On the L2n 1– Extension Properties

We have proved that for all compact linear operator u from R into an L_p ([0,1], ν) (0 < p < 1) extends to L ₁ ([0,1], ν), where R denotes the closed linear subspace in L ₁ ([0,1], ν) of the Rademacher functions {r_n }_{n ? N}. In this paper, we study this type of extension for E_n ? L_2n ¹ where E_n is the n–dimensional subspace which appears in Kasin's theorem such that L_2n ¹ = E_n ⊕ E ^⊥ _n and the L_2n ¹ , L_2n ² norms are universally equivalent on both E_n , E ^⊥ _n. We show that, the precedent extension fails for the pair (E_n , L_2n ¹ ) and we generalize this to any E in an L ₁(Ω, A, P) by giving some conditions on E.     

Stable Functions and Extension of Vietoris’ Theorem

In this work, using subordination results for the Cesáro sum of certain analytic functions, a concept called Cesáro stable is given and two conjectures in this direction are also proposed. Using an extension of Vietoris’ theorem on positivity of cosine sums, some results on positivity of cosine and sine sums are obtained. These results are useful in discussing some particular cases of the proposed conjectures.     

Extension of Pauli’s theorem to Clifford algebras

Doklady Mathematics -     

Extension of Overbeck’s attack for Gabidulin-based cryptosystems

Cryptosystems based on codes in the rank metric were introduced in 1991 by Gabidulin, Paramanov, and Tretjakov (GPT) and have been studied as a promising alternative to cryptosystems based on codes in the Hamming metric. In particular, it was observed that the combinatorial solution for solving the rank analogy of the syndrome decoding problem appears significantly harder. Early proposals were often made with an underlying Gabidulin code structure. Gibson, in 1995, made a promising attack which was later extended by Overbeck in 2008 to cryptanalyze many of the systems in the literature. Improved systems were then designed to resist the attack of Overbeck and yet continue to use Gabidulin codes. In this paper, we generalize Overbeck’s attack to break the GPT cryptosystem for all possible parameter sets, and then extend the attack to cryptanalyze particular variants which explicitly resist the attack of Overbeck.     

Extension of Euler’s method to parabolic equations

Euler generalized d’Alembert’s solution to a wide class of linear hyperbolic equations with two independent variables. He introduced in 1769 the quantities that were rediscovered by Laplace in 1773 and became known as the Laplace invariants. The present paper is devoted to an extension of Euler’s method to linear parabolic equations with two independent variables. The new method allows one to derive an explicit formula for the general solution of a wide class of parabolic equations. In particular, the general solution of the Black–Scholes equation is obtained.     

Sur Une Classe D’Espaces D’Interpolation

Sans résumé Les A. ont été soutenus par l’Interpol.     

Extension of Mood’s median test for survival data

Mood’s median test for testing the equality of medians is a nonparametric approach, which has been widely used for uncensored data in practice. For survival data, many nonparametric methods have been proposed to test for the equality of survival curves. However, if the survival medians, rather than the curves, are compared, those methods are not applicable. Some approaches have been developed to fill this gap. Unfortunately, in general those tests have inflated type I error rates, which make them inapplicable to survival data with small sample sizes. In this paper, Mood’s median test for uncensored data is extended for survival data. The results from a comprehensive simulation study show that the proposed test outperforms existing methods in terms of controlling type I error rate and detecting power.     

An Extension of Mercer’s Theorem via Pontryagin Spaces

We extend Mercer’s theorem to a composition of the form RS, in which R and S are integral operators acting on a space L ²(X) generated by a locally finite measure space (X, ν). The operator R is compact and positive while S is continuous and having spectral decomposition based on well distributed eigenvalues. The proof is based on a Pontryagin space structure for L ²(X) constructed via the operators R and S themselves.     

模糊D0L幂级数

将Lindenmayer代数系统推广到模糊半环上,引入模糊L代数系统及模糊L代数幂级数的概念。定义由模糊代数系统生成的模糊D0L幂级数,并研究模糊D0L幂级数的性质。模糊D0L幂级数的重数序列具有很好的性质,且两个模糊D0L幂级数的等价性是可判定的。此外,模糊D0L幂级数的F-代数性、F-上下文无关性及F-有理性也是可判定的。     

Décompte dans une conjecture de Lang

Faltings has proven the following conjecture of Lang: if A is an abelian variety over a number field and X any subvariety then all rational points of X lie on a finite number N of translates, contained in X, of abelian subvarieties of A. We provide an upper bound for N whose main feature is uniformity in X since it does not depend on the height of X. Moreover, the bound is completely explicit. Together with the result of a previous paper, the heart of the proof is a suitable generalization of Mumford’s theorem for curves.

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Décompte dans une conjecture de Lang

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Oblatum 20-III-2000 & 3-V-2000?Published online: 16 August 2000