stability of large amplitude ekman hartmann boundary layers in mhd the case of ill prepared data in this paper we study an incompressible highly rotating fluid submitted to a high magnetic field between two planes with a dirichlet boundary condition we investigate the nonlinear stability of ekman hartmann boundary layers under a spectral assumption for general initial data this means that the data can be chosen as an arbitrary but smooth enough three dimensional divergence free vector field independent of the small parameter

singular pseudodifferential operators symmetrizers and oscillatory multidimensional shocks abstract we introduce a calculus of singular pseudodifferential operators spos depending on wavelength e and use them to solve three different types of singular quasilinear hyperbolic systems such systems arise in nonlinear geometric optics and also for example in the study of incompressible limits and of nonlinear wave equations with small nonlinear terms or small data the spos act in both slow and fast variables and are singular not only because their symbols have finite regularity and depend on 1 e but also because their derivatives fail to decay in the usual way in the dual variables there is a necessarily crude calculus with large parameter e g residual operators are just bounded on l2 but the calculus admits the proof of garding inequalities and enables us to symmetrize and sometimes even diagonalize the singular systems being considered by microlocalizing simultaneously in both slow and fast variables the paper culminates in a proof of the existence of oscillatory multidimensional shocks on a fixed time interval independent of the wavelength e as e 0 the use of spos allows us to eliminate the small divisor assumptions made in earlier work and also to construct more general oscillatory solutions in which elliptic boundary layers are present on one or both sides of the shock

existence of global weak solutions for a 2d viscous shallow water equations and convergence to the quasi geostrophic model we consider a two dimensional viscous shallow water model with friction term existence of global weak solutions is obtained and convergence to the strong solution of the viscous quasi geostrophic equation with free surface term is proven in the well prepared case the ill prepared data case is also discussed

low mach number flows in time dependent domains we perform a multiple time scale single space scale analysis of a compressible fluid in a time dependent domain when the time variations of the boundary are small with respect to the acoustic velocity we introduce an average operator with respect to the fast time the averaged leading order variables satisfy modified incompressible equations which are coupled to linear acoustic equations with respect to the fast time we discuss possible initial boundary data for the asymptotic equations inherited from the initial boundary data for the compressible equations

quasi hopf algebras and representations of octonions and other quasialgebras modules over a quasialgebra here by quasialgebra we mean a left h module algebra where h is a quasi hopf algebra as defined by albuquerque and majid coincide with modules over a certain associative algebra a quasi hopf smash product as a consequence of this we get that the category of modules over the octonions is isomorphic to the category of modules over the algebra of 8 8 real matrices we provide a new approach to the endomorphism quasialgebra associated to a left h module which in the finite dimensional case yields the same results as the one of albuquerque and majid we discuss possible definitions as endomorphism quasialgebras for heisenberg doubles of a finite dimensional quasi hopf algebra

semiclassical and spectral analysis of oceanic waves in this work we prove that the shallow water flow subject to strong wind forcing and linearized around an adequate stationary profile develops for large times closed trajectories due to the propagation of rossby waves while poincare waves are shown to disperse the methods used in this paper involve semi classical analysis and dynamical systems for the study of rossby waves while some refined spectral analysis is required for the study of poincare waves due to the large time scale involved which is of diffractive type

a simple global model for the general circulation of the atmosphere in this article we present a new method of rossby asymptotics for the equations of the atmosphere similar to the geostrophic asymptotics we depart from the classical geostrophics see j g charney 5 and our previous article 29 by considering an asymptotics valid for the whole atmosphere not only in midlatitude regions and by taking into account the spherical form of the earth we obtain in this way a very simple global circulation model of the atmosphere for which the equations of motion for wind and temperature are linear evolution equations similar to the linear stokes equations furthermore the solutions are independent of longitude and winds travel exactly to the east or to the west in this mathematically oriented article we do not discuss the physical significance of the model that we derive except for observing that this picture coincides in general terms with the classically averaged data obtained by experimental measurements we also note that different global geostrophic asymptotics called planetary geostrophic asymptotics are considered elsewhere in the literature for example in j pedlosky 33 in a less mathematically rigorous way h lamb 21 observed that the only globally valid geostrophic flow that maintains a slow time scale is zonally symmetric see the comments in n phillips 35 and an explicit derivation in h jeffreys 19 c 1997 john wiley sons inc

active control trials with binary data a comparison of methods for testing superiority or non inferiority using the odds ratio this paper considers methods for testing for superiority or non inferiority in active control trials with binary data when the relative treatment effect is expressed as an odds ratio three asymptotic tests for the log odds ratio based on the unconditional binary likelihood are presented namely the likelihood ratio wald and score tests all three tests can be implemented straightforwardly in standard statistical software packages as can the corresponding confidence intervals simulations indicate that the three alternatives are similar in terms of the type i error with values close to the nominal level however when the non inferiority margin becomes large the score test slightly exceeds the nominal level in general the highest power is obtained from the score test although all three tests are similar and the observed differences in power are not of practical importance

