Volume 101, Issue 1
April 1991, pages 1-61
pp 1-17 April 1991
Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces
We show that ifG is a semisimple algebraic group defined overQ and Γ is an arithmetic lattice inG:=G_{R} with respect to theQ-structure, then there exists a compact subsetC ofG/Γ such that, for any unipotent one-parameter subgroup {u_{t}} ofG and anyg∈G, the time spent inC by the {u_{t}}-trajectory ofgΓ, during the time interval [0,T], is asymptotic toT, unless {g^{−1}u_{t}g} is contained in aQ-parabolic subgroup ofG. Some quantitative versions of this are also proved. The results strengthen similar assertions forSL(n,Z),n≥2, proved earlier in [5] and also enable verification of a technical condition introduced in [7] for lattices inSL(3,R), which was used in our proof of Raghunathan’s conjecture for a class of unipotent flows, in [8].
pp 19-24 April 1991
On the ratio of the maximum term and the maximum modulus of the sum of two entire functions
Some results on the sum of two entire functions pertaining to the ratio of the maximum term and the maximum modulus are proved.
pp 25-36 April 1991
Linear flow induced in fluid particle suspension by an infinite differentially rotating disk
C N B Rao V Vasudeva Murty V Somaraju
The steady, axisymmetric laminar flow of a homogeneous incompressible fluid with suspended particles occupying the half-infinite space over a differentially rotating rigid plane boundary is analyzed in this paper. The effect of suspended particles is described by two parametersf and τ. The mass concentration parameterf is a measure of the concentration of suspended dust particles. The interaction parameter τ is a measure of the rate at which the velocity of dust particles adjusts to changes in the fluid velocity and depends upon the size of the individual particles. Due to Ekman suction, the particle density remains no longer a constant in the boundary layer but varies with the axial coordinate ξ. Flow characteristics and density variations are studied as functions off, τ and ξ. Possible limiting cases for τ≪1 and τ≫1 which correspond to the case of fine dust and coarse dust respectively are derived and discussed.
pp 37-41 April 1991
Integrals involving Fox’sH-function
We evaluate four integrals involving Fox’sH-functions and a general class of polynomialsS_{n}^{m}[x], introduced earlier by Srivastava.
pp 43-47 April 1991
An extension of bilateral generating functions of modified Laguerre polynomials
In this note a theorem concerning the extension of bilateral generating functions of the modified Laguerre polynomials is derived. Some applications of the theorem are also pointed out.
pp 49-54 April 1991
Bilateral generating functions for Jacobi polynomials
In this paper, we have obtained three theorems on generating functions. We derive from these theorems a large number of bilateral generating functions for Jacobi polynomials. Certain interesting expansions of triple hypergeometric series are also obtained from one of the theorems.
pp 55-61 April 1991
Summability of Laguerre series at the pointx=0
In this paper, the authors prove a theorem on matrix summability of Laguerre series at the point x=0. Various results on Casàro, Nörlund and generalized Nörlund summability method have been deduced.
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