numerical solution of fractional differential equations with a collocation method based on muntz polynomials this paper presents a computational technique based on the collocation method and muntz polynomials for the solution of fractional differential equations an appropriate representation of the solution via the muntz polynomials reduces its numerical treatment to the solution of a system of algebraic equations the main advantage of the present method is its superior accuracy and exponential convergence consequently one can obtain good results even by using a small number of collocation points the accuracy and performance of the proposed method are examined by means of some numerical experiments

spectral methods for weakly singular volterra integral equations with smooth solutions we propose and analyze a spectral jacobi collocation approximation for the linear volterra integral equations vies of the second kind with weakly singular kernels in this work we consider the case when the underlying solutions of the vies are sufficiently smooth in this case we provide a rigorous error analysis for the proposed method which shows that the numerical errors decay exponentially in the infinity norm and weighted sobolev space norms numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence

ls svr based solving volterra integral equations abstract in this paper a novel hybrid method is presented for solving the second kind linear volterra integral equations due to the powerful regression ability of least squares support vector regression ls svr we approximate the unknown function of integral equations by using ls svr in intervals with known numerical solutions the trapezoid quadrature is used to approximate subsequent integrations in intervals with unknown numerical solutions the feasibility of the proposed method is examined on some integral equations experimental results of comparison with analytic and repeated modified trapezoid quadrature method s solutions show that the proposed algorithm could reach a very high accuracy the proposed algorithm could be a good tool for solving the second kind linear volterra integral equations

a generalization of algebraic geometry codes a generalization of algebraic geometry codes based on function fields over finite fields with many places of small degree is presented it turns out that many good linear codes can be obtained from these generalized algebraic geometry codes in particular we calculate some examples of q ary linear codes for q 2 3 5 these examples show that many best possible linear codes can be found from our construction

some mu ntz orthogonal systems abstract let 0 1 be a given sequence of complex numbers such that i 1 and re i j 1 0 for each i and j for muntz polynomials p x i 0npix i and q x j 0mqjx j we define an inner product p q by p q 0 1 p q x d x x 2 where p q x i 0 n j 0 m p i q j x i j we obtain the muntz polynomials qn x orthogonal with respect to this inner product and connect them with the malmquist rational functions w z v 0 n 1 z 1 v v 0 n z v orthogonal on the unit circle with respect to the inner product u v 1 2 i 1 u z v z d z z several interesting properties of polynomials qn x are given

constructions of algebraic geometry codes based on curves over finite fields with many rational points we present two constructions of linear codes from local expansions of functions at a fixed rational point it turns out that codes from our constructions have the same bound on their parameters as goppa s 1981 geometry codes furthermore we prove that our second construction is equivalent to goppa s construction finally an additional construction of linear codes from maximal curves shows that these codes have better parameters than goppa s geometry codes from maximal curves for a certain interval of parameters

numerical solution of linear volterra integral equations of the second kind with sharp gradients collocation methods are a well developed approach for the numerical solution of smooth and weakly singular volterra integral equations in this paper we extend these methods through the use of partitioned quadrature based on the qualocation framework to allow the efficient numerical solution of linear scalar volterra integral equations of the second kind with smooth kernels containing sharp gradients in this case the standard collocation methods may lose computational efficiency despite the smoothness of the kernel we illustrate how the qualocation framework can allow one to focus computational effort where necessary through improved quadrature approximations while keeping the solution approximation fixed the computational performance improvement introduced by our new method is examined through several test examples the final example we consider is the original problem that motivated this work the problem of calculating the probability density associated with a continuous time random walk in three dimensions that may be killed at a fixed lattice site to demonstrate how separating the solution approximation from quadrature approximation may improve computational performance we also compare our new method to several existing gregory sinc and global spectral methods where quadrature approximation and solution approximation are coupled