infinite prandtl number limit of rayleigh benard convection we rigorously justify the infinite prandtl number model of convection as the limit of the boussinesq approximation to the rayleigh benard convection as the prandtl number approaches infinity this is a singular limit problem involving an initial layer 2003 wiley periodicals inc

two sided two cosided hopf modules and doi hopf modules for quasi hopf algebras let h be a finite dimensional quasi hopf algebra over a field k and a a right h comodule algebra we introduce the category of two sided hopf modules and prove that it is isomorphic to a module category we also show that two sided hopf modules are coalgebra over a certain comonad we introduce doi hopf modules and show that they are comodules over a certain coring if the underlying h module coalgebra is finite dimensional then doi hopf modules are modules over a certain smash products a similar result holds for two sided two cosided hopf modules

an approach to quasi hopf algebras via frobenius coordinates abstract we study quasi hopf algebras and their subobjects over certain commutative rings from the point of view of frobenius algebras we introduce a type of radford formula involving an anti automorphism and the nakayama automorphism of a frobenius algebra then view several results in quantum algebras from this vantage point in addition separability and strong separability of quasi hopf algebras are studied as frobenius algebras

low mach number limit of viscous polytropic fluid flows abstract this paper studies the singular limit of the non isentropic navier stokes equations with zero thermal coefficient in a two dimensional bounded domain as the mach number goes to zero a uniform existence result is obtained in a time interval independent of the mach number provided that the initial data satisfy the bounded derivative conditions that is the time derivatives up to order two are bounded initially and navier s slip boundary condition is imposed

stability of large ekman boundary layers in rotating fluids the aim of this paper is to investigate the stability of ekman boundary layers for rotating fluids when the ekman number and the rossby number go to zero more precisely we prove that spectral stability implies linear and nonlinear stabilities of approximate solutions in particular we replace the smallness condition obtained with energy methods in 5 by a weaker spectral condition which is sharp

incompressible limits of the navier stokes equations for all time abstract we study the asymptotic behaviors of the regular solutions to the compressible navier stokes equations for well prepared initial data for all time as the mach number tends to zero by deriving a differential inequality with certain decay property the estimates obtained in this paper are uniform both in time and mach number

global existence and long time asymptotics for rotating fluids in a 3d layer the navier stokes coriolis system is a simple model for rotating fluids which allows to study the influence of the coriolis force on the dynamics of three dimensional flows in this paper we consider the nsc system in an infinite three dimensional layer delimited by two horizontal planes with periodic boundary conditions in the vertical direction if the angular velocity parameter is sufficiently large depending on the initial data we prove the existence of global infinite energy solutions with nonzero circulation number we also show that these solutions converge toward two dimensional lamb oseen vortices as t

ekman layers of rotating fluids the case of general initial data in this paper we describe the weak solutions of the navier stokes equations with a large coriolis term as the rossby and the ekman numbers go to zero in a special domain with various boundary conditions this work extends the results in the case of well prepared initial data in 19 30 2000 john wiley sons inc

a simple justification of the singular limit for equatorial shallow water dynamics the equatorial shallow water equations at low froude number form a symmetric hyperbolic system with large variable coefficient terms although such systems are not covered by the classical klainerman majda theory of singular limits the first two authors recently proved that solutions exist uniformly and converge to the solutions of the long wave equations as the height and froude number tend to 0 their proof exploits the special structure of the equations by expanding solutions in series of parabolic cylinder functions a simpler proof of a slight generalization is presented here in the spirit of the classical theory 2008 wiley periodicals inc

the euler limit of the navier stokes equations and rotating fluids with boundary in this paper we study the convergence of weak solutions of the navier stokes equations in some particular domains with different horizontal and vertical viscosities when they go to zero with different speeds the difficulty here comes from the dirichlet boundary conditions precisely we show that if the ratio of the vertical viscosity to the horizontal viscosity also goes to zero then the solutions converge to the solution of the euler system we study the same limit for rotating fluids with rossby number also going to zero

boundary layer associated with the darcy brinkman boussinesq model for convection in porous media abstract we study the asymptotic behavior of the infinite darcy prandtl number darcy brinkman boussinesq system for convection in porous media at a small brinkman darcy number the existence of a boundary layer with thickness proportional to the square root of the brinkman darcy number for the velocity field is established in both the l h 1 norm in 2 and 3 d and the l l norm in 2d this improves in several respects an earlier result of payne and straughan 1998 60 where the vanishing brinkman darcy number limit is studied without resolving the boundary layer

