 for all such c we obtain multiplicativity factors for r c i e constant 0 for which r c is submultiplicative on c n x n

q lorentz group and braided coaddition on q minkowski space we present a new version ofq minkowski space which has both a coaddition law and anslq 2 decomposition the additive structure forms a braided group rather than a quantum one in the process we obtain aq lorentz group which coacts covariantly on thisq minkowski space

a class of seminorms on function algebras abstract let a be a function algebra on a set t in this paper we study seminorms on a of the form sc x cx where c 0 c a is a fixed element and is the sup norm on t we begin by proving that under suitable assumptions elements c d a satisfy c d on t if and only if for some p 0 b of a these results are then used in order to study multiplicativity and quadrativity factors for sc on b i e constants 0 and 0 for which sc xy sc x sc y and sc x2 sc x 2 for all x y b finally for a family t of functions in a we define the seminorm s f x sup sf x f f and provide conditions under which s f has multiplicativity and quadrativity factors by exhibiting an element c a such that s f s c on a

the numerical range of a nonnegative matrix abstract we offer an almost self contained development of perron frobenius type results for the numerical range of an irreducible nonnegative matrix rederiving and completing the previous work of issos nylen and tam and tam and yang on this topic we solve the open problem of characterizing nonnegative matrices whose numerical ranges are regular convex polygons with center at the origin some related results are obtained and some open problems are also posed

free boundaries in optimal transport and monge ampere obstacle problems given compactly supported 0 f g 2 l 1 r n the problem of trans porting a fraction m min kfkl1 kgkl1 of the mass of f onto g as cheaply as possible is considered where cost per unit mass transported is given by a cost function c typically quadratic c x y x y 2 2 this question is shown to be equivalent to a double obstacle problem for the monge ampere equation for which sucient conditions are given to guarantee uniqueness of the solution such as f vanishing on sptg in the quadratic case the part of f to be transported increases monotonically with m and if sptf and sptg are separated by a hyperplane h then this part will separated from the balance of f by a semiconcave lipschitz graph over the hyperplane if f f and g g are bounded away from zero and infinity on separated strictly convex domains r n for the quadratic cost this graph is shown to be a c 1 loc hypersurface in whose normal coincides with the direction transported the optimal map between f and g is shown to be holder continuous up to this free bound ary and to those parts of the fixed boundary which map to locally convex parts of the path connected target region

braided affine geometry and q analogs of wave operators the main goal of this review is to compare different approaches to constructing the geometry associated with a hecke type braiding in particular with that related to the quantum group uq sl n we place emphasis on the affine braided geometry related to the so called reflection equation algebra rea all objects of such a type of geometry are defined in the spirit of affine algebraic geometry via polynomial relations on generators we begin by comparing the poisson counterparts of quantum varieties and describe different approaches to their quantization also we exhibit two approaches to introducing q analogs of vector bundles and defining the chern connes index for them on quantum spheres in accordance with the serre swan approach the q vector bundles are treated as finitely generated projective modules over the corresponding quantum algebras besides we describe the basic properties of the rea used in this construction and compare different ways of defining q analogs of partial derivatives and differentials on the rea and algebras close to them in particular we present a way of introducing a q differential calculus via koszul type complexes the elements of the q calculus are applied to defining q analogs of some relativistic wave operators

stability condition for difference schemes for parabolic systems recently goldberg studied in m goldberg siam j numer anal 35 1998 pp 478 493 m goldberg siam j numer anal 35 1998 pp 1995 2003 stability conditions of a well known family of difference schemes for the following multidimensional parabolic system of second order frac partial bu bf x t partial t sum 1 le p le q le s a pq frac partial 2 bu bf x t partial x p partial x q sum 1 le p le s b p frac partial bu bf x t partial x p c bu bf x t here we present a modified stability condition for the above problem and prove that this condition is optimal in some sense

