Volume 106, Issue 2
May 1996, pages 105-216
pp 105-125 May 1996
Limit distributions of expanding translates of certain orbits on homogeneous spaces
LetL be a Lie group and λ a lattice inL. SupposeG is a non-compact simple Lie group realized as a Lie subgroup ofL and$$\overline {GA} = L$$. LetaεG be such that Ada is semisimple and not contained in a compact subgroup of Aut(Lie(G)). Consider the expanding horospherical subgroup ofG associated toa defined as U^{+} ={gεG:a^{−n} ga^{n}} →e asn → ∞. Let Ω be a non-empty open subset ofU^{+} andn_{i} → ∞ be any sequence. It is showed that$$\overline { \cup _{i = 1}^\infty a^n \Omega \Lambda } = L$$. A stronger measure theoretic formulation of this result is also obtained. Among other applications of the above result, we describeG-equivariant topological factors of L/gl × G/P, where the real rank ofG is greater than 1,P is a parabolic subgroup ofG andG acts diagonally. We also describe equivariant topological factors of unipotent flows on finite volume homogeneous spaces of Lie groups.
pp 127-132 May 1996
In this paper we extend a classical result due to Cauchy and its improvement due to Datt and Govil to a class of lacunary type polynomials.
pp 133-137 May 1996
Quasi-parabolic Siegel formula
The result of Siegel that the Tamagawa number ofSL_{r} over a function field is 1 has an expression purely in terms of vector bundles on a curve, which is known as the Siegel formula. We prove an analogous formula for vector bundles with quasi-parabolic structures. This formula can be used to calculate the Betti numbers of the moduli of parabolic vector bundles using the Weil conjuctures
pp 139-153 May 1996
Degree of approximation of functions by their fourier series in the generalized Hölder metric
The paper studies the degree of approximation of functions by matrix means of their Fourier series in the generalized Hölder metric, generalizing many known results in the literature
pp 155-162 May 1996
A note on multidimensional modified fractional calculus operators
In the present investigation some new formulas giving the images under multidimensional modified fractional operators of the celebratedH-function of Fox [Trans. Am. Math. Soc.98 (1961) 395–429] are obtained. Special cases are briefly pointed out and the results are also studied on general spaces of functionsM_{γ}(R_{+}^{n})
pp 163-168 May 1996
Changing the variable in convolution of distributions
In this paper the author has extended the concept of changing the variables in distributions to the convolution of distributions. For an infinitely differentiable functionh(x), he has first defined the convolution of two distributions f(h(x)) and g(h(x)) and then proved some of its properties. Finally, he has applied his results to the fractional integral and fractional differential operators
pp 169-176 May 1996
Linearized oscillations for higher order neutral differential equations
In this paper, the oscillation of certain nonlinear neutral differential equations has been studied with the help of the oscillation of associated linear neutral differential equations
pp 177-182 May 1996
A note on a class of singular integro-differential equations
A simplified analysis is employed to handle a class of singular integro-differential equations for their solutions
pp 183-199 May 1996
Wave propagation in a micropolar generalized thermoelastic body with stretch
In the present investigation, we discuss two different problems namely
Rayleigh-Lamb problem in micropolar generalized thermoelastic layer with stretch and
Rayleigh wave in a micropolar generalized thermoelastic half-space with stretch. The frequency and wave velocity equations for symmetric and anti-symmetric vibrations are obtained for the first problem. The frequency equation has also been derived for the second problem. The special cases of the above said problems of micropolar generalized thermoelasticity with stretch for Green-Lindsay and Lord-Shulman theory have been discussed in detail. Results of these analysis reduce to those without thermal and stretch effects
pp 201-216 May 1996
New families of graceful banana trees
Vasanti N Bhat-Nayak Ujwala N Deshmukh
Consider a family of stars. Take a new vertex. Join one end-vertex of each star to this new vertex. The tree so obtained is known as abanana tree. It is proved that the banana trees corresponding to the family of stars
(K_{1,1}, K_{1,2},…, K_{1,t −1}, (α + l) K_{1,t}, K_{1,t + 1}, …, K_{1,n}), α ⩽ 0
(2K_{1,1}, 2K_{1,2},…, 2K_{1,t− 1}, (α + 2)K_{1,t}, 2K_{1,t + 1, …}, 2K_{1,n}), 0 ⩽ α <t and
(3K_{1,t}, 3K_{1,2}, …, 3K_{1,n}) are graceful.
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