carleson measures and multipliers for dirichlet spaces abstract we characterize carleson measures on the dirichlet spaces our result leads to necessary and sufficient conditions for multipliers of the dirichlet spaces

non linearizable algebraic k actions on affine spaces non linearizable faithful algebraic r r actions of torus on the real affine n space r n are given for each r 1 n 3 when n 4

a semi local spectral hp element solver for linear elasticity problems summary we develop an efficient semi local method for speeding up the solution of linear systems arising in spectral hp element discretization of the linear elasticity equations the main idea is to approximate the element wise residual distribution with a localization operator we introduce in this paper and subsequently solve the local linear system additionally we decouple the three directions of displacement in the localization operator hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver this approach is effective for both nodal and modal bases in the spectral hp element method but here we focus on the modal hierarchical basis in numerical tests we verify that there is no loss of accuracy in the semi local method and we obtain good parallel scalability and substantial speed up compared to the original formulation in particular our tests include both structure only and fluid structure interaction problems with the latter modeling a 3d patient specific brain aneurysm copyright 2014 john wiley sons ltd

semigroup characterization of besov type morrey spaces and well posedness of generalized navier stokes equations abstract the well posedness of generalized navier stokes equations with initial data in some critical homogeneous besov spaces and in some critical q spaces was known in this paper we establish a wavelet characterization of besov type morrey spaces under the action of semigroup as an application we obtain the well posedness of smooth solution for the generalized navier stokes equations with initial data in some critical homogeneous besov type morrey spaces b p p 1 2 n 1 2 1 1 2 1 2 1 p 2 and n p 2 2 2 n p or 2 p and max n p 2 2 1 2 n p with divergence free these critical homogeneous besov type morrey spaces are larger than corresponding classical besov spaces and cover q spaces

construction of shape functions for the h and p versions of the fem using tensorial product this paper presents an uniform and unified approach to construct h and p shape functions for quadrilaterals triangles hexahedral and tetrahedral based on the tensorial product of one dimensional lagrange and jacobi polynomials the approach uses indices to denote the one dimensional polynomials in each tensorization direction the appropriate manipulation of the indices allows to obtain hierarchical or non hierarchical and inter element c continuous or non continuous bases for the one dimensional elements quadrilaterals triangles and hexahedral the optimal weights of the jacobi polynomials are determined the sparsity profiles of the local mass and stiffness matrices plotted and the condition numbers calculated a brief discussion of the use of sum factorization and computational implementation is considered

a hypersurace which has the abhyankar moh property let x be an algebraic subset of cn we say that x has the abhyankarmoh property a m p if for any polynomial embedding f x cn there exists a polynomial automorphism f of cn such that f is a restriction of this automorphism to the set x in 6 10 11 20 it was shown that if dim x is sufficiently small relatively to n and if x has nice singularities then x has the a m p and the problem of extending the polynomial embedding of x into cn has in general many solutions unfortunately if dim x is big enough in comparison with n the situation is more difficult in particular if x is a generic hypersurface of degree n in cn n 2 then the problem of extending the polynomial embedding of x into cn has no more than one solution see 8 abhyankar and moh proved see 1 2 that a line in c2 has the a m p it can be easily inferred from this that the cross k2 x c2 x1 x2 0 has the a m p the analogous questions for a hyperplane and the n cross kn x cn x1 xn 0 in the n space n 2 has been open cf 1 and conjecture 12 in 12 the question for a hyperplane is still open moreover in the case n 2 no example of a hypersurface which had the a m p has been known

new basis functions and computational procedures for p version finite element analysis new basis functions and solution procedures for p version finite element analysis are described they are used in a highly efficient p version finite element solver for linear elastostatics and dynamics which has been used in an industrial environment for over two years using two sample applications it is shown that using the techniques proposed here p version finite element analysis can have a substantially lower computational cost for given accuracy than standard finite element methods this makes the industrial applicability of p version finite element analysis much wider than is commonly believed

a john nirenberg type inequality for qα rn abstract the john nirenberg inequality characterizes functions in the space bmo in terms of the decay of the distribution function of their oscillations over a cube in this paper we prove separate necessary and sufficient john nirenberg type inequalities for functions in the space q r n introduced by essen janson peng and xiao who conjectured a version of this inequality our results are a modified version of their conjecture and we give a counterexample to show the necessity for this modification the counterexample also shows that these necessary and sufficient conditions cannot be reconciled

