• Volume 109, Issue 3

August 1999,   pages  231-332

• Equations of similitude

A general technique is developed to enlarge the Galois group of an equation from a subgroup of a finite classical isometry group towards the corresponding similitude group.

• Remarks on the wonderful compactification of semisimple algebraic groups

We prove that ifG is a semisimple algebraic group of adjoint type over the field of complex numbers,H is the subgroup of all fixed points of an involution σ ofG that is induced by an involution σ of the simply connected coveringĜ ofG, then the wonderful compactification$$\overline {G/H}$$ of the homogeneous spaceG/H is isomorphic to the G.I.T quotientGss(L)//H of the wonderful compactificationG ofG for a suitable choice of a line bundleL onG. We also prove a functorial property of the wonderful compactifications of semisimple algebraic groups of adjoint type.

• Seiberg-Witten invariants — An expository account

The Seiberg-Witten monopole equations, and a new invariant for 4-manifolds which results from these equations, are introduced in this paper.

• The theorem of Kronheimer-Mrowka

A proof of the conjecture of Thom (algebraic curves in the complex projective plane minimize genus within their homology class) due to Kronheimer-Mrowka is presented. The proof uses the mod-2 Seiberg-Witten invariants.

• Infinitely divisible probabilities on linearp-adic groups

In this paper we extend the work of Shah, on the structure of infinitely divisible probabilities onp-adic linear groups, to give a classification for all such probabilities.

• A short note on weighted mean matrices

In the present paper we have established a relation between (N, pn) and (N, qn) weighted mean matrices, when considered as bounded operators on 1p, 1 &lt; p &lt; ∞.

• L1 (μ, X) as a constrained subspace of its bidual

In this note we consider the property of being constrained in the bidual, for the space of Bochner integrable functions. For a Banach spaceX having the Radon-Nikodym property and constrained in its bidual and forY ⊂ X, under a natural assumption onY, we show thatL1 (μ, X/Y) is constrained in its bidual andL1 (μ, Y) is a proximinal subspace ofL1(μ, X). As an application of these results, we show that, ifL1(μ, X) admits generalized centers for finite sets and ifY ⊂ X is reflexive, thenL1μ, X/Y) also admits generalized centers for finite sets.

• A result on the composition of distributions

LetF be a distribution and letf be a locally summable function. The distributionF(f) is defined as the neutrix limit of the sequenceFn(f), whereFn(x) = F(x) * δn(x) andδn(x) is a certain sequence of infinitely differentiable functions converging to the Dirac delta-functionδ(x). The distribution (xr)−s is valuated forr, s = 1,2, ….

• Existence of solutions of neutral functional integrodifferential equation in Banach spaces

In this paper we prove the existence of mild solutions for neutral functional integrodifferential equation in a Banach space. The results are obtained by using the Schaefer fixed-point theorem.

• # Proceedings – Mathematical Sciences

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Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019