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

quantum group covariant noncommutative geometry an algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the r matrix approach to the theory of quantum groups is given structure groups are considered taking values in the quantum groups the notion of noncommutative connections and curvatures is introduced transforming as comodules under the local coaction of the structure group that is an exterior extension of glq n these noncommutative connections and curvatures generate glq n covariant quantum algebras for these algebras combinations of generators are found which are coinvariants under the local coaction of the exterior extension of the quantum group and one can formally consider these coinvariants as noncommutative images of the lagrangians for the topological chern simons models non abelian gauge theories and the einstein gravity also an explicit realization of such covariant quantum algebras is presented via the investigation of the coset construction glq n 1 glq n glq 1

wigner eckart theorem for the quantum group uq n tensor operators transforming under finite dimensional irreducible representations of the quantum group uq n are defined using them tensor operators transforming under representations of the quantum algebra uq u n are introduced the wigner eckart theorem on matrix elements of tensor operators defined is derived

optimal solution of a monge kantorovitch transportation problem abstract suppose that p and q are probabilities on a separable banach space e it is known that if p q satisfies certain regularity conditions and a random variable x has law p then there exists a function f e e such that the function f x has the law q and the random pair x f x is an optimal coupling for the monge kantorovitch problem in this paper we provide an approximation of the function f when the law q is discrete thenwe extend this main result to any law q the proofs are based on a relationship between optimal couplings and nonlinear equations

unbounded elements affiliated with c algebras and non compact quantum groups the affiliation relation that allows to include unbounded elements operators into thec algebra framework is introduced investigated and applied to the quantum group theory the quantum deformation of the two fold covering of the group of motions of euclidean plane is constructed a remarkable radius quantization is discovered it is also shown that the quantumsu 1 1 group does not exist on thec algebra level for real value of the deformation parameter

on joint spectral radius of commuting operators in hilbert spaces abstract our aim in this paper is to give a new formula of the joint spectral radius of commuting d tuples of operators on a complex hilbert space also we show that r t t for a commuting d tuple of operators t where r t and t denote respectively the joint spectral radius and the joint numerical radius of t this generalizes the well known relation between the spectral and the numerical radii of hilbert space operators which is proved in 10

a bipartite separable ball and its applications in this paper based on a matrix norm we first present a ball of separable un normalized states around the identity matrix for the bipartite quantum system which is larger than the separable ball in frobenius norm then the proposed ball is used to get not only simple sufficient conditions for the separability of pseudopure states and the states with strong positive partial transposes but also a separable ball centered at the identity matrix for the multipartite quantum system

the quantized universal enveloping algebras uq iso n uq e 3 1 and uq e n and the representation theory of uq e 3 we construct the hopf algebras of uq iso n and uq iso 3 1 as regular functionals on their function algebras examine the possible involutions on these objects derive the quantized euclidean algebras uq e n and finally give the irreducible representations of uq e 3 depending on two parameters which fix the value of the casimir operators

a note on soderlind s conjecture abstract let f be a lipschitz operator from a path connected set d c m into c m with the lub lipschitz constant l f and the so called gerschgorim range radius r f subordinate to a given vector norm of c m in 1986 numer math 50 1986 27 soderlind s conjectured that if r f l f then there exists a new vector norm of c m such that the induced lub lipschitz constant l f r f in this paper we affirmatively prove soderlind s conjecture for several class of lipschitz operators f whilst we construct a counterexample to disprove soderlind s conjecture

a fixed point approach to barycenters in wasserstein space abstract let p 2 a c be the set of borel probabilities on r d with finite second moment and absolutely continuous with respect to lebesgue measure we consider the problem of finding the barycenter or frechet mean of a finite set of probabilities 1 k p 2 a c with respect to the l 2 wasserstein metric for this task we introduce an operator on p 2 a c related to the optimal transport maps pushing forward any p 2 a c to 1 k under very general conditions we prove that the barycenter must be a fixed point for this operator and introduce an iterative procedure which consistently approximates the barycenter the procedure allows effective computation of barycenters in any location scatter family including the gaussian case in such cases the barycenter must belong to the family thus it is characterized by its mean and covariance matrix while its mean is just the weighted mean of the means of the probabilities the covariance matrix is characterized in terms of their covariance matrices 1 k through a nonlinear matrix equation the performance of the iterative procedure in this case is illustrated through numerical simulations which show fast convergence towards the barycenter

