error estimation and adaptation for functional outputs in time dependent flow problems the paper presents an adjoint based approach for determining global error in the time domain that is relevant to functional outputs from unsteady flow simulations the algorithm is derived for the unsteady euler equations that are discretized for second order accuracy in both space and time and takes into account the effect of dynamic meshes in addition to error due to temporal resolution the formulation also takes into account algebraic error arising from partial convergence of the governing equations at each implicit time step the resulting error distributions are then used to drive adaptation of the temporal resolution and the convergence tolerances for the governing equations at each time step the method is demonstrated in the context of both time integrated and instantaneous functionals and the results are compared against traditional adaptation methods

rough singular integrals on triebel lizorkin space and besov space abstract in this paper the authors prove that the homogeneous singular integral t with h 1 s n 1 is bounded on the triebel lizorkin spaces and the besov spaces these results answer an open problem proposed by chen and zhang in j chen c zhang boundedness of rough singular integral on the triebel lizorkin spaces j math anal appl 337 2008 1048 1052 the same results hold also for the rough singular integral operators t h with radial function kernels

harmonic analysis on nilpotent groups and singular integrals ii singular kernels supported on submanifolds on etudie des operateurs de convolution singuliers sur des groupes de lie nilpotents generaux et plus specifiquement des operateurs dont les noyaux ont pour supports des varietes de faible dimension et qui peuvent aussi contenir des facteurs polynomiaux exponentiels oscillatoires

p blocks relative to a character of a normal subgroup abstract let g be a finite group let n g and let irr n be a g invariant character we fix a prime p and we introduce a canonical partition of irr g relative to p we call each member b of this partition a block and to each block b we naturally associate a conjugacy class of p subgroups of g n which we call the defect groups of b if n is trivial then the blocks are the brauer p blocks using blocks we can unify the gluck wolf navarro tiep theorem and brauer s height zero conjecture in a single statement which after work of b sambale turns out to be equivalent to the height zero conjecture we also prove that the k b conjecture is true if and only if every block b has size less than or equal the size of any of its defect groups thus bringing normal subgroups to the k b conjecture

implicit time discretization schemes for mixed least squares finite element formulations abstract this work is an extension of the ideas in averweg et al 2019 with the focus on a detailed investigation of implicit time discretization schemes to model instationary fluid flow based on the incompressible navier stokes equations and linear elastodynamic structural behavior the variational approaches for fluid and solid mechanics are based on a mixed least squares finite element method the l 2 norm minimization of the residuals of the constructed first order systems of the governing differential equations is based on two field stress velocity sv functionals for the time discretization of the sv fluid formulation four different types of implicit integration schemes are investigated namely the houbolt method the crank nicolson method and two explicit singly diagonally implicit runge kutta methods esdirk the sv formulation for the solid is discretized applying the houbolt method the presented time integration schemes are validated investigating an unsteady fluid flow and an elastodynamic structural benchmark since both fluid and solid sv formulations are discretized using conforming finite element spaces in h div and h 1 respectively the inherent fulfillment of coupling conditions when modeling fluid structure interaction problems is given a priori therefore the applicability is also examined by two simplified fsi problems for small deformations in order to represent the main characteristics of the presented approach

on marcinkiewicz integral with homogeneous kernels abstract in this paper the authors study the boundedness of the marcinkiewicz integral on bmo r n and the campanato spaces e p r n here is homogeneous of degree zero satisfying a class of lq dini conditions the results in this paper are a substantial improvement of some known results

a rough hypersingular integral operator with an oscillating factor abstract we study certain hypersingular integrals t f defined on all test functions f s r n where the kernel of the operator t has a strong singularity y n 0 at the origin an oscillating factor e i y 0 and a distribution h r s n 1 0 r 1 we show that t extends to a bounded linear operator from the sobolev space l p l p to the lebesgue space l p for p if the distribution is in the hardy space h r s n 1 with 0 r n 1 n 1 0 and 2 0

weighted weak 1 1 and weighted estimates for oscillating kernels weak type 1 1 and strong type p p inequalities are proved for operators defined by oscillating kernels the techniques are sufficiently general to derive versions of these inequalities using weighted norms 0 introduction given a positive real number a o a 7 1 define the oscillating kernel ka by ka x 1 x leilxla and consider the convolution operator ka f in an earlier paper 2 we studied the boundedness properties of such operators on weighted lp spaces 1 1 we define l p f 1l p w a e f x lpw x dx r and say f e lp r if llfllp w 1 the multiplier operator t associated to ka is defixled by t d 0 1 l e 1tl f where 0 is a c function defined by i 0 4 0 if 1 when p 0

ell p left mathbb z d right estimates for discrete operators of radon type variational estimates we prove ell p left mathbb z d right bounds for p in 1 infty of r variations r in 2 infty for discrete averaging operators and truncated singular integrals of radon type we shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts

the hilbert transform and maximal function for approximately homogeneous curves let 9ckf x p v f i f x y t dt t and 6 yf x sup1 h 0 h f if x y t l dt it is proved that for f e i rn the schwartz class and for an approximately homogeneous curve y t e ri i ilyf 112 ciifii2 116xyfi12 s c11fi12a homogeneous curve is one which satisfies a differential equation y t a t y t 0 t oo where a is a nonsingular matrix all of whose eigenvalues have positive real part an approximately homogeneous curve y t has the form y1 t y2 t where y2 t is a carefully specified error such that 4yi is also restricted for 2 n 1 the approximately homogeneous curves generalize the curves of standard type treated by stein and wainger

lp boundedness of marcinkiewicz integral operators abstract in this paper we prove the l p boundedness of marcinkiewicz integral operators associated to compact submanifolds of finite type under the l log l 1 2 condition on the kernel functions the exponent 1 2 is optimal we also show that the l p boundedness may fail to hold if the underlying submanifold is not required to be of finite type

a characterization of campanato space via commutator of fractional integral abstract a new characterization of campanato space is given it is here shown that the boundedness of commutators formed by fractional integrals can produce a version of creative characterization of campanato space the corresponding boundedness for the certain commutators with rough kernels was also considered

adjoint based sensitivity formulation for fully coupled unsteady aeroelasticity problems a method to compute sensitivities for use in gradient based shape optimization applied to unsteady aeroelasticity problems is presented the method takes into account the coupling between all three fundamental aspects of computational aeroelasticity namely unsteady flow equations time varying structural response to aerodynamic loads and dynamic meshes that accommodate geometric deformations the devised method provides discretely exact sensitivities of time integrated and non time integrated objective functions with respect to design variables that control the shape of geometry the algorithm is formulated in a general manner and can be readily extended to coupled multidisciplinary problems involving any number of disciplines the algorithm is applied to a simple two dimensional flutter model to demonstrate the proof of concept

uniform estimates for bilinear hilbert transforms and bilinear maximal functions associated to polynomials we study the bilinear hilbert transforms and bilinear maximal functions associated to non flat polynomial curves and obtain uniform l r estimates for r d 1 over d where d is the degree of the polynomial in addition the lower bound of r is sharp up to the end point

mesh deformation strategy optimized by the adjoint method on unstructured meshes an adjoint based optimization procedure is proposed for improving the robustness and extending the range of linear elasticity based mesh deformation techniques using the values of the modulus of elasticity e defined in each mesh cell as the design variables the procedure seeks to determine an optimum distribution of e throughout the mesh in order to minimize a global objective function which reflects the skewness or lack of quality of the deformed mesh the technique is applied to highly stretched mixed element meshes in two and three dimensions on complex geometries and is shown to be capable of recovering a valid mesh in a small number of optimization cycles for cases where the non optimized linear elasticity approach fails however the solution of the optimization problem remains relatively costly in terms of cpu time compared to a non optimized mesh deformation calculation making this technique best suited for precomputing improved e distributions prior to the simulation or for use as a plug in module to be invoked in cases where the non optimized procedure fails

directional agglomeration multigrid techniques for high reynolds number viscous flows a preconditioned directional implicit agglomeration algorithm is developed for solving two and three dimensional viscous flows on highly anisotropic unstructured meshes of mixed element types the multigrid smoother consists of a pre conditioned point or line implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm directional coarsening or agglomeration is achieved using a similar weighted graph algorithm a tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm which in turn reduces the cost of a multigrid cycle convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions further improvement of the three dimensional convergence rates through a gmres technique is also demonstrated

second order time accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes abstract we consider the solution of two and three dimensional flow problems with moving boundaries using the arbitrary lagrangian eulerian formulation or dynamic meshes we focus on the case where spatial discretization is performed by unstructured finite volumes and or finite elements we formulate the consequence of the geometric conservation law on the second order implicit temporal discretization of the semi discrete equations governing such problems and use it as a guideline to construct a new family of second order time accurate and geometrically conservative implicit numerical schemes for flow computations on moving grids we apply these new algorithms to the solution of three dimensional flow problems with moving and deforming boundaries demonstrate their superior accuracy and computational efficiency and highlight their impact on the simulation of fluid structure interaction problems

weighted boundedness for rough marcinkiewicz integrals with different weights in this paper the authors give the weighted boundedness of the marcinkiewicz integral operators for different weight functions where the kernel functions of the operators discussed here are without smoothness not only on the sphere but also in the radial direction

a note on marcinkiewicz integral operators abstract this paper is primarily concerned with proving the l p boundedness of marcinkiewicz integral operators with kernels belonging to certain block spaces we also show the optimality of our condition on the kernel for the l 2 boundedness of the marcinkiewicz integral

torsional springs for two dimensional dynamic unstructured fluid meshes abstract dynamic fluid grids are commonly used for the solution of flow problems with moving boundaries they are often represented by a network of fictitious lineal springs that can become unreliable when the fluid mesh undergoes large displacements and or deformations in this paper we propose to control the arbitrary motion of two dimensional dynamic unstructured fluid grids with additional torsional springs we show that such springs can be designed to prohibit the interpenetration of neighboring triangles and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications we illustrate our new dynamic mesh motion algorithm with several examples that highlight its advantages in terms of robustness quality and performance

relative partial characters and relative blocks of p solvable groups abstract suppose that g is a finite p solvable group and let n be a normal subgroup let irr n with inertial group t in g suppose extends to a subgroup r of t containing n such that r n is a sylow p subgroup of the quotient group t n we show that the set irr g of irreducible characters of g lying over can be partitioned into blocks which behave like the classical brauer p blocks we also establish a well behaved one to one correspondence between the blocks of g and certain brauer p blocks of a central extension of t n by a p subgroup

brauer characters and the harris knorr correspondence in p solvable groups abstract if b is a p block of a normal subgroup n of a p solvable group g and b is its brauer correspondent in n n l where l is a defect group of b then harris knorr correspondents over b and b contain equal numbers of irreducible brauer characters over height zero brauer characters

hilbert integrals singular integrals and radon transforms i on introduit deux nouvelles classes d operateurs on etudie leur relation et on montre comment on peut les appliquer a l etude des problemes aux valeurs limites

operators with rough singular kernels for 0 we study the singular integral operators t and the marcinkiewicz integral operator the kernels of these operators behave like y n near y 0 and contain a distribution on the unit sphere s n 1 we prove that if h r s n 1 r n 1 n 1 satisfying certain cancellation condition then both t and can be extend to be the bounded operators from the sobolev space l p r n to the lebesgue space l p r n the result improves and extends some known results

l p bounds for the commutators of singular integrals and maximal singular integrals with rough kernels the commutator of convolution type calderon zygmund singular integral operators with rough kernels p v x n are studied the authors established the l p 1 p boundedness of the commutators of singular integrals and maximal singular integrals with the kernel condition which is different from the condition h1 sn 1 mr 2000 subject classification 42b20 42b25 42b99

rough singular integrals supported on submanifolds abstract in this paper the authors study the boundedness of the singular integral operators associated to submanifolds on triebel lizorkin spaces and besov spaces moreover the authors also establish an l q valued inequality for the maximal operators associated to submanifolds in this paper

boundedness for the commutator of convolution operator a boundedness result is established for sublinear operators on homogeneous herz spaces as applications a new result about the weighted boundedness of commutators of convolution operators is obtained

implicit method for the computation of unsteady flows on unstructured grids an implicit method for the computation of unsteady flows on unstructured grids is presented following a finite difference approximation for the time derivative the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure the method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage inviscid and viscous unsteady flows are computed to validate the procedure the issue of the mass matrix which arises with vertex centered finite volume schemes is addressed the present formulation allows the mass matrix to be inverted indirectly a mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies as an example of flow over bodies in relative motion flow over a multi element airfoil system undergoing deployment is computed

maximal operators along surfaces of revolution in lebesgue mixed norm spaces in this paper we establish the boundedness of certain maximal operators along hyperspaces in lebesgue mixed norm spaces