on the influence of gravity on density dependent incompressible periodic fluids abstract the present work is devoted to the analysis of density dependent incompressible fluids in a 3d torus when the froude number e goes to zero we consider the very general case where the initial data do not have a zero horizontal average where we only have smoothing effect on the velocity but not on the density and where we can have resonant phenomena on the domain we explicitly determine the limit system when e 0 and prove its global wellposedness finally we prove that for large initial data the density dependent incompressible fluid system is globally wellposed provided that e is small enough

incompressible limits and propagation of acoustic waves in large domains with boundaries we study the incompressible limit for the full navier stokes fourier system on unbounded domains with boundaries supplemented with the complete slip boundary condition for the velocity field using an abstract result of tosio kato we show that the energy of acoustic waves decays to zero on any compact subset of the physical space this in turn implies strong convergence of the velocity field to its limit in the incompressible regime

uniform regularity for the navier stokes equation with navier boundary condition we prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the navier stokes equation with the navier boundary condition has a strong solution this solution is uniformly bounded in a conormal sobolev space and has only one normal derivative bounded in l this allows us to obtain the vanishing viscosity limit to the incompressible euler system from a strong compactness argument

frobenius and separable functors for the category of entwined modules over cowreaths ii applications abstract let h be a quasi hopf algebra we apply results obtained in 8 to give necessary and sufficient conditions for the forgetful functor from doi hopf modules two sided hopf modules or yetter drinfeld modules over h to representations of the underlying algebra to be frobenius resp separable we show that in some situations these conditions reduce to the unimodularity and or co semisimplicity of the quasi hopf algebra h

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

a two dimensional model for quasigeostrophic flow comparison with the two dimensional euler flow abstract a simple two dimensional model for quasigeostrophic flow is contrasted with the two dimensional incompressible euler equations the model arises under the assumptions of fast rotation uniform stratification and uniform potential vorticity it is found that the more loca feed back of the quasigeostrophic model gives rise to strongly nonlinear front formation as opposed to two dimensional euler where the steepening process of mature fronts obeys a nonlocal nearly linear mechanism

quasi quantum groups knots three manifolds and topological field theory we show how to construct starting from a quasi hopf algebra or quasiquantum group invariants of knots and links in some cases these invariants give rise to invariants of the three manifolds obtained by surgery along these links this happens for a finite dimensional quasi quantum group whose definition involves a finite groupg and a 3 cocycle which was first studied by dijkgraaf pasquier and roche we treat this example in more detail and argue that in this case the invariants agree with the partition function of the topological field theory of dijkgraaf and witten depending on the same datag

on integrals and cointegrals for quasi hopf algebras abstract using the theory of frobenius algebras we study how the antipode of a quasi hopf algebra h acts on the space of left and right integrals and cointegrals we obtain formulas that allow us to find out the explicit form of the integrals and cointegrals for the drinfeld double d h in terms of the integrals and cointegrals of h this leads to an answer to a conjecture made by hausser and nill at the end of the nineties

generalized diagonal crossed products and smash products for quasi hopf algebras applications in this paper we introduce generalizations of diagonal crossed products two sided crossed products and two sided smash products for a quasi hopf algebra h the results we obtain may then be applied to h hopf bimodules and generalized yetter drinfeld modules the generality of our situation entails that the generating matrix formalism cannot be used forcing us to use a different approach this pays off because as an application we obtain an easy conceptual proof of an important but very technical result of hausser and nill concerning iterated two sided crossed products

comments on active control trials with binary data a comparison of methods for testing superiority or non inferiority using the odds ratio by a l siqueira a whitehead and s todd statistics in medicine 2008 27 353 370

relative hopf modules for dual quasi hopf algebras univ bucharest fac math ro 70109 bucharest 1 romania limburgs univ ctr dept math b 3590 diepenbeek belgium bulacu d univ bucharest fac math str acad 14 ro 70109 bucharest 1 romania

the incompressible limit of the non isentropic euler equations we study the euler equations for slightly compressible fluids that is after rescaling the limits of the euler equations of fluid dynamics as the mach number tends to zero in this paper we consider the general non isentropic equations and general data we first prove the existence of classical solutions for a time independent of the small parameter then on the whole space d we prove that the solution converges to the solution of the incompressible euler equations

long wave short wave resonance for nonlinear geometric optics the aim of this paper is to study oscillatory solutions of nonlinear hyperbolic systems in the framework developped during the last decade by joly metivier and rauch here we mainly focus on rectification effects that is the interaction of oscillations with a mean field created by the nonlinearity a real interaction can occur only under some geometric conditions described in jmr1 and l1 that are generally not satisfied by the physical models except in the 1 d case we introduce here a new type of ansatz that allows us to obtain rectification effects under weaker asumptions we obtain a new class of profile equations and construct solutions for a subclass finally the stability of the asymptotic expansion is proved in the context of maxwell bloch type systems

fast averaging for long and short wave scaled equatorial shallow water equations with coriolis parameter deviating from linearity the equatorial shallow water equations at low froude number form a symmetric hyperbolic system with large terms containing a variable coefficient the coriolis parameter f which depends on the latitude the limiting behavior of the solutions as the froude number tends to zero was investigated rigorously a few years ago using the common approximation that the variations of f with latitude are linear in that case the large terms have a peculiar structure due to special properties of the harmonic oscillator hamiltonian which can be exploited to prove strong uniform a priori estimates in adapted functional spaces it is shown here that these estimates still hold when f deviates from linearity even though the special properties on which the proofs were based have no obvious generalization as in the linear case existence uniqueness and convergence properties of the solutions corresponding to general unbalanced data are deduced from the estimates

test statistics and sample size formulae for comparative binomial trials with null hypothesis of non zero risk difference or non unity relative risk when it is required to establish a materially significant difference between two treatments or alternatively to show that two treatments are equivalent standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply this paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non zero difference or non unity relative risk methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine

new finite volume method for rotating channel flows involving boundary layers we investigate in this article the boundary layers appearing in a fluid under moderate rotation when the viscosity is small the fluid is modeled by the time dependent rotating stokes equations also known as the stokes coriolis equations the equations are considered in an infinite channel with periodicity on the lateral boundary and dirichlet boundary conditions on the top and bottom of the channel first we analytically derive the correctors which describe the sharp variations at large reynolds number i e small viscosity second thanks to a modified finite volume method mfvm we give the numerical solutions of the stokes coriolis system at small viscosity 10 3 10 3 10 10 10 10 we follow the common idea which consists of adding the corrector functions to the galerkin basis or its analogous for the classical finite volume method see gie et al discrete contin dyn syst 36 5 2521 2583 2016 gie and temam int j numer anal model 12 3 536 566 2015 shih and bruce siam j math anal 18 5 1467 1511 1987 the mfvm introduced here can be applied to a large class of singular perturbation problems

doubles of quasi quantum groups in dr1 drinfeld showed that any finite dimensional hopf algebra extends to a quasitriangular hopf algebra the quantum double of based on the construction of a so called diagonal crossed product developed by the authors in hn we generalize this result to the case of quasi hopf algebras as for ordinary hopf algebras as a vector space the quasi quantum double is isomorphic to where denotes the dual of we give explicit formulas for the product the coproduct the r matrix and the antipode on and prove that they fulfill drinfeld s axioms of a quasitriangular quasi hopf algebra in particular becomes an associative algebra containing as a quasi hopf subalgebra on the other hand is not a subalgebra of unless the coproduct on is strictly coassociative it is shown that the category of finite dimensional representations of coincides with what has been called the double category of modules by s majid m2 thus our construction gives a concrete realization of majid s abstract definition of quasi quantum doubles in terms of a tannaka krein like reconstruction procedure the whole construction is shown to generalize to weak quasi hopf algebras with now being linearly isomorphic to a subspace of

slow convergence to vortex patches in quasigeostrophic balance taking advantage of dispersive effects which supposes a flow extended in the whole space a sluggish convergence of the solutions of the boussinesq equations to a solution of the quasigeostrophic system when the rossby number tends to zero can be proved under weaker assumptions on the initial data than usual in particular no assumption of well preparedness is needed two examples are given both involving fields with striated potential vorticity a result of convergence to a vortex patch is deduced from one of them

integrals for dual quasi hopf algebras applications abstract a classical result in the theory of hopf algebras concerns the uniqueness and existence of integrals for an arbitrary hopf algebra the integral space has dimension 1 and for a finite dimensional hopf algebra this dimension is exactly one we generalize these results to quasi hopf algebras and dual quasi hopf algebras in particular it will follow that the bijectivity of the antipode follows from the other axioms of a finite dimensional quasi hopf algebra we give a new version of the fundamental theorem for quasi hopf algebras we show that a dual quasi hopf algebra is co frobenius if and only if it has a non zero integral in this case the space of left or right integrals has dimension one

low mach number limit of full navier stokes equations in a 3d bounded domain abstract this paper studies the low mach number limit of the full compressible navier stokes equations in a three dimensional bounded domain where the velocity field and the temperature satisfy the slip boundary conditions and the neumann boundary condition respectively the uniform estimates in the mach number for the strong solutions are derived in a short time interval provided that the initial density and temperature are close to the constant states and satisfy the bounded derivative conditions thus the solutions of the full compressible navier stokes equations converge to the one of the isentropic incompressible navier stokes equations as the mach number vanishes

renormalization group method applied to the primitive equations abstract in this article we study the limit as the rossby number e goes to zero of the primitive equations of the atmosphere and the ocean from the mathematical viewpoint we study the averaging of a penalization problem displaying oscillations generated by an antisymmetric operator and by the presence of two time scales