d 3 real quantum conformal algebra using the equivalence of o 3 2 with d 3 conformal algebras we describe the d 3 quantum conformal algebra by the q deformed cartan weyl basis of a real hopf algebra uq o 3 2 with mod q mod 1 the universal r matrix written in terms of d 3 conformal generators is investigated the hopf subalgebras of uq o 3 2 and their quasitriangularity are discussed the analogies with d 4 quantum conformal algebra are pointed out

on the structure of inhomogeneous quantum groups we investigate inhomogeneous quantum groups g built from a quantum group h and translations the corresponding commutation relations contain inhomogeneous terms under certain conditions which are satisfied in our study of quantum poincare groups 12 we prove that our construction has correct size find the r matrices and the analogues of minkowski space for g

trimmed comparison of distributions this article introduces an analysis of similarity of distributions based on the l2 wasserstein distance between trimmed distributions our main innovation is the use of the impartial trimming methodology already considered in robust statistics which we adapt to this setup instead of simply removing data at the tails to provide some robustness to the similarity analysis we develop a data driven trimming method aimed at maximizing similarity between distributions dissimilarity is then measured in terms of the distance between the optimally trimmed distributions we provide illustrative examples showing the improvements over previous approaches and give the relevant asymptotic results to justify the use of this methodology in applications

on the classification of quantum poincare groups using the general theory of 10 quantum poincare groups without dilatations are described and investigated the description contains a set of numerical parameters which satisfy certain polynomial equations for most cases we solve them and give the classification of quantum poincare groups each of them corresponds to exactly one quantum minkowski space the poincare series of these objects are the same as in the classical case we also classify possibler matrices for the fundamental representation of the group

cross products by braided groups and bosonization let h be a braided cocommutative hopf algebra in a braided monoidal category c and b a hopf algebra in c on which h acts we construct a cross product hopf algebra b formula h in c as an application we show that every b in a certain class can be converted to an equivalent ordinary hopf algebra by a process of bosonization the class includes for example all super hopf algebras the constructions respect any quasitriangular structures on b as a corollary we show that if h r is an ordinary quasitriangular hopf algebra then the smash product by the adjoint action of h on itself had formula h can be given the structure of a hopf algebra we prove a similar result for any hopf algebra to which a quasitriangular hopf algebra maps

deformed minkowski spaces classification and properties using general but simple covariance arguments we classify the quantum minkowski spaces for dimensionless deformation parameters this requires a previous analysis of the associated lorentz groups which reproduces a previous classification by woronowicz and zakrzewski as a consequence of the unified analysis presented we give the commutation properties the deformed and central length element and the metric tensor for the different spacetime algebras

quantum deformation of the poincare supergroup and kappa deformed superspace the classical r matrix for the n 1 super poincare algebra given by lukierski et al 1993 is used to describe the graded poisson structure on the n 1 poincare supergroup the standard correspondence principle between the even odd poisson brackets and anti commutators leads to the consistent quantum deformation of the super poincare group with the deformation parameter q described by the fundamental mass parameter k k 1 in q the k deformation of n 1 superspace as dual to the k deformed supersymmetry algebra is discussed

center outward r estimation for semiparametric varma models we propose a new class of r estimators for semiparametric varma models in which the innovation density plays the role of the nuisance parameter our estimators are based on the novel concepts of mu

the euclidean hopf algebra u q e n and its fundamental hilbert space representations the euclidean hopf algebra uq en dual of fun rnq soq 1 n is constructed by realizing it as a subalgebra of the differential algebra diff rnq on the quantum euclidean space rnq in fact the previous realization g fiore commun math phys 169 475 500 1995 of uq 1 so n is extended within diff rnq through the introduction of q derivatives as generators of q translations the fundamental hilbert space representations of uq en turn out to be of highest weight type and rather simple lattice regularized versions of the classical ones the vectors of a basis of the singlet i e zero spin irrep can be realized as normalizable functions on rnq going to distributions in the limit q 1