singular integral operators on function spaces we study the singular integral operator fx t y f x ty defined on all test functions f w hereb is a bounded function 0 is suitable distribution on the unit sphere s n 1 satisfying some cancellation conditions we prove certain boundedness properties of t on the triebel lizorkin spaces and on the besov spaces we also use our results to study the littlewood paley functions these results improve and extend some well known results

maximal functions associated to surfaces of revolution on product domains abstract the author establishes the l p boundedness for a class of maximal functions related to singular integrals associated to surfaces of revolution on product domains with rough kernels in l log l s n 1

rough maximal singular integral and maximal operators supported by subvarieties on triebel lizorkin spaces abstract in this paper our object of investigation is the maximal singular integrals with rough kernels associated to polynomial mapping p as well as the corresponding compound submanifolds which is defined by t h p f x sup 0 y f x p y h y y y n d y we show that the operator t h p is bounded on triebel lizorkin spaces and besov spaces when the rough kernel l log l s n 1 for some 0 1 similar results can be extended to hardy littlewood maximal operators with rough kernels associated to the mapping p

maximal singular integral operators along surfaces abstract let b y be a bounded radial function and y 1 y 2 y m y where each j y j 1 m is a real valued radial function for x y r n and x r m we define the maximal singular integral along the surface y y by t f x x sup e 0 y e f x y x y b y y n y dy suppose that is an h1 function on the sphere sn 1 satisfying sn 1 x d x 0 we prove that t is bounded on lp r n m 1 m g x 1 x sup k z 2 k 2 k 1 2 k g x 1 t x t dt is bounded on lp r m 1 for all p 1 the result is an extension and improvement of the main theorem in s lu y pan and d yang rough singular integrals associated to surfaces of revolution proc amer math soc 129 2001 2931 2940

higher order time integration schemes for aeroelastic applications on unstructured meshes efficient techniques for computational aeroelasticity on unstructured meshes are investigated these include the formulation of a fourth order implicit runge kutta time integration scheme a third order backward difference time integration scheme and a second order backward difference time integration scheme for the coupled system of flow and structural equations strong coupling between the flow solution and structural equations is maintained by fully converging the fully coupled system at each time step or stage the time integration schemes are constructed such that discrete conservation is maintained in the flow solution in the presence of dynamically deforming meshes by verifying the discrete geometric conservation law efficient multigrid solution techniques are devised for solving both the governing flow equations and the mesh motion equations using the same agglomerated coarse levels for both problems the flutter boundary prediction of the agard 445 6 wing is used to demonstrate the accuracy and efficiency of these techniques as well as the sensitivity of flutter boundary prediction to time step size and temporal errors

singular integral operators associated to curves with rational components we prove l p r n 1 0 where rj t p j t q j t j 1 2 n are rational functions our bounds depend only on the degrees of the polynomials pj qj and in particular they do not depend on the coefficients of these polynomials

harmonic analysis on nilpotent groups and singular integrals i oscillatory integrals abstract this paper is devoted to the study of the operator given by where k is a standard calderon zygmund kernel and p is a real polynomial on r n r n we show t is bounded on lp to itself when 1

weak type 1 1 bounds for rough operators ii in this paper we consider four operators arising in harmonic analysis in r n 1 they share one feature each is known to be bounded on lp for all 1 p o but for each it has been an open question whether a weak type 1 1 bound also holds in two cases we show that the weak 1 1 bound does hold and for the others we establish weaker estimates which are still sharper than the lp boundedness although the four operators are quite distinct they all involve convolution kernels which are related to the singular integrals of calderon and zygmund but which lack the smoothness required for the usual analysis in each case this defect is mitigated by the presence of some form of curvature consider the bochner riesz means

estimates for singular integrals on homogeneous groups we consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups we prove certain estimates for the operators that imply lp boundedness of them by an extrapolation argument under a sharp condition for the kernels also we prove some weighted lp inequalities for the operators

singular integrals with rough kernels along real analytic submanifolds in r n l p mapping properties will be established in this paper for singular radon transforms with rough kernels defined by translated of a real analytic submanifold in r n

singular integrals related to the radon transform and boundary value problems abstract two classes of integral operators are introduced that combine features of calderon zygmund singular integrals the hilbert integral and the radon transform examples and applications arising from integral geometry and several complex variables are discussed

jump estimates for operators associated with polynomials abstract in this study we prove the jump inequalities for singular integrals and averages of radon type with rough kernels