Ionic hydrogenation of benzofurans

Benzofurans are arranged in the order 2-methylbenzofuran > 3-methylbenzofuran > benzofuran with respect to the case with which they undergo ionic hydrogenation. Benzofuran and 2-methylbenzofuran are protonated in the 3 position of the heterocyclic ring, whereas 3-methylbenzofuran is protonated in the 2 position. Individual monodeuterated 2,3-dihydrobenzofurans can be obtained in high yields by ionic hydrogenation.     

Mössbauer and DTA studies of the decomposition of iron oxalates

Results are reported for FeC₂O₄·2H₂O and Fe₂(C₂O₄)₃·5H₂O; various stages in the decomposition are demonstrated. The second compound on decomposition in nitrogen gives rise to finely divided Fe₃O₄ containing a little free metal. The conditions for this are established.     

Properties of Josephson junctions in the nonuniform field of ferromagnetic particles

Experimental and theoretical studies of ferromagnet-superconductor hybrid systems consisting of a Josephson junction placