A note on the gl constant ofE \mathop \otimes \limits^ \vee F F

LetX andY be Banach spaces. TFAE (1)X andY do not contain subspaces uniformly isomorphic to (2) The local unconditional structure constant of the space of bounded operatorsL (X*_k,Y _k) tends to infinity for every increasing sequence and of finite-dimensional subspaces ofX andY respectively.     

The Invariance Principle for p-θ^→ Chain

There are two parts in this paper. In the first part we construct the Markov chain in random environment（MCRE）, the skew product Markov chain and p-θ^→ chain from a random transition matrix and a two-dimensional probability distribution, and in the second part we prove that the invarianee principle for p-θ^→ chain, a more complex non-homogeneous Markov chain, is true under some reasonable conditions. This result is more powerful.     

Holomorphic deformations of the Ricci-flat $$\partial \overline \partial $$-manifolds

We present a construction of globally convergent power series of integrable Beltrami differentials on the Ricci-flat \(\partial \overline \partial \)-manifolds and also a construction of global canonical family of holomorphic (n, 0)-forms on the deformation spaces of the Ricci-flat \(\partial \overline \partial \)-manifolds.     

L-Factor of Irreducible x1×x2(×)σ

The L-factor of irreducible x1×x2(×)σ defined by Piatetski-Shapiro is computed by using non-split Bessel functional.     

Approximation of functions from the class {\ifmmode\expandafter\hat\else\expandafter\^\fi{C}}^\psi_{\beta,\infty} by Poisson biharmonic operators in the uniform metric

We obtain asymptotic equalities for upper bounds of approximations of functions from the class by Poisson biharmonic operators in the uniform metric. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 669–693, May, 2008.     

On the Evaluation of the Integral $$\int_0^{{\pi \mathord{\left/ {\vphantom {\pi 4}} \right. \kern-\nulldelimiterspace} 4}} {\ln \left( {\cos ^{{m \mathord{\left/ {\vphantom {m n}} \right. \kern-\nulldelimiterspace} n}} \theta \pm \sin ^{{m \mathord{\left/ {\vphantom {m n}} \right. \kern-\nulldelimiterspace} n}} \theta } \right)d\theta } $$

The integral $$\int_0^{{\pi \mathord{\left/ {\vphantom {\pi 4}} \right. \kern-\nulldelimiterspace} 4}} {\ln \left( {\cos ^{{m \mathord{\left/ {\vphantom {m n}} \right. \kern-\nulldelimiterspace} n}} \theta \pm \sin ^{{m \mathord{\left/ {\vphantom {m n}} \right. \kern-\nulldelimiterspace} n}} \theta } \right)d\theta } $$ where m and n are relatively prime positive integers, is evaluated exactly in terms of elementary functions and the Catalan constant G.     

On the Convergence of Products γ^-sh1hn in the Adams Spectral Sequence

Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by （b0hn-h1bn-1）∈ ExtA^3,（p^n＋p）q（Zp,Zp） in the Adams spectral sequence. At the same time, he proved that i.（hlhn） ∈ExtA^2,（p^n＋P）q（H^＊M, Zp） is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π（p^n＋p）q-2M. In this paper, with Lin＇s results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq ＋ sp^2q ＋ spq ＋ （s - 2）q ＋ s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s＋2,＊-term of the Adams spectral sequence, where p ≥ 7, q = 2（p - 1）, n ≥ 4 and 3 ≤ s 〈 p.     

Remarks on the local regularity of the\overline \partial

Summary Let Ω⊂⊂C ⁿ be a pseudo-convex domain with smooth real-analytic boundarybΩ; the local regularity in of the is then strictly related not only with the subellipticity of such problem, but also with certain geometric conditions onbΩ: ifn=2 and α is a (0,1)-form, such relations are equivalences.

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Riassunto Se Ω⊂⊂C ⁿ è un dominio pseudo-convesso con frontierabΩ definita da una funzione analitica reale e ?liscia?, la regolarità locale delle soluzioni in del αè in stretta relazione non solo con la subellitticità di tale problema ma anche con certe condizioni geometriche sulla struttura dibΩ: sen=2 ed α è una (0,1)-forma, tali relazioni sono delle equivalenze.

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Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R.     

A nonstandard set theory in the \displaystyle\in-language

Abstract. We demonstrate that a comprehensive nonstandard set theory can be developed in the standard -language. As an illustration, a nonstandard is obtained. Received: 17 March 1998 / Revised version: 30 October 1998     

On the regularity of the locally integrable solutions of the functional equations $$\sum\limits_{i = 1}^k {a_i \left( {x,t} \right)f\left( {x + \varphi _i \left( t \right)} \right) = b\left( {x,t} \right)} $$

Aequationes mathematicae -