Divergent Cesàro and Riesz means of Jacobi and Laguerre expansions

We show that for below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order .

     

Lévy–Khintchine Formula and Dual Convolution Semigroups Associated with Laguerre and Bessel Functions

In this work we consider a system of partial differential operators D ₁,D ₂ on K=[0,+[×R, whose eigenfunctions are the functions (x,t), (x,t)K, =((R0)×N)(0×[0,+[), which are related to the Laguerre functions for ((R 0)×N)(0,0) and which are the Bessel functions for (0×[0,+[). We provide K and with a convolution structure. We prove a Lévy–Khintchine formula on K, which permits us to characterize dual convolution semigroups on .     

Composite Legendre-Laguerre pseudospectral approximation in unbounded domains

A composite Legendre–Laguerre pseudospectral approximationin unbounded domains is developed. Some approximation resultsare obtained. As an application, a composite pseudospectralscheme is proposed for the Burgers equation on the half-line.The stability and convergence of the scheme are proved. By choosingappropriate base functions, the resulting system of this methodhas a sparse structure and can be solved in parallel. Numericalresults are given to show the efficiency of this new method.     

Weierstrass'' Theorem in Weighted Sobolev Spaces

We characterize the set of functions which can be approximated by polynomials with the following norm

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for a big class of weights w₀, w₁, …, w_k     

IR laser ablation of doped poly(methyl methacrylate)

We investigate the TEA CO₂ laser ablation of films of poly(methyl methacrylate), PMMA, with average M_W 2.5, 120 and 996 kDa doped with photosensitive compounds iodo-naphthalene (NapI) and iodo-phenanthrene (PhenI) by examining the induced morphological and physicochemical modifications. The films casted on CaF₂ substrates were irradiated with a pulsed CO₂ laser (10P(20) line at 10.59 μm) in resonance with vibrational modes of PMMA and of the dopants at fluences up to 6 J/cm². Laser induced fluorescence probing of photoproducts in a pump and probe configuration is carried out at 266 nm. Formation of naphthalene (NapH) and phenanthrene (PhenH) is observed in NapI and PhenI doped PMMA, respectively, with relatively higher yields in high M_W polymer, in similarity with results obtained previously upon irradiation in the UV at 248 nm. Above threshold, formation of photoproducts is nearly complete after 200 ms. As established via optical microscopy, bubbles are formed in the irradiated areas with sizes that depend on polymer M_W and filaments are observed to be ejected out of the irradiated volume in the samples made with high M_W polymer. The implications of these results for the mechanisms of polymer IR laser ablation are discussed and compared with UV range studies.     

Retention Behaviors of Uronic Acid-containing Polysaccharides and Neutral Polysaccharides in HPGPC

The determination of molecular weights (Mw) of polysaccharides has served as an important process since the physical properties of the polysaccharides are closely related to their Mw and/or molecular weights distribution (MWD). For Mw and MWD determinations, high performance gel permeation chromatography (HPGPC) has gained wide acceptance as a preferred method due to its high sensitivity, speed and reproducibility. In chromatography, it is well known that the molecular weights are determ…     

On the Multi-Dimensional Duality Principle of Sawyer Type

A multi-dimensional version of the duality principle of Sawyer type [1] is obtained whenever the corresponding weight satisfies some doubling property. Received June 27, 2000, Accepted September 14, 2000     

Inequalities for formal power series and entire functions

We present several integral and exponential inequalities for formal power series and for both arbitrary entire functions of exponential type and generalized Borel transforms. They are obtained through certain limit procedures which involve the multiparameter binomial inequalities, integral inequalities for continuous functions, and weighted norm inequalities for analytic functions. Some applications to the confluent hypergeometric functions, Bessel functions, Laguerre polynomials, and trigonometric functions are discussed. Also some generalizations are given.     

Harnack inequality and smoothness for quasilinear degenerate elliptic equations

We prove local and global regularity for the positive solutions of a quasilinear variational degenerate equation, assuming minimal hypothesis on the coefficients of the lower order terms. As an application we obtain Hölder continuity for the gradient of solutions to nonvariational quasilinear equations.     

Classification of hypersurfaces with constant Laguerre eigenvalues in R~n

Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.