uncertainty principles for kac algebras in this paper we introduce the notation of bi shift of biprojections in subfactor theory to unimodular kac algebras we characterize the minimizers of the hirschman beckner uncertainty principle and the donoho stark uncertainty principle for unimodular kac algebras with biprojections and prove hardy s uncertainty principle in terms of the minimizers

minimizers of the entropic uncertainty principle for locally compact quantum groups in this paper we give an alternative proof of the hirschman beckner uncertainty principle for locally compact quantum groups and characterize the minimizers of the uncertainty principles in this paper we give an alternative proof of the hirschman beckner uncertainty principle for locally compact quantum groups and characterize the minimizers of the uncertainty principles

spreading speeds and traveling waves for periodic evolution systems abstract the theory of spreading speeds and traveling waves for monotone autonomous semiflows is extended to periodic semiflows in the monostable case then these abstract results are applied to a periodic system modeling man environment man epidemics a periodic time delayed and diffusive equation and a periodic reaction diffusion equation on a cylinder

spatial dynamics of a dengue transmission model in time space periodic environment abstract this study is devoted to the investigation of dengue spread via a time space periodic reaction advection diffusion model we establish the existence of the spreading speeds and its coincidence with the minimal speed of almost pulsating waves

tannaka krein duality for compact matrix pseudogroups twisted su n groups the notion of concrete monoidalw category is introduced and investigated a generalization of the tannaka krein duality theorem is proved it leads to new examples of compact matrix pseudogroups among them we have twistedsu n groups denoted bys u n it is shown that the representation theory fors u n is similar to that ofsu n irreducible representations are labeled by young diagrams and formulae for dimensions and multiplicity are the same as in the classical case

multiresolution analysis of a class of nonstationary processes processing nonstationary signals is an important and challenging problem we focus on the class of nonstationary processes with stationary increments of an arbitrary order and place them in a multiscale framework unlike other related studies we concentrate on the discrete time analysis and derive a number of new results in addition to placing the related existing ones in the same framework we extend the study to various parametric models for which we derive the resulting multiresolution description we show that wide sense stationarity may be achieved by adequately selecting the analysis wavelet after generalizing the study to wavelet packet analysis we show that the latter possesses additional properties which are useful in the presence of other types of nonstationarities

generalized transition waves and their properties in this paper we generalize the usual notions of waves fronts and propagation speeds in a very general setting these new notions which cover all usual situations involve uniform limits with respect to the geodesic distance to a family of hypersurfaces that are parametrized by time we prove the existence of new such waves for some time dependent reaction diffusion equations as well as general intrinsic properties some monotonicity properties and some uniqueness results for almost planar fronts the classification results which are obtained under some appropriate assumptions show the robustness of our general definitions 2012 wiley periodicals inc

time periodic traveling wave solutions for periodic advection reaction diffusion systems abstract we study the existence uniqueness and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection reaction diffusion systems under certain conditions we prove that there exists a maximal wave speed c such that for each wave speed c c there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system it is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co moving frame coordinate we also show that the traveling wave solutions with wave speed c c are asymptotically stable in certain sense in addition we establish the nonexistence of time periodic traveling waves with speed c c

an uncertainty principle for unimodular quantum groups we present a generalization of hirschman s entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups as a corollary we strengthen a well known uncertainty principle for compact groups and generalize the relation to compact quantum groups of kac type we also establish the complementarity of finite dimensional quantum group algebras in the non unimodular setting we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the haar weight as the measure of uncertainty we also show that when restricted to q traces of discrete quantum groups the relative entropy with respect to the haar weight reduces to the canonical entropy of the random walk generated by the state

new methods for the existence and uniqueness of traveling waves of non monotone integro difference equations with applications abstract a class of non monotone integro difference equations are investigated it is shown that the spreading speed coincides with the minimal wave speed as well as the uniqueness of traveling waves up to translations our methods are different from those in 7 12 and rely on the priori estimate of the decay speed of wave profile and allow i to deal with the iterative map without compactness ii to incorporate the critical case which corresponds to the slowest wavefronts into consideration iii to weaken or to remove various restrictions on kernels and nonlinearities finally these results are applied to some population models

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

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

yang baxter matrix and calculi on quantum groups of a series the authors prove that the differential calculi on quantum groups of a series given in this letter and in previous papers are calculi

nonstandard comodules for quantum matrix bialgebras we carry out a construction of nonstandard matrix quantum groups comodules through a generalization of the coaction on tensor powers of a comodule this generalization amounts to consider the situation where quantum space coordinates and its endomorphism matrix entries belong to a noncommutative quadratic algebra

traveling waves and spreading speeds for time space periodic monotone systems abstract in this paper we first establish the existence of traveling waves and spreading speeds for time space periodic monotone systems with monostable structure via the poincare maps approach combined with an evolution viewpoint our construction of time space periodic wave profiles also gives rise to a family of almost pulsating waves which is a new observation in time and space periodic media we then apply the developed theory to two species competitive reaction advection diffusion systems and prove that the minimal wave speed exists and coincides with the single spreading speed for such a system no matter whether the spreading speed is linearly determinate we further obtain a set of sufficient conditions for the linear determinacy

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

correlation structure of the discrete wavelet coefficients of fractional brownian motion it is shown that the discrete wavelet coefficients of fractional brownian motion at different scales are correlated and that their auto and cross correlation functions decay hyperbolically fast at a rate much faster than that of the autocorrelation of the fractional brownian motion itself the rate of decay of the correlation function in the wavelet domain is primarily determined by the number of vanishing moments of the analyzing wavelet

uncertainty principles for locally compact quantum groups abstract in this paper we prove the donoho stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi shifts of group like projections we also prove the hirschman beckner uncertainty principle for compact quantum groups and discrete quantum groups furthermore we show hardy s uncertainty principle for locally compact quantum groups in terms of bi shifts of group like projections

on stationarizability for nonstationary 2 d random fields using discrete wavelet transforms the emphasis in this article is on the study of nonstationary two dimensional 2 d random fields with wide sense stationary increments wide sense stationary jumps and 2 d fractional brownian motion fbm fields the effort made in this work is to develop a realizable method of stationarization provided for nonstationary 2 d random fields we also present the correlation functions of the discrete wavelet transform relating to 2 d fbm fields that will decay hyperbolically fast

resampling methods for improved wavelet based multiple hypothesis testing of parametric maps in functional mri abstract two or three dimensional wavelet transforms have been considered as a basis for multiple hypothesis testing of parametric maps derived from functional magnetic resonance imaging fmri experiments most of the previous approaches have assumed that the noise variance is equally distributed across levels of the transform here we show that this assumption is unrealistic fmri parameter maps typically have more similarity to a 1 f type spatial covariance with greater variance in 2d wavelet coefficients representing lower spatial frequencies or coarser spatial features in the maps to address this issue we resample the fmri time series data in the wavelet domain using a 1d discrete wavelet transform dwt to produce a set of permuted parametric maps that are decomposed using a 2d dwt to estimate level specific variances of the 2d wavelet coefficients under the null hypothesis these resampling based estimates of the wavelet variance spectrum are substituted in a bayesian bivariate shrinkage operator to denoise the observed 2d wavelet coefficients which are then inverted to reconstitute the observed denoised map in the spatial domain multiple hypothesis testing controlling the false discovery rate in the observed denoised maps then proceeds in the spatial domain using thresholds derived from an independent set of permuted denoised maps we show empirically that this more realistic resampling based algorithm for wavelet based denoising and multiple hypothesis testing has good type i error control and can detect experimentally engendered signals in data acquired during auditory linguistic processing

brst cohomology for uq sl 2 representations a nilpotent brst operator qq is constructed for the q deformation of the universal enveloping algebra of sl 2 an associated operator rq such that qq rq cq is introduced where cq is the q deformed casimir invariant cq fe 1 2h q 1 2h 1 q the related operator qq conjugate to qq is also considered the resulting brst cohomology of uq sl 2 representations is discussed