euler equations and real harmonic analysis we re prove various existence theorems of regular solutions for the euler equations using classical tools of real harmonic analysis such as singular integrals atomic decompositions and maximal functions

homogeneous locally nilpotent derivations having slices and embeddings of affine spaces abstract let m and n be positive integers such that n m and let b be a polynomial ring in m n 1 variables over a field k of characteristic 0 we give a bijective correspondence between the equivalence classes of embeddings a m a n and the equivalence classes of sequences of mutually commuting locally nilpotent derivations i 1 i m on b in some form which are homogeneous with respect to a z grading on b and have slices the intersection a of the kernels of i for 1 i m inherits the z grading on b we show that a is a polynomial ring with homogeneous coordinates if and only if the corresponding embedding is rectifiable

tensor based gauss jacobi numerical integration for high order mass and stiffness matrices in this work we choose the points and weights of the gauss jacobi gauss radau jacobi and gauss lobatto jacobi quadrature rules that optimize the number of operations for the mass and stiffness matrices of the high order finite element method the procedure is particularly applied to the mass and stiffness matrices using the tensor based nodal and modal shape functions given in int j numer meth engng 2007 71 5 529 563 for square and hexahedron elements we show that it is possible to use tensor product of the 1d mass and stiffness matrices for the poisson and elasticity problem for the triangular and tetrahedron elements an analogous analysis given in int j numer meth engng 2005 63 2 1530 1558 was considered for the selection of the optimal points and weights for the stiffness matrix coefficients for triangles and mass and stiffness matrices for tetrahedra copyright 2009 john wiley sons ltd

fully tensorial nodal and modal shape functions for triangles and tetrahedra this paper presents nodal and modal shape functions for triangle and tetrahedron finite elements the functions are constructed based on the fully tensorial expansions of one dimensional polynomials expressed in barycentric co ordinates the nodal functions obtained from the application of the tensorial procedure are the standard h lagrange shape functions presented in the literature the modal shape functions use jacobi polynomials and have a natural global c0 inter element continuity an efficient gauss jacobi numerical integration procedure is also presented to decrease the number of points for the consistent integration of the element matrices an example illustrates the approximation properties of the modal functions copyright 2005 john wiley sons ltd

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

q spaces and morrey spaces abstract we characterize functions in morrey space by p carleson measures we then reveal a simple relation between q space and morrey space that is q space can be viewed as a fractional integration of the morrey space therefore many results for morrey space can be translated onto q space for example we show that q space is a dual space by identifying its predual

some results on q p spaces 0lpl1 for p is an element of 0 1 let q p be a proper subspace of bmoa defined by means of a modified garcia norm we give a boundary value criterion for a function to be in q p and a necessary and sufficient condition in terms of p carleson measure for an

hierarchical finite element bases for triangular and tetrahedral elements we describe a hierarchical basis for the p version of the finite element method in two and three dimensions the corresponding stiffness matrices are shown to have good sparsity properties and better conditioning than those generated from existing hierarchical bases

hierarchal triangular elements using orthogonal polynomials hierarchal elements are finite elements which have the useful property that elements with different polynomial orders can be used together in the same mesh without causing discontinuities this paper introduces a new hierarchal triangular element in which the basis functions are constructed from orthogonal polynomials jacobi polynomials the resulting element is shown to be better conditioned than the earlier hierarchal element of rossow and katz 1 recursive formulas allow the complete set of basis functions for an element to be efficiently evaluated at a given point in addition the formulas can be used to generate pre computed universal matrices examples are given of universal matrices up to order 4 for the generalized helmholtz equation an electromagnetic problem involving a length of transmission line is used to show the usefulness of the new elements

fefferman stein decomposition for q spaces and micro local quantities abstract in this paper we study the fefferman stein decomposition of q r n and give an affirmative answer to an open problem posed by essen et al 2000 one of our main methods is to characterize the structure of the predual of q r n by the micro local quantities this result indicates that the norm of the predual space of q r n depends on the micro local structure in a self correlation way

