• Volume 115, Issue 3

      August 2005,   pages  241-369

    • Some properties of complex matrix-variate generalized Dirichlet integrals

      Joy Jacob Sebastian George A M Mathai

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      Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of the type-2 or inverted Dirichlet is looked into in this article. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.

    • Homeomorphisms and the homology of non-orientable surfaces

      Siddhartha Gadgil Dishant Pancholi

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      We show that, for a closed non-orientable surfaceF, an automorphism ofH1(F, ℤ) is induced by a homeomorphism ofF if and only if it preserves the (mod 2) intersection pairing. We shall also prove the corresponding result for punctured surfaces.

    • Higher order Hessian structures on manifolds

      R David Kumar

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      In this paper we define nth order Hessian structures on manifolds and study them. In particular, whenn = 3, we make a detailed study and establish a one-to-one correspondence betweenthird-order Hessian structures and acertain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on the second-order tangent bundle. Also we define second-order geodesics of special second-order connection which gives a geometric characterization of symmetric third-order Hessian structures.

    • Degree-regular triangulations of torus and Klein bottle

      Basudeb Datta Ashish Kumar Upadhyay

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      A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices.

      In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.

    • Estimates and nonexistence of solutions of the scalar curvature equation on noncompact manifolds

      Zhang Zonglao

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      This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results for complete solutions of scalar curvature equation.

    • Ideal amenability of Banach algebras on locally compact groups

      M Eshaghi Gordji S A R Hosseiniun

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      In this paper we study the ideal amenability of Banach algebras. LetA be a Banach algebra and letI be a closed two-sided ideal inA, A isI-weakly amenable ifH1(A,I*) = {0}. Further,A is ideally amenable ifA isI-weakly amenable for every closed two-sided idealI inA. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal amenability of Banach algebras on locally compact groups.

    • The Socle and finite dimensionality of some Banach algebras

      Ali Ghaffari Ali Reza Medghalchi

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      The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact groupG, G is compact if there exists a measure μ in Soc(L1(G)) such that μ(G) ≠ 0. We also prove thatG is finite if Soc(M(G)) is closed and every nonzero left ideal inM(G) contains a minimal left ideal.

    • Multipliers ofAp((0, ∞) with order convolution

      Savita Bhatnagar

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      The aim of this paper is to study the multipliers fromAr(I) toAp(I),rp, whereI = (0, ∞) is the locally compact topological semigroup with multiplication max and usual topology andAr(I) =fL1(I): f ∈Lr(Î) with norm ¦¦¦f¦¦¦r = ¦¦f¦¦1 + ¦¦f¦¦r.

    • Fixed point theory for composite maps on almost dominating extension spaces

      Ravi P Agarwal Jong Kyu Kim Donal O’Regan

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      New fixed point results are presented forUck(X, X) maps in extension type spaces.

    • Wavelet characterization of Hörmander symbol classSρ,δm and applications

      Q X Yang

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      In this paper, we characterize the symbol in Hormander symbol classSρm,δ (m ∈ R, ρ, δ ≥ 0) by its wavelet coefficients. Consequently, we analyse the kerneldistribution property for the symbol in the symbol classSρm,δ (mR, ρ > 0, δ 0) which is more general than known results ; for non-regular symbol operators, we establish sharp L2-continuity which is better than Calderón and Vaillancourt’s result, and establishLp (1 ≤p ≤∞) continuity which is new and sharp. Our new idea is to analyse the symbol operators in phase space with relative wavelets, and to establish the kernel distribution property and the operator’s continuity on the basis of the wavelets coefficients in phase space.

    • Erratum

      M S Raghunathan

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