numerical solution of volterra fredholm integral equations using the collocation method based on a special form of the muntz legendre polynomials abstract this paper presents a computational technique based on a special family of the muntz legendre polynomials to solve a class of volterra fredholm integral equations the relationship between the jacobi polynomials and muntz legendre polynomials in a particular state are expressed the proposed method reduces the integral equation into algebraic equations via the chebyshev gauss lobatto points so that the system matrix coefficients are obtained by the least squares approximation method the useful properties of the jacobi polynomials are exploited to analyze the approximation error the performance and accuracy of our method are examined with some illustrative examples

a class of linear codes with good parameters a construction of linear codes with good parameters is given based on brouwer s table more than 100 new codes are obtained from our construction

new binary linear codes from algebraic curves many new binary linear codes compared with brouwer s 2000 table are found from a construction based on algebraic curves over finite fields

muntz galerkin methods and applications to mixed dirichlet neumann boundary value problems solutions for many problems of interest exhibit singular behaviors at domain corners or points where the boundary condition changes type for these types of problems direct spectral methods with the usual polynomial basis functions do not lead to a satisfactory convergence rate we develop in this paper a muntz galerkin method which is based on specially tuned muntz polynomials to deal with the singular behaviors of the underlying problems by exploring the relations between jacobi polynomials and muntz polynomials we develop efficient implementation procedures for the muntz galerkin method and provide optimal error estimates as an example of applications we consider the poisson equation with mixed dirichlet neumann boundary conditions whose solution behaves like o r 1 2 near the singular point and demonstrate that the muntz galerkin method greatly improves the rates of convergence of the usual spectral method

asymptotically good quantum codes exceeding the ashikhmin litsyn tsfasman bound it is known that quantum error correction can be achieved using classical binary codes or additive codes over f sub 4 asymptotically good quantum codes have been constructed from algebraic geometry codes and a bound on spl delta r was computed from the tsfasman vladut zink bound of the theory of classical algebraic geometry codes in this correspondence by the use of a concatenation technique we construct a family of asymptotically good quantum codes exceeding the bound in a small interval

hardy spaces and the szegő projection of the non smooth worm domain dβ we define hardy spaces hp d p 1 on the non smooth worm domain d z1 z2 c2 imz1 log z2 2 2 log z2 2 2 and we prove a series of related results such as the existence of boundary values on the distinguished boundary d of the domain and a fatou type theorem i e pointwise convergence to the boundary values thus we study the szeg projection operator s and the associated szeg kernel kd more precisely if hp d denotes the space of functions which are boundary values for functions in hp d we prove that the operator s extends to a bounded linear operator s lp d hp d for every p 1 and s wk p d wk p d for every k 0 here wk p denotes the sobolev space of order k and underlying lp norm p 1 as a consequence of the lp boundedness of s we prove that hp d c d is a dense subspace of hp d

global and local analyticity for second order operators constructed from rigid vector fields on products of tori we prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid variable coefficient quadratic polynomials in real vector fields satisfying the h6rmander condition and where p satisfies a maximal estimate we also prove an analyticity result that is local in some variables and global in others for operators whose prototype is 0z 09x2 t1 with analytic a x a o 0 naturally but not identically zero the results because of the flexibility of the methods generalize recent work of cordaro and himonas in 4 and himonas in 8 which showed that certain operators known not to be locally analytic hypoelliptic those of baouendi and goulaouic 1 hanges and himonas 6 and christ 3 were globally analytic hypoelliptic on products of tori

constructions of codes from residue rings of polynomials we present one construction for nonlinear codes and one construction for binary constant weight codes based on residue rings of polynomials it turns out that the first construction yields nonlinear codes with reasonable parameters and a bound of graham and sloane 1980 is improved by the second construction

nonlinear codes from algebraic curves improving the tsfasman vladut zink bound in the present paper we construct a class of nonlinear codes by making use of higher order derivatives of certain functions of algebraic curves it turns out that the asymptotic bound derived from the goppa geometry codes can be improved for the entire interval 0 1 in particular the tsfasman vladut zink tvz bound is ameliorated for the entire interval 0 1

the szegő kernel as a singular integral kernel on a family of weakly pseudoconvex domains the szego kernels on the weakly pseudoconvex domains im z2 izl12k k e z have been computed by greiner and stein after constructing a global nonisotropic pseudometric suitable for calderon zygmund singular integral theory on the boundaries of the domains we study principal value operators associated to these szego kernels we prove that the principal value operators are bounded on lp for 1 p oo and that they preserve certain nonisotropic lipschitz classes we then derive a plemelj formula that relates the principal value operators to the szego projections from this formula we deduce that the szego projections are also bounded on lp for 1 p oo and that they preserve the same nonisotropic lipschitz classes

global analytic hypoellipticity of the neumann problem on circular domains in this paper we show that if d subseteq mathbb c n n geqq 2 is a smooth bounded pseudoconvex circular domain with real analytic defining functionr z such that sum limits k 1 n z k frac partial r partial z k ne 0 for allz near the boundary then the solutionu to the bar partial neumann problem square u bar partial bar partial bar partial bar partial u f is real analytic up to the boundary if the given formf is real analytic up to the boundary in particular if d subseteq mathbb c n n geqq 2 is a smooth bounded complete reinhardt pseudoconvex domain with real analytic boundary then is analytic hypoelliptic

numerical solution of nonlinear volterra fredholm hammerstein integral equations via tau collocation method with convergence analysis in this paper we consider the nonlinear volterra fredholm hammerstein integral equations the approximate solution for the nonlinear volterra fredholm hammerstein integral equations is obtained by using the tau collocation method to do this the nonlinear volterra fredholm hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form thus by solving this system unknown coefficients are obtained the spectral rate of convergence for the proposed method is established in the l 2 norm the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the tau collocation method is of high accuracy more convenient and efficient for solving nonlinear volterra fredholm hammerstein integral equations

non analytic bergman and szego kernels for weakly pseudoconvex tube domains in mathbb c 2 for any weakly pseudoconvex tube domain in mathbb c 2 with real analytic boundary there exist points on the boundary off the diagonal where the bergman kernel and the szego kernel fail to be real analytic

the szegő projection sobolev estimates in regular domains the szego projection preserves global smoothness in weakly pseudoconvex domains that are regular in the sense of diederich fornxess and catlin it preserves local smoothness near boundary points of finite type the bergman projection being linked to the 8 problem plays an important role in several complex variables as demonstrated by recent applications to the boundary behavior of holomorphic maps 7 16 the szego projection is interesting both by analogy and by its connection with the ab problem and hence with unsolvable equations of lewy type while in strictly pseudoconvex domains the bergman and szego projections are both well understood in general much more is known about the bergman projection this is no surprise for the theory of the 8 problem is further advanced than the theory of the 8b problem nonetheless i believe that the szego projection ought not be any more mysterious than the bergman projection this paper is intended to support this contention the most important domains for which the bergman projection is known to be regular are domains with a good a neumann operator here it is shown that in such domains the szego projection also is regular more precisely in smooth bounded pseudoconvex domains satisfying catlin s property p the most general condition presently known that guarantees global regularity of the neumann operator the szego projection is shown to be globally regular theorem 4 1 moreover at boundary points of finite type the szego projection is locally regular theorem 5 1 in both cases the szego projection exactly preserves the degree of differentiability measured in sobolev norms the method of proof is not the obvious one of directly generalizing from the strictly peudoconvex case for there are serious obstacles to such a generalization for instance the approach of analysis on the heisenberg group used by phong and stein 29 to derive estimates for both the bergman and szego projections cannot yet be extended because the theory of singular integrals on weakly pseudoconvex surfaces is still in its early stages 28 15 similarly one does not know how to carry over the fourier integral operator approach of boutet de monvel and sjostrand 10 to the weakly pseudoconvex case explicit construction of cauchy fantappie forms received by the editors march 11 1986 paper presented april 11 1986 to the 826th meeting of the american mathematical society indianapolis special session on several complex variables 1980 mathematics subject classification 1985 revision primary 32a25 32h10 partially supported by national science foundation grants mcs 8201063 and dms 8501758 1987 american mathematical society 0002 9947 87 1 00 25 per page

new linear codes and algebraic function fields over finite fields in this correspondence we present 129 new linear codes over f8 and f9 based on the construction by xing and niederreiter using algebraic function fields and places of small degrees in addition we construct some global function fields in which the number of rational places improves the lower bounds given by van der geer and van der vlugt

generalized algebraic geometric codes from maximal curves some new results on generalized algebraic geometric gag codes are obtained first we provide some constructions which significantly improve the general lower bounds on the minimum distance of a gag code gag codes associated to specific maximal curves over finite fields are then investigated as a result 2895 improvements on mint s tables are obtained finally we construct asymptotically good gag codes with better parameters with respect to those constructed by spera in 2005 maximal curves play a role in this context as well

nonlinear eigenvalues and analytic hypoellipticity motivated by the problem of analytic hypoellipticity we show that a special family of compact non self adjoint operators has a nonzero eigenvalue we recover old results obtained by ordinary differential equations techniques and show how it can be applied to the higher dimensional case this gives in particular a new class of hypoelliptic but not analytic hypoelliptic operators

muntz systems and orthogonal muntz legendre polynomials the muntz legendre polynomials arise by orthogonalizing the muntz system xio x l with respect to lebesgue measure on 0 1 in this paper differential and integral recurrence formulae for the muntz legendre polynomials are obtained interlacing and lexicographical properties of their zeros are studied and the smallest and largest zeros are universally estimated via the zeros of laguerre polynomials the uniform convergence of the christoffel functions is proved equivalent to the nondenseness of the muntz space on 0 1 which implies that in this case the orthogonal muntz legendre polynomials tend to 0 uniformly on closed subintervals of 0 1 some inequalities for muntz polynomials are also investigated most notably a sharp l2 markov inequality is proved

analytic hypoellipticity for generalized baouendi goulaouic operators abstract this work studies the analytic regularity of solutions to certain second order equations defined by a sum of squares of vector fields it describes a method for constructing singular solutions to generalized baouendi goulaouic type operators this construction is quite explicit and it involves the study of the first eigenvalue and the first eigenfunction of a generalized harmonic oscillator with potential depending on a large parameter

algebraic geometry codes the theory of error correcting codes derived from curves in an algebraic geometry was initiated by the work of goppa as generalizations of bose chaudhuri hocquenghem bch reed solomon rs and goppa codes the development of the theory has received intense consideration since that time and the purpose of the paper is to review this work elements of the theory of algebraic curves at a level sufficient to understand the code constructions and decoding algorithms are introduced code constructions from particular classes of curves including the klein quartic elliptic and hyperelliptic curves and hermitian curves are presented decoding algorithms for these classes of codes and others are considered the construction of classes of asymptotically good codes using modular curves is also discussed

numerical solution of volterra fredholm integral equations using parameterized pseudospectral integration matrices the main purpose of this work is to provide parameterized pseudospectral integration matrices ppims for solving volterra fredholm integral equations we present an exact efficient and stable approach for computing ppims furthermore we provide a rigorous convergence analysis for the pseudospectral scheme with collocation at the jacobi type points in both l and l 2 spaces numerical results confirm the spectral rate of convergence for the proposed pseudospectral schemes

global analytic regularity for sums of squares of vector fields we consider a class of operators in the form of a sum of squares of vector fields with real analytic coefficients on the torus and we show that the zero order term may influence their global analytic hypoellipticity also we extend a result of cordaro himonas

estimates for the bergman and szego kernels in mathbf c 2 the purpose of this paper some of whose conclusions were announced in nrsw is to study the bergman and szegd projection operators on pseudoconvex domains q of finite type in c2 the results we obtain are of three kinds i the size estimates of the bergman and szeg6 kernels and their derivatives ii the cancellation properties of those kernels expressed in terms of the actions of these operators on suitable bump functions these properties have an interest in their own right but are also crucial in iii below iii the sharp mapping properties of these operators on functions spaces such as lp the nonisotropic sobolev spaces and the nonisotropic lipschitz spaces which are naturally attached to the geometry of the boundary this also leads ultimately to sharp results in the regularity properties of solutions of the equation du f in q and 9bu f on the boundary let us describe these matters in more detail our starting points are certain basic geometric constructs associated to q a metric p defined in terms of the vector fields x1 and x2 which are the real and imaginary parts of the tangential levi vector field on d 2 and a function a p 8 a polynomial in 8 for p e d 2 which represents the higher levi invariant attached to d 9 the significance of these to the geometry of d q can be understood from the following facts the ball b p 8 c d q centered at p of radius 8 in the metric p when viewed in the appropriate coordinates has width 8 in the complex tangential directions but its width is a p 8 in the complementary direction thus the volume of the ball is 82a p 8 among other crucial properties

continuous time collocation methods for volterra fredholm integral equations integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study continuous time collocation time discretization and their global and discrete convergence properties

constructing linear unequal error protection codes from algebraic curves we show that the concept of generalized algebraic geometry codes which was introduced by xing niederreiter and lam see ibid vol 45 p 2498 2501 nov 1999 gives a natural framework for constructing linear unequal error protection codes

a hybrid legendre block pulse method for mixed volterra fredholm integral equations abstract mixed volterra fredholm integral equations can arise from mathematical modelling of the spatio temporal development of an epidemic in this paper a hybrid legendre block pulse method is used to provide solutions to a general integral equation of this type the main idea of this approach is to reduce a volterra fredholm integral equation to a system of algebraic equations an order convergence analysis is provided the accuracy of the proposed method is then confirmed by solving some problems the first being a nonlinear epidemic problem

one point codes using places of higher degree in ieee transactions on information theory vol 48 no 2 pp 535 537 feb 2002 xing and chen show that there exist algebraic geometry ag codes from the hermitian function field over f sub q sup 2 constructed using f sub q sup 2 rational divisors which are improvements over the much studied one point hermitian codes in this correspondence we construct such codes by using a place p of degree r 1 this motivates a study of gap numbers and pole numbers at places of higher degree in fact the code parameters are estimated using the weierstrass gap set of the place p and relating it to the gap set of the r tuple of places of degree one lying over p in a constant field extension of degree r

counterexamples to analytic hypoellipticity for domains of finite type consider the hypersurface z1 z2 q z2 p zi cc c2 where p r is a subharmonic nonharmonic polynomial such a surface is pseudoconvex more precisely is the boundary of a pseudoconvex domain and of finite type it is the boundary of a model domain f z2 p zi so called because such domains provide good approximations to general pseudoconvex domains of finite type in c2 see 37 11 a nonvanishing antiholomorphic tangent vector field is a oaz 1 2i ap oaz i o a29z as coordinates for the surface we use c x jr 3 z t z t ip z the vector field pulls back to l o oz i op 9z a3 t equip c x jr with lebesgue measure and consider the orthogonal projection from l2 onto its intersection with the kernel of l the intersection of this kernel with the schwartz space may be shown to have infinite dimension and it is well known that l fails to be c hypoelliptic however c hypoellipticity does hold in a modified form see 30 if lu e c in an open set and if in addition u lv for some v e l2 where l is the formal adjoint of l then u e c there our main purpose is to point out that the analogous assertion for real analytic hypoellipticity is false if p z rz m m an even integer 4 specifically for p a general homogeneous subharmonic nonharmonic polynomial let s z t w s be the szeg6 kernel that is the distribution kernel associated to the operator defined by the orthogonal projection of l2 c x jr with respect to lebesgue measure onto the kernel of l we shall see in section 5 that this projection maps co to c further s is smooth off the diagonal by 37 define the distribution

fredholm volterra integral equation of the first kind and contact problem regular and singular asymptotic methods are applied to one and two dimensional fredholm volterra integral equation f vie of the first kind that arise in the treatment of various two dimensional axisymmetric and three dimensional problems with mixed boundary conditions in the mechanics of continuous media the solution of the integral equation is obtained in the space l 2 w xc 0 t 0

generalized legendre polynomials abstract orthogonal polynomials have been extensively investigated in this paper we construct a sequence of orthogonal dirichlet polynomials which generalize legendre polynomials we show that our new system satisfies a generalized rodrigues formula we also extend a well known result concerning the distribution of the zeros of legendre polynomials

numerical solution of volterra fredholm integral equations based on e svr method in this paper we try to study the numerical methods for solving integral equations from a new perspective machine learning method by means of the idea of kernel e support vector regression machine e svr we construct an optimization modeling for a class of volterra fredholm integral equations and propose a novel numerical method for solving them the proposed method has a certain versatility and can be used to solve some other kinds of integral equations in order to verify the effectiveness of the proposed method we perform a series of comparative experiments with six specific volterra fredholm integral equations and a method proposed in wang et al 2014 experimental results show that the proposed method has a good approximation property

construction of global function fields from linear codes and vice versa we introduce a new connection between linear codes and global function fields which in turn allows us to construct new global function fields with improved lower bounds on the number of rational places the genus and number of rational places of subfields of certain families of cyclotomic function fields are given as well

local equivalence of symmetric hypersurfaces in s 2 x r and h 2 x r the chern moser normal form and its analog on finite type hypersurfaces in general do not respect symmetries extending the work of n k stanton we consider the local equivalence problem for symmetric levi degenerate hypersurfaces of finite type in mathbb c 2 the results give complete normalizations for such hypersurfaces which respect the symmetries in particular they apply to tubes and rigid hypersurfaces providing an effective classification the main tool is a complete normal form constructed for a general hypersurface with a tube model as an application we describe all biholomorphic maps between tubes answering a question posed by n hanges similar results for hypersurfaces admitting nontransversal symmetries are obtained

a new construction of block codes from algebraic curves since discovery of goppa geometric codes people have been asking the question are there different constructions of block codes from algebraic curves that give the same parameters as goppa geometric codes despite of great effort by researchers no such constructions have been found so far although in literature there are many constructions of block code from algebraic curves most of them are quite different from the one by goppa in nature and thus they have different parameters some of these constructions have the same parameters as goppa geometric codes however it was proved that these are essentially the same codes defined by goppa in this paper we solve this question for the case where the characteristic of the ground field is 2 namely we present a different construction of block codes from algebraic curves that give the same parameters as goppa geometric codes for the characteristic 2 case

conditions ne cessaires d hypoanalyticite pour des ope rateurs invariantsa gauche homoge nes sur un groupe nilpotent gradue

a property of the functions and distributions annihilated by a locally integrable system of complex vector fields page introduction 387 1 basic notation and ingredients 389 2 approximation and constancy on the fibers of the classical solutions of the homogeneous equations 393 3 first consequences and interpretation of the fundamental theorem 398 4 distribution solutions of the homogeneous equations 402 5 regularity of the solutions of the homogeneous equations 409 6 example of a system that is analytic hypo elliptic but not co hypo elliptic 413 references 420

hardy spaces for the strip abstract in this paper we shall study hardy spaces of analytic functions in a strip s our main result is on one hand an intrinsic characterization of the spaces and on the second that polynomials are dense we also present an orthogonal in h 2 s basis of polynomials

analytic regularity for an operator with treves curves we study a partial differential operator h with analytic coefficients which is of the form sum of squares h is hypoelliptic on any open subset of r3 yet possesses the following properties 1 h is not analytic hypoelliptic on any open subset of r3 that contains 0 2 if u is any distribution defined near 0 r3 with the property that hu is analytic near 0 then u must be analytic near 0 3 the point 0 lies on the projection of an infinite number of treves curves bicharacteristics these results are consistent with the treves conjectures however it follows that the analog of treves conjecture in the sense of germs is false as far as we know h is the first example of a sum of squares operator which is not analytic hypoelliptic in the usual sense yet is analytic hypoelliptic in the sense of germs

numerical solution of volterra fredholm integral equations using legendre collocation method a numerical method for solving the volterra fredholm integral equations is presented the method is based upon shifted legendre polynomials approximation the properties of shifted legendre polynomials are first presented these properties together with the shifted gauss legendre nodes are then utilized to reduce the volterra fredholm integral equations to the solution of a matrix equation an estimation of the error is given illustrative examples are included to demonstrate the validity and applicability of the technique

remarks about global analytic hypoellipticity we present a characterization of the operators l 8 ot a t ib t x which are globally analytic hypoelliptic on the torus we give information about the global analytic hypoellipticity of certain overdetermined systems and of sums of squares

a class of linear codes with good parameters from algebraic curves a class of linear codes with good parameters is constructed in this correspondence it turns out that linear codes of this class are subcodes of the subfield subcodes of goppa s geometry codes in particular we find 61 improvements on brouwer s table based on our codes

some new codes from algebraic curves based on a construction of xing niederreiter and lam see ibid vol 45 p 2498 2501 1999 some new linear codes are found from suitable algebraic curves over finite fields these codes have better parameters compared with brouwer s table

behavior of the bergman projection on the diederich fornaess worm w 1 introduction in this paper we show that the bergman projection operator for certain smooth bounded pseudoconvex domains does not preserve smoothness as measured by sobolev norms let q be a smooth bounded pseudoconvex domain in c and let p t denote the orthogonal projection from l2 f onto the bergman subspace b ff l2 f3 r with respect to the weighted norm i fll j olf z l 2 e t lzll2dv l 2 let wk t denote the sobolev space consisting of functions whose derivatives of order to k g2 on the other hand there is a large collection of results implying that for certain types of domains the unweighted bergman projection p pr preserves w k for all k 0 see fk for the strictly pseudoconvex case for results on weakly pseudoconvex domains the reader may consult ko2 ca si and the recent bstl ch as well as the references cited therein most of these results are focused on the a neumann operator rather than p see bst2 for the connection also except for kol positive results in this area are typically valid for any choice of smooth positive weight function on 0 the question of whether or not p is similarly well behaved for all weakly pseudoconvex domains has remained open for many years in this paper we show that this is not the case in fact when q is the so called worm domain of diederich and forna ss then p does not map w to w k when k zr total amount of winding this latter quantity is explained in section 4 below where the construction of the worm is reviewed and the main result is proved the proof depends on computations for a piecewise levi flat model domain depending in turn on certain one dimensional computations these are treated in sections 3 and 2 respectively section 5 contains additional remarks and questions

linear codes from narrow ray class groups of algebraic curves by employing the narrow ray class groups of algebraic curves and the hurwitz genus formula we construct a class of linear codes over prime fields with reasonable parameters in particular we obtain some new codes compared with brouwer s table

analytic hypoellipticity in the presence of nonsymplectic characteristic points abstract recently n hanges proved that the operator p t 2 t 2 x x 2 in r 3 is analytic hypoelliptic in the sense of germs at the origin and yet fails to be analytic hypoelliptic in the strong sense in any neighborhood of the origin there is no neighborhood u of the origin such that for every open subset v of u and distribution u in u pu analytic in v implies that u is analytic in v here x x 1 x 2 x 2 x 1 we give a short l 2 proof of this result which generalizes easily and suggestively to other operators with nonsymplectic characteristic varieties

least squares approximation method for the solution of volterra fredholm integral equations in this paper an efficient numerical method is developed for solving the volterra fredholm integral equations by least squares approximation method which is based on a polynomial of degree n to compute an approximation to the solution of volterra fredholm integral equations the convergence analysis of the approximation solution relative to the exact solution of the integral equation is proved the reliability and efficiency of the proposed method are demonstrated by some numerical experiments

constructing codes from algebraic curves we discuss some previous constructions of codes from algebraic curves due to xing niederreiter and lam see ibid vol 45 no 7 p 2498 2501 1999 and we investigate their relations with goppa s 1981 algebraic geometric codes