embeddings of hypersurfaces in affine spaces abstract in this paper we address the following two general problems given two algebraic varieties in cn find out whether or not they are 1 isomorphic and 2 equivalent under an automorphism of cn although a complete solution of either of those problems is out of the question at this time we give here some handy and useful invariants of isomorphic as well as of equivalent varieties furthermore and more importantly we give a universal procedure for obtaining all possible algebraic varieties isomorphic to a given one and use it to construct numerous examples of isomorphic but inequivalent algebraic varieties in cn among other things we establish the following interesting fact for isomorphic hypersurfaces p x1 xn 0 and q x1 xn 0 the number of zeros of grad p might be different from that of grad q this implies in particular that although the fibers p 0 and q 0 are isomorphic there are some other fibers p c and q c which are not we construct examples like this for any n 2

two level domain decomposition preconditioning for the p version finite element method in three dimensions this paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain convergence factors can be bounded using properties of the local stiffness matrices only the method is applied to the p version finite element method for three dimensional elasticity we treat each element as a subdomain and compute explicit convergence bounds

a new class of function spaces connecting triebel lizorkin spaces and q spaces abstract let s r 0 p 1 and q 1 in this paper we introduce a new class of function spaces f p q s r n which unify and generalize the triebel lizorkin spaces with both p 1 and p and q spaces by establishing the carleson measure characterization of q space we then determine the relationship between triebel lizorkin spaces and q spaces which answers a question posed by dafni and xiao in g dafni j xiao some new tent spaces and duality theorem for fractional carleson measures and q r n j funct anal 208 2004 377 422 moreover via the hausdorff capacity we introduce a new class of tent spaces f t p q s r n 1 and determine their dual spaces f w p q s q r n where s r p q 1 max p q 1 0 q max p q and t denotes the conjugate index of t 1 as an application of this we further introduce certain hardy hausdorff spaces f h p q s r n and prove that the dual space of f h p q s r n is just f p q s q r n when p q 1

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

the jacobian conjecture and the extensions of polynomial embeddings let x be an algebraic subset of c we say that x has the abhyanka r moh property amp if for any polynomial embedding 4 x of there exists a polynomial au tomorphism b of c such that b is a restriction of this au tomorphism to the set x in 3 9 it was shown that if dim x is sufficiently small relatively to n and if x has nice singularities then x has the am p and the problem of extending the polynomial embedding of x into c has in general many solutions unfortunately if dim x is big enough in compar ison with n the situation is more difficult in particular if x is a generic hypersurface of degree n in n 2 then the problem of extending the polynomial embedding of x into c has no more than one solution see 5 abhyankar and mob proved see 1 that a line in c 2 has the amp it can be easily inferred from this that the c r o s s k 2 x g 2 xl x2 0 has the amp the analogous questions for a hyperplane and the n cross k x c x l x 0 in the n space n 3 are open cf 1 and conjecture 12 in 6 moreover in the case n 3 no example of a hypersurface which has the a m p is known on the other hand in 4 we showed that for every n 2 the smooth hypersurface x x c xl x 2 2 is any non zero complex constant does not have the amp we recall an important conjecture connected with this subject

carleson measure for analytic morrey spaces abstract let be a positive borel measure on the unit disc d in this note we show that the inclusion mapping from analytic morrey spaces l 2 d to quadratic tent type spaces t is bounded compact if and only if is a carleson measure vanishing carleson measure as a byproduct we get a new version of well known carleson measure theorem of hardy spaces the inverse carleson measure problem of l 2 d is also studied

a new triangular and tetrahedral basis for high order hp finite element methods in this paper we describe the foundations of a new hierarchical modal basis suitable for high order hp finite element discretizations on unstructured meshes it is based on a generalized tensor product of mixed weight jacobi polynomials the generalized tensor product property leads to a low operation count with the use of sum factorization techniques variable p order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two and three dmensional computational domains employing standard meshes

the problem of selecting the shape functions for a p type finite element abstract the paper addresses the question of the optimal selection of the shape functions for p type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system the selection of the shape functions is of major importance for the performance of the solver based on iterative methods neither the theory nor practice of the optimal selection of the shape functions is available yet we have seen that the condensation approach which has obvious advantages from the point of parallel computations is a very effective tool for keeping the condition number under the control and is especially advantageous for the conjugate gradient method

wavelets and the well posedness of incompressible magneto hydrodynamic equations in besov type q space abstract in this paper we introduce a class of besov type q spaces b p p 1 2 r n to study the well posedness of the fractional magneto hydrodynamic fmhd equations applying wavelets and multi resolution analysis we obtain the boundedness of a semigroup operator from b p p 1 2 r n to some tent spaces b p m m 1 2 as an application we prove the global well posedness of equations fmhd with data in b p p 1 2 r n compared with the method of fourier transform the advantage of our method can be applied to the well posedness with initial data in b p p 1 2 r n where p 2

exotic embeddings of smooth affine varieties we find examples of exotic embeddings of smooth affine varieties into cn in large codimensions we show also examples of affine smooth rational algebraic varieties x for which there are algebraically exotic embeddings x x cl which are holomorphically trivial using this we construct an infinite family c2p 3 p is a prime number of complex manifolds such that every c2p 3 has at least two different algebraic quasi affine structures we show also that there is a natural connection between abhyankar sathaye conjecture and the famous quillen suslin theorem

new besov type spaces and triebel lizorkin type spaces including q spaces let s tau in mathbb r and q in 0 infty we introduce besov type spaces dot b s tau p q mathbb r n for p in 0 infty and triebel lizorkin type spaces dot f s tau p q mathbb r n rm for p in 0 infty which unify and generalize the besov spaces triebel lizorkin spaces and q spaces we then establish the varphi transform characterization of these new spaces in the sense of frazier and jawerth using the varphi transform characterization of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n we obtain their embedding and lifting properties moreover for appropriate we also establish the smooth atomic and molecular decomposition characterizations of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n for s in mathbb r p in 1 infty q in 1 infty and tau in 0 frac 1 max p q via the hausdorff capacity we introduce certain hardy hausdorff spaces b dot h s tau p q mathbb r n and prove that the dual space of b dot h s tau p q mathbb r n is just dot b s tau p q mathbb r n where t denotes the conjugate index of t in 1 infty

homogeneous endpoint besov space embeddings by hausdorff capacity and heat equation two embeddings of a homogeneous endpoint besov space are established via the hausdorff capacity and the heat equation meanwhile a co capacity formula and a trace inequality are derived from the besov space

equivalent birational embeddings ii divisors two divisors in mathbb p n are said to be cremona equivalent if there is a cremona modification sending one to the other we produce infinitely many non equivalent divisorial embeddings of any variety of dimension at most 14 then we study the special case of plane curves and rational surfaces for the latter we characterise surfaces cremona equivalent to a plane

simple hironaka resolution in characteristic zero building upon work of villamayor and bierstone milman we give a proof of the canonical hironaka principalization and desingularization the idea of homogenized ideals introduced in the paper gives a priori the canonicity of algorithm and radically simplifies the proof

bounded functions in mobius invariant dirichlet spaces abstract for p 0 1 let q p q p 0 be the space of analytic functions f on the unit disk with sup w f w d p w 1 f w d p 0 where d p means the weighted dirichlet norm and w is the mobius map of onto itself with w 0 w in this paper we prove the corona theorem for the algebra q p h q p 0 h then we provide a fefferman stein type decomposition for q p q p 0 and finally we describe the interpolating sequences for q p h q p 0 h

a constructive proof of the fefferman stein decomposition of bmo rn let s vec r left left f r 1 f cdots r n f right f in h 1 left text r n text r right right subset h 1 left text r n text r n 1 right 22 1 begin gathered s vec r left vec g left g j right j 0 cdots n right in text bmo left text r n text r n 1 right sum limits j 0 n vec r j g j 0 text in bmo left text r n text r n 1 right left text r right end gathered 22 2 j 0

embeddings of danielewski surfaces a danielewski surface is defined by a polynomial of the form p x nz p y define also the polynomial p x nz r x p y where r x is a non constant polynomial of degree n 1 and r 0 1 we show that when n 2 and deg p y 2 the general fibers of p and p are not isomorphic as algebraic surfaces but that the zero fibers are isomorphic consequently for every non special danielewski surface s there exist non equivalent algebraic embeddings of s in 3 using different methods we also give non equivalent embeddings of the surfaces xz y d n 1 for an infinite sequence of integers d n we then consider a certain algebraic action of the orthogonal group mathcal o 2 on 4 which was first considered by schwarz and then studied by masuda and petrie who proved that this action could not be linearized this was done by comparing the strata of this action to those of the induced tangent space action inequivalent embeddings of a certain singular danielewski surface s in 3 are found we generalize their result and show how this leads to an example of two smooth algebraic hypersurfaces in 3 which are algebraically non isomorphic but holomorphically isomorphic

characterization of multiplier spaces by wavelets and logarithmic morrey spaces in this paper we consider multipliers from sobolev spaces to lebesgue spaces we establish some wavelet characterization of multiplier spaces without using capacity further we give a sharp logarithmic morrey space condition for multipliers which lessens fefferman s morrey space condition to the logarithm level and generalizes lemarie s counter example to non integer cases and expresses his results in a more precise way

testing sets for properness of polynomial mappings in this paper we characterize testing sets for properness of polynomial mappings f mathbb c n rightarrow mathbb c m we also study the set of points at which such mappings are not proper as the first application we give a proof of the complementary conjecture of mckay and wang conjecture 12 in 16 the second application is an answer to the problem of kraft russell about a characterization of mathbb c n the third application is given in 13 a solution of the problem of van den essen and shpilrain about endomorphism of the ring mathbb c x 1 x n the fourth application is a theorem about extensions of affine varieties

the h p adaptive finite element method for the numerical simulation of compressible flow an h p adaptive finite element method is presented for the numerical simulation of compressible fluid flow in addition to refining the mesh in regions where the estimated error is large the polynomial degree of the elements is increased it is shown that by using high order polynomials highly accurate approximations are obtained to a regularized form of the equations governing viscous compressible flow

about the conditioning of matrices in the p version of the finite element method for second order elliptic problems abstract in the framework of adaptive methods bases of hierarchical type are used in the p version of the finite element method we have studied the matrices corresponding to the most used basis introduced by babuska and szabo in the case of d dimensional rectangular elements for the internal nodes we show that the condition number is o p4 d 1 resp o p4d for the stiffness resp mass matrix moreover we show that the usual diagonal preconditioning divides the exponents by two

some new tent spaces and duality theorems for fractional carleson measures and qα rn several duality questions for fractional carleson measures and the spaces q rn are resolved using a new type of tent spaces these tent spaces are defined in terms of choquet integrals with respect to hausdorff capacity a predual for q rn is then defined as a space of distributions containing the hardy space h1 and an atomic decomposition is proved

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

effective and practical h p version adaptive analysis procedures for the finite element method two practical and effective h p type finite element adaptive procedures are presented the procedures allow not only the final global energy norm error to be well estimated using hierarchic p refinement but in addition give a nearly optimal mesh the design of this is guided by the local information computed on the previous mesh the desired accuracy can always be obtained within one or at most two h p refinements the rate of convergence of the adaptive h p version analysis procedures has been tested for some examples and found to be very strong the presented procedures can easily be incorporated into existing p or h type code structures

the transport equation in the scaling invariant besov or essen janson peng xiao space abstract this paper addresses a well posedness of the weak solution to the transport equation describing how a scalar quantity is transported in a space with an initial data in the scaling invariant besov or essen janson peng xiao space via the boundedness of the left and right compositions acting on each space

irreducible identity sets for polynomial automorphisms in this paper we study polynomial automorphisms of some algebraic affine varieties the main tool of our investigations is the notion of the uniruled set the paper is divided into five parts sections 1 5 respectively the first one is an introduction in the second one we set up notations definitions and terminology in section 3 we study the set of fixed points of a polynomial automorphism of cn the nature of this set is not well known even in the case when an automorphism has a finite order see 10 let us recall the notions which we shall use in the sequel let x cn be an algebraic set we say that x is an identity set for polynomial automorphisms of cn if every two polynomial automorphisms that coincide on x must be equal x is a set determining polynomial automorphisms of cn if the same holds under the weaker assumption that these two automorphisms transforms x onto the same set in 13 wang and mckay proved that two intersecting lines are an identity set in c2 later in 14 they generalized this result on n hyperplanes in general position in cn n 2 in our paper 8 we generalized these results and we proved that the union of every n hypersurfaces in general position in cn is an identity set in cn n 2

the strong nagata conjecture it is proved that there exist wild coordinates in the polynomial algebra in three variables over a field of characteristic zero this result implies the famous nagata conjecture