generalized q exponentials related to orthogonal quantum groups and fourier transformations of noncommutative spaces essential prerequisites for the study of q deformed physics are particle states in position and momentum representation in order to relate x and p space by fourier transformations the appropriate q exponential series related to orthogonal quantum symmetries is constructed it turns out to be a new q special function giving rise to q plane wave solutions that transform with a noncommutative phase under translations

stable difference schemes for parabolic systems a numerical radius approach ii in this paper a numerical radius approach is taken in order to further discuss stability conditions for a well known family of finite difference schemes for the initial value problem associated with the petrowski well posed multispace dimensional parabolic system dst frac partial mathbf u mathbf x t partial t dst sum 1 leq p leq q leq s a pq dst frac partial 2 mathbf u mathbf x t partial x p partial x q sum 1 leq p leq s b p frac partial mathbf u mathbf x t partial x p c mathbf u mathbf x t noindent where a pq b p and c are constant matrices a pq being hermitian

multiplicativity factors and mixed multiplicativity abstract a number of authors have discussed multiplicativity factors associated with a single norm on an operator algebra we extend this concept to multiplicativity factors associated with three norms on spaces not necessarily algebras of bounded linear operators we generalize previous results and give several finite and infinite dimensional examples

the distance between two random vectors with given dispersion matrices for two p dimensional random vectors x and y with dispersion matrices 11 and 22 respectively we determine that covariance matrix 0 of x and y that minimizes the l2 distance between x and y there is a dual to this problem that is of interest in another context

irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras the defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms in each case it is shown that there are two types of irreducible tensor operator which may be called ordinary and twisted the consistency of the definitions is demonstrated and various consequences are deduced including generalizations of the wigner eckart theorem for both the ordinary and twisted operators also included are discussions within the regular coaction formalisms for compact quantum group algebras of inner products basis functions projection operators clebsch gordan coefficients and two types of tensor product of corepresentations the formulation of quantum homogeneous spaces for compact quantum group algebras is discussed and the defining conditions for the irreducible tensor operators associated with such quantum homogeneous spaces and with the uni

bicovariant differential calculus on quantum groups su q n and so q n following woronowicz s proposal the bicovariant differential calculus on the quantum groupssu q n andso q n is constructed a systematic construction of bicovariant bimodules by using the hat r q matrix is presented the relation between the hopf algebras generated by the linear functionals relating the left and right multiplication of these bicovariant bimodules and theq deformed universal enveloping algebras is given imposing the conditions of bicovariance and consistency with the quantum group structure the differential algebras and exterior derivatives are defined as an application the maurer cartan equations and theq analogue of the structure constants are formulated

q deformed poincare algebra theq differential calculus for theq minkowski space is developed the algebra of theq derivatives with theq lorentz generators is found giving theq deformation of the poincare algebra the reality structure of theq poincare algebra is given the reality structure of theq differentials is also found the real laplacian is constructed finally the comultiplication counit and antipode for theq poincare algebra are obtained making it a hopf algebra

irreducible unitary representations of quantum lorentz group a complete classification of irreducible unitary representations of a one parameter deformations q l 2 c 0 q 1 ofsl 2 c is given it shows that in spite of a popular belief the representation theory fors q l 2 c is not a smooth deformation of the one forsl 2 c

kappa deformation of poincare superalgebra with classical lorentz subalgebra and its graded bicrossproduct structure the kappa deformed d 4 poincare superalgebra written in hopf superalgebra form is transformed to the basis with classical lorentz subalgebra generators we show that in such a basis the kappa deformed d 4 poincare superalgebra can be written as a graded bicrossproduct we show that the kappa deformed d 4 superalgebra acts covariantly on a kappa deformed chiral superspace