wavelets and functional magnetic resonance imaging of the human brain the discrete wavelet transform dwt is widely used for multiresolution analysis and decorrelation or whitening of nonstationary time series and spatial processes wavelets are naturally appropriate for analysis of biological data such as functional magnetic resonance images of the human brain which often demonstrate scale invariant or fractal properties we provide a brief formal introduction to key properties of the dwt and review the growing literature on its application to fmri we focus on three applications in particular i wavelet coefficient resampling or wavestrapping of 1 d time series 2 to 3 d spatial maps and 4 d spatiotemporal processes ii wavelet based estimators for signal and noise parameters of time series regression models assuming the errors are fractional gaussian noise fgn and iii wavelet shrinkage in frequentist and bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps we conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fmri data

classification of arithmetic root systems arithmetic root systems are invariants of nichols algebras of diagonal type with a certain finiteness property they can also be considered as generalizations of ordinary root systems with rich structure and many new examples on the other hand nichols algebras are fundamental objects in the construction of quantized enveloping algebras in the noncommutative differential geometry of quantum groups and in the classification of pointed hopf algebras by the lifting method of andruskiewitsch and schneider in the present paper arithmetic root systems are classified in full generality as a byproduct many new finite dimensional pointed hopf algebras are obtained

fractal estimation from noisy data via discrete fractional gaussian noise dfgn and the haar basis the authors show that the application of the discrete wavelet transform dwt using the haar basis to the increments of fractional brownian motion fbm also known as discrete fractional gaussian noise dfgn yields coefficients which are weakly correlated and have a variance that is exponentially related to scale similar results were derived by flandrin 1989 tewfik and kim for a continuous time fbm going through a continuous wavelet transform cwt the new theoretical results justify an improvement to a fractal estimation algorithm recently proposed by wornell and oppenheim the performance of the new algorithm is compared with that of wornell and oppenheim s see ieee trans signal processing vol 40 p 611 623 mar 1992 algorithm in numerical simulation

quantum mechanics as noncommutative symplectic geometry the authors construct consistent differential calculi on the algebra generated by operators satisfying the canonical commutation relation this leads to a mathematical framework in which quantum mechanics can be understood as noncommutative symplectic geometry they point out the possibility to describe interactions geometrically as deformations of the differential calculus

quantum supergroup structure of 1 1 dimensional quantum superplane its dual and its differential calculus we show that the 1 1 dimensional quantum superplane introduced by manin is a quantum supergroup according to the faddeev reshetikhin takhtajan approach when it is extended by the inverse of the bosonic variable we then give its supermatrix element its corresponding r matrix and its hopf structure this new point of view allows us first to realize its dual hopf superalgebra starting from postulated initial pairings second we construct a right invariant differential calculus on it and then deduce the corresponding quantum lie superalgebra which as a commutation superalgebra appears classical and as hopf structure is a non cocommutative q deformed one

quantum groups acting on 4 points we classify the compact quantum groups acting on 4 points these are the quantum subgroups of the quantum permutation group q4 our main tool is a new presentation for the algebra c q4 corresponding to an isomorphism of type q4 so 1 3 the quantum subgroups of q4 are subject to a mckay type correspondence that we describe at the level of algebraic invariants

quantum groups differential calculi and the eigenvalues of the laplacian we study differential calculi over compact quantum groups in the sense of s l woronowicz our principal results are the construction of a hodge operator commuting with the laplacian the derivation of a corresponding hodge decomposition of the calculus of forms and for woronowicz first calculus the calculation of the eigenvalues of the laplacian 1

propagation dynamics for monotone evolution systems without spatial translation invariance abstract in this paper under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance then we apply the developed theory to study traveling waves and spatio temporal propagation patterns for time delayed nonlocal equations reaction diffusion equations in a cylinder and asymptotically homogeneous kpp type equations we also obtain the existence of steady state solutions and asymptotic spreading properties of solutions for a time delayed reaction diffusion equation subject to the dirichlet boundary condition

