Volume 105, Issue 3
August 1995, pages 259-369
pp 259-267 August 1995
Lifting orthogonal representations to spin groups and local root numbers
Dipendra Prasad Dinakar Ramakrishnan
Representations ofD_{k}^{*}k^{*} for a quaternion division algebraD_{k} over a local fieldk are orthogonal representations. In this note we investigate when these orthogonal representations can be lifted to the corresponding spin group. The results are expressed in terms of local root number of the representation.
pp 269-271 August 1995
Irrationality of linear combinations of eigenvectors
A givenn ×n matrix of rational numbers acts onC^{π} and onQ^{π}. We assume that its characteristic polynomial is irreducible and compare a basis of eigenvectors forC^{π} with the standard basis forQ^{π}. Subject to a hypothesis on the Galois group we prove that vectors from these two bases are as independent of each other as possible.
pp 273-279 August 1995
On the zeros ofζ^{(1)(s)} —a (on the zeros of a class of a generalized Dirichlet series — XVII)
Some very precise results (see Theorems 4 and 5) are proved about thea-values of thelth derivative of a class of generalized Dirichlet series, forl≥l_{o} =l_{o}(a) (l_{o} being a large constant). In particular for the precise results on the zeros ofζ^{(1)}(s) —a (a any complex constant andl≥l_{o}) see Theorems 1 and 2 of the introduction.
pp 281-285 August 1995
A note on the growth of topological Sidon sets
We give an estimate for the number of elements in the intersection of topological Sidon sets inR^{n} with compact convex subsets and deduce a necessary and sufficient conditions for an orbit of a linear transformation ofR^{n} to be a topological Sidon set.
pp 287-290 August 1995
Characterization of polynomials and divided difference
For distinct points x_{1},x_{2},…,x_{n} in ℛ (the reals), letϕ[x_{1}, x_{2},…,x_{n}] denote the divided difference ofϕ. In this paper, we determine the general solutionϕ,g: ℛ → ℛ of the functional equationϕ[x_{1},x_{2},…,x_{n}] =g(x_{1},+ x_{2} + … + x_{n}) for distinct x_{1},x_{2},…, x_{n} in ℛ without any regularity assumptions on the unknown functions.
pp 291-296 August 1995
V B L Chaurasia Rajendra Pal Sharma
A theorem concerning a product of a general class of polynomials and theH-function of several complex variables is given. Using this theorem certain integrals and expansion formula have been obtained. This general theorem is capable of giving a number of new, interesting and useful integrals, expansion formulae as its special cases.
pp 297-301 August 1995
Certain bilateral generating relations for generalized hypergeometric functions
Maya Lahiri Bavanari Satyanarayana
Recently, we introduced a class of generalized hypergeometric functionsIn:(b_{q})/α:(a_{p}) (x, w) by using a difference operator Δ_{x,w}, where$$\Delta _{x,w} f(x)\frac{{f(x + w) - f(x)}}{w}$$. In this paper an attempt has been made to obtain some bilateral generating relations associated withI_{n}^{ga}(x, w). Each result is followed by its applications to the classical orthogonal polynomials.
pp 303-314 August 1995
A localization theorem for Laguerre expansions
Regularity properties of Laguerre means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As an application we prove a localization theorem for Laguerre expansions.
pp 315-327 August 1995
Degree of approximation of functions in the Hölder metric by (e, c) means
Degree of approximation of functions by the (e, c) means of its Fourier series in the Hölder metric is studied.
pp 329-339 August 1995
The algebraA_{p}((0, ∞)) and its multipliers
LetI =xεR: 0≤x≤∞ be the locally compact semigroup with addition as binary operation and the usual interval topology. The purpose of this note is to study the algebraA_{p}(I) of elements inL_{1}(I) whose Gelfand transforms belong toL_{p}(Î), whereÎ denotes maximal ideal space ofL_{1}(I). The multipliers ofA_{p}(I) have also been identified.
pp 341-351 August 1995
Reflection of P-waves in a prestressed dissipative layered crust
The paper deals with overall reflection and transmission response of seismic P-waves in a multilayered medium where the whole medium is assumed to be dissipative and under uniform compressive initial stress. The layers are assumed to be homogeneous, each having different material properties. Using Biot’s theory of incremental deformation, analytical solutions are obtained by matrix method. Numerical results for a stack of four layers — modelling earth’s upper layers, show a decreasing trend in both the Reflection CoefficientsR_{D}^{PP} andR_{D}^{PS} of the reflected P and S-waves.
pp 353-369 August 1995
Computer extended series solution to viscous flow between rotating discs
The problem of injection (suction) of a viscous incompressible fluid through a rotating porous disc onto a rotating co-axial disc is studied using computer extended series. The universal coefficients in the low Reynolds number perturbation expansion are generated by delegating the routine complex algebra to computer. Various cases leading to specific types of flows are studied. Analytic continuation of the series solution yields results which agree favourably with pure numerical findings up to moderately large Reynolds number. The precise variation of lift as a function of R is established in each case.
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