on stability of staggered schemes this paper investigates the theoretical stability bound of a lagrangian staggered scheme used to solve hydrodynamics equations we present the two dimensional 2d wave equation as a possible model for this study and by using the numerical radius of the amplification matrix we prove that the family of schemes defined with two time centering parameters is limited by a nonclassical stability bound limit defined with an analytical curve we further show that 2d numerical experiments agree with this theoretical result

on the numerical radius and its applications abstract we give a brief account of the numerical radius of a linear bounded operator on a hilbert space and some of its better known properties both finite and infinite dimensional aspects are discussed as well as applications to stability theory of finite difference approximations for hyperbolic initial value problems

q deformed relativistic wave equations based on the representation theory of the q deformed lorentz and poincare symmetries q deformed relativistic wave equation are constructed the most important cases of the dirac proca rarita schwinger and maxwell equations are treated explicitly the q deformed wave operators look structurally like the undeformed ones but they consist of the generators of a noncommutative minkowski space the existence of the q deformed wave equations together with previous results on the representation theory of the q deformed poincare symmetry solve the q deformed relativistic one particle problem

complex jacobi matrices complex jacobi matrices play an important role in the study of asymptotics and zero distribution of formal orthogonal polynomials fops the latter are essential tools in several fields of numerical analysis for instance in the context of iterative methods for solving large systems of linear equations or in the study of pade approximation and jacobi continued fractions in this paper we present some known and some new results on fops in terms of spectral properties of the underlying infinite jacobi matrix with a special emphasis to unbounded recurrence coefficients here we recover several classical results for real jacobi matrices the inverse problem of characterizing properties of the jacobi operator in terms of fops and other solutions of a given three term recurrence is also investigated this enables us to give results on the approximation of the resolvent by inverses of finite sections with applications to the convergence of pade approximants

stair matrices and their generalizations with applications to iterative methods i a generalization of the successive overrelaxation method stair matrices and their generalizations are introduced some properties of the matrices are presented like triangular matrices this class of matrices provides bases of matrix splittings for iterative methods a remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation in particular a generalization of the successive overrelaxation sor method is introduced the sor theory on determination of the optimal parameter is extended to the generalized method to include a wide class of matrices the asymptotic rate of convergence of the new method is derived for hermitian positive definite matrices using bounds of the eigenvalues of jacobi matrices and numerical radius finally numerical tests are presented to corroborate the obtained results

fields of values and iterative methods abstract the performance of an iterative scheme to solve x t x c t c n n c c n is often judged by spectral properties of t if t is not normal it is however well known that only conclusions about the assymptotic behavior of an iterative method can be drawn from spectral information to anticipate the progress of the iteration after a finite number of steps the knowledge of the eigenvalues alone is often useless in addition the spectrum of t may be highly sensitive to perturbations if t is not normal an iterative method which on the basis of some spectral information is predicted to converge rapidly for t may well diverge if t is slightly perturbed in practice the convergence of the iteration x m t x m 1 c is therefore frequently measured by some norm verbar t verbar rather than by the spectral radius t but apart from the fact that norms lead to error estimates which are often too pessimistic they cannot be used to analyze more general schemes such as e g the chebyshev iterative methods here we discuss another tool to analyze the behavior of an iterative method namely the field of values w t the collection of all rayleigh quotients of t w t contains the eigenvalues of t and the numerical radius t max z w t z defines a norm on c n n the field of values represents therefore an intermediate concept to judge an iterative scheme by it is related to the spectral approach but has also certain norm properties

on the decoupling of the homogeneous and inhomogeneous parts in inhomogeneous quantum groups we show that if there exists a realization of a hopf algebra h in a h module algebra then one can split their cross product into the tensor product algebra of itself with a subalgebra isomorphic to h and commuting with this result applies in particular to the algebra underlying inhomogeneous quantum groups like the euclidean groups which are obtained as cross products of the quantum euclidean spaces qn with the quantum groups of rotation uq so n of qn for which it has no classical analogue

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159