spreading speeds and traveling waves for abstract monostable evolution systems abstract this paper is devoted to the development of the theory of spreading speeds and traveling waves for abstract monostable evolution systems with spatial structure under appropriate assumptions we show that the spreading speeds coincide with the minimal wave speeds for monotone traveling waves in the positive and negative directions then we use this theory to study the spatial dynamics of a parabolic equation in a periodic cylinder with the dirichlet boundary condition a reaction diffusion model with a quiescent stage a porous medium equation in a tube and a lattice system in a periodic habitat

a monoidal approach to splitting morphisms of bialgebras the main goal of this paper is to investigate the structure of hopf algebras with the property that either its jacobson radical is a hopf ideal or its coradical is a subalgebra let us consider a hopf algebra a such that its jacobson radical j is a nilpotent hopf ideal and h a j is a semisimple algebra we prove that the canonical projection of a on h has a section which is an h colinear algebra map furthermore if h is cosemisimple too then we can choose this section to be an h h bicolinear algebra morphism this fact allows us to describe a as a generalized bosonization of a certain algebra r in the category of yetter drinfeld modules over h as an application we give a categorical proof of radford s result about hopf algebras with projections we also consider the dual situation let a be a bialgebra such that its coradical is a hopf sub bialgebra with antipode then there is a retraction of the canonical injection of h into a which is an h linear coalgebra morphism furthermore if h is semisimple too then we can choose this retraction to be an h h bilinear coalgebra morphism then also in this case we can describe a as a generalized bosonization of a certain coalgebra r in the category of yetter drinfeld modules over h

double product integrals and enriquez quantization of lie bialgebras i the quasitriangular identities let t l be the space of all tensors over a lie algebra l in which the lie bracket is obtained by taking commutators in an associative algebra we show that t l becomes a hopf algebra when equipped with a noncommutative modification of the shuffle product together with the standard coproduct a definition is given of directed double product integrals as iterated single product integrals driven by formal power series with coefficients in the tensor product of l with an appropriate associative algebra for the hopf algebra t l h of formal power series we show that elements r h of t l t l h satisfying id r h r h 13r h 23 id r h r h 13r h 12 and which are unitalized by the counit in either copy of t l can be characterized as such directed double product integrals 1 d d r h where r h is a formal power series with coefficients in l l and vanishing constant term

on an abstract competition model and applications is a map such that the coordinates of f x x2 represent the population or population densities which have evolved from the state xi x2 at a fixed time later setting yi y2 f x x2 it is natural to suppose that an increase in x coupled with a decrease in x2 results in an increase in y and a decrease in y2 and symmetrically a decrease in x1 coupled with an increase in x2 results in a decrease in yr and an increase in yz we define an order in e x e2 as follows if x xi e e x2 xi e e x1 i xi and xi i x2 then we write x1 7 1 5 4 9 x

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

spreading speeds and linear determinacy of time dependent diffusive cooperative competitive systems abstract the current paper is devoted to the study of spreading speeds and linear determinacy of diffusive cooperative competitive systems of the form u t t x a u t x f t u t x x h where h r n or z n a is a random or nonlocal dispersal operator in the cases h r n and is a discrete dispersal operator in the case h z n f t u is cooperative or competitive in u and is recurrent in t which includes f t u is periodic and almost periodic in t as special cases first the notion of spreading speed intervals for diffusive cooperative systems is introduced via the natural features of spreading speeds and some basic spreading properties are established next some principal lyapunov exponent and principal floquent bundle theory for linear cooperative systems of ordinary differential equations is developed which plays an important role in the study of spreading speeds of diffusive cooperative competitive systems with time dependence and is also of independent interest in terms of the principal lyapunov exponent and principal floquent bundle theory some upper and lower bounds for the spreading speed intervals for diffusive cooperative systems are then established under certain conditions it is proved that a diffusive cooperative system has a single spreading speed and is linearly determinant finally by transforming a diffusive competitive system to a diffusive cooperative system and applying established results for diffusive cooperative systems upper and lower bounds for the spreading speed intervals for diffusive competitive systems are obtained and linearly determinacy for such systems is discussed

wavelet analysis and synthesis of fractional brownian motion fractional brownian motion fbm offers a convenient modeling for nonstationary stochastic processes with long term dependencies and 1 f type spectral behavior over wide ranges of frequencies statistical self similarity is an essential feature of fbm and makes natural the use of wavelets for both its analysis and its synthesis a detailed second order analysis is carried out for wavelet coefficients of fbm it reveals a stationary structure at each scale and a power law behavior of the coefficients variance from which the fractal dimension of fbm can be estimated conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed consequences of discretization are considered and some connections between the wavelet point of view and previous approaches based on length measurements analysis or dyadic interpolation synthesis are briefly pointed out

pulsating fronts and front like entire solutions for a reaction advection diffusion competition model in a periodic habitat abstract this paper is devoted to the study of pulsating fronts and pulsating front like entire solutions for a reaction advection diffusion model of two competing species in a periodic habitat under certain assumptions the competition system admits a leftward and a rightward pulsating fronts in the bistable case in this work we construct some other types of entire solutions by interacting the leftward and rightward pulsating fronts some of these entire solutions behave as the two pulsating fronts approaching each other from both sides of the x axis which turn out to be unique and liapunov stable 2 dimensional manifolds of solutions furthermore the leftward and rightward pulsating fronts are on the boundary of these 2 dimensional manifolds the others behave as the two pulsating fronts propagating from one side of the x axis the faster one then invades the slower one as t these kinds of pulsating front like entire solutions then provide some new spreading ways other than pulsating fronts for two strongly competing species interacting in a heterogeneous habitat

existence and stability of time periodic traveling waves for a periodic bistable lotka volterra competition system abstract this paper is concerned with the time periodic lotka volterra competition diffusion system u t d 1 t u x x u r 1 t a 1 t u b 1 t v v t d 2 t v x x v r 2 t a 2 t u b 2 t v x r t 0 where d i t r i t a i t b i t c 2 r are t periodic functions 0 1 i 1 2 under certain conditions the system admits two stable semi trivial periodic solutions p t 0 and 0 q t and a unique coexistence periodic solution u 0 t v 0 t which is unstable and satisfies 0 u 0 t p t and 0 v 0 t q t for t 0 t in this paper we prove that the system admits a time periodic traveling wave solution u x t v x t u x c t t v x c t t connecting two periodic solutions p t 0 and 0 q t as x where c is the wave speed by using a dynamical method we show that the time periodic traveling wave solution u x c t t v x c t t is asymptotically stable and unique modulo translation for front like initial values

accelerating propagation in a recursive system arising from seasonal population models with nonlocal dispersal abstract the system of interest is defined by iterations of the poincare map of a time periodic population model with symmetric nonlocal dispersal and periodic time delay under the kpp type setting we show that the system admits the spreading speed c 0 that coincides with the minimal speed of traveling waves where c if the nonlocal dispersal kernel j is exponentially bounded and c if j is exponentially unbounded further the latter case gives rises to an accelerating propagation that the level set of solutions with compactly supported initial values locate in between two exponential functions in time

estimation of 2 d noisy fractional brownian motion and its applications using wavelets the two dimensional 2 d fractional brownian motion fbm model is useful in describing natural scenes and textures most fractal estimation algorithms for 2 d isotropic fbm images are simple extensions of the one dimensional 1 d fbm estimation method this method does not perform well when the image size is small say 32 spl times 32 we propose a new algorithm that estimates the fractal parameter from the decay of the variance of the wavelet coefficients across scales our method places no restriction on the wavelets also it provides a robust parameter estimation for small noisy fractal images for image denoising a wiener filter is constructed by our algorithm using the estimated parameters and is then applied to the noisy wavelet coefficients at each scale we show that the averaged power spectrum of the denoised image is isotropic and is a nearly 1 f process the performance of our algorithm is shown by numerical simulation for both the fractal parameter and the image estimation applications to coastline detection and texture segmentation in a noisy environment are also demonstrated

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed