On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

Metallocene copolymers of propene and 1‐hexene: The influence of the comonomer content and thermal history on the structure and mechanical properties

The relationships between the structure and properties have been established for copolymers of propylene and 1‐hexene synthesized with an isotactic metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is the comonomer content. The thermal treatment, that is, the rate of cooling from the melt, is also important. These factors affect the thermal properties, the degree of crystallinity, and therefore the structural parameters and the viscoelastic behavior. A slow cooling from the melt favors the formation of the γ phase instead of the α modification. Regarding the viscoelastic behavior, the β relaxation, associated with the glass‐transition temperature, is shifted to lower temperatures and its intensity is increased as the 1‐hexene content raises. The microhardness values are correlated with those of the storage modulus deduced from dynamic mechanical thermal analysis curves, and good linear relations have been obtained between these parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1253–1267, 2006     

On error operators related to the arbitrary functions principle

The error on a real quantity Y due to the graduation of the measuring instrument may be asymptotically represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator does not depend on the probability law of Y as soon as this law possesses a continuous density. This feature is related to the “arbitrary functions principle” (Poincaré, Hopf). We give extensions of this property to Rd and to the Wiener space for some approximations of the Brownian motion. This gives new approximations of the Ornstein-Uhlenbeck gradient. These results apply to the discretization of some stochastic differential equations encountered in mechanics.     

L-functions of second-order cusp forms

We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establish a criterion for a Dirichlet series to originate from a second order form. In the last section we investigate the effect of adding an assumption of periodicity to this criterion. 2000 Mathematics Subject Classification Primary—11F12, 11F66 G. Mason: Research supported in part by NSF Grant DMS 0245225. C. O’Sullivan: Research supported in part by PSC CUNY Research Award No. 65453-00 34.     

On random walks arising in queueing systems: ergodicity and transience via quadratic forms as lyapounov functions — Part I

A simple and quite general approach is proposed to derive criteria for transience and ergodicity of a certain class of irreducibleN-dimensional Markov chains in ₊ ^N assuming a boundedness condition on the second moment of the jumps. The method consists in constructing convenient smooth supermartingales outside some compact set. The Lyapounov functions introduced belong to the set of quadratic forms in ₊ ^N and do not always have a definite sign. Existence and construction of these forms is shown to be basically equivalent to finding vectors satisfying a system of linear inequalities.Part I is restricted toN=2, in which case a complete characterization is obtained for the type of random walks analyzed by Malyshev and Mensikov, thus relaxing their condition of boundedness of the jumps. The motivation for this work is partly from a large class of queueing systems that give rise to random walks in ₊ ^N      

Purification and partial characterization of two lectin isoforms fromCratylia mollis mart. (camaratu bean)

Two additional electrophoretically distinct molecular forms, isoforms (iso) 2 and 3, with lectin properties were isolated fromCratylia mollis Mart, seeds (FABACEAE), by extraction with 0.15M NaCl and ammonium sulfate fractionation, followed by chromatography on Sephadex G-75 and Bio-Gel P-200 (iso 2), as well as CM-Cellulose and Sephadex G-75 (iso 3). Both isoforms were human group nonspecific and showed distinct specificity. Polyacrylamide gel electrophoresis resolved iso 2 and 3 in polypeptides of apparent mol wts 60 and 31 kDa, respectively; a distinct isoelectric focusing pattern was obtained for iso 2 and 3, under denaturing and reducing conditions.     

On a characterization of the normal distribution by means of identically distributed linear forms

Let X₁, X₂,…, be independent, identically distributed random variables. Suppose that the linear forms L₁ = Σ_j=1^∞a_jX_j and L₂ = Σ_j=1^∞b_jX_j exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X₁ is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L₁ and L₂ have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions.     

Lifschitz singularities for periodic operators plus random potentials

UsingX-bounding (lower bounds by Laplacians with mixed boundary conditions and discrete analogs), we obtain the Lifschitz exponent at the bottom of the spectrum for random operators of typeH =T+V , withT a (periodic) generator of a positivity-preserving semigroup, extending results by Kirsch and Simon.     

Die multikomponenten Formen von Cellulase (EC 3.2.1.4) ausAspergillus oryzae

The enzyme cellulase fromAspergillus oryzae was resolved into four multiple forms, using anion exchange chromatography on DEAE Sephadex A-50 and gel filtration on Sephadex G-75. The stages of fractionation were followed by electrophoresis on cellulose acetate strips. These enzyme forms are characterized by different enzyme activities and isoelectric points.

Herrn Univ.-Prof. Dr.Hans Tuppy zum 65. Geburtstag herzlichst gewidmet.     

Alkylhydrazides and their protonated forms: Physical methods andab initio calculations

The basicity of hydrazides of the highest aliphatic carboxylic acids RC(O)NHNH₂ (R = C_nH_2n+1,n = 5-12) has been studied by potentiometric titration, and IR and¹H NMR spectroscopy.Ab initio Hartree-Fork calculations using the 6–31G^* basis set with full optimization of geometry were carried out on the simplest acy1hydrazines and their possible protonated forms. Based on these calculations, and the 1R and¹H NMR spectra, the tautomerism of alkylhydrazides and the structures of their protonated forms are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2645–2649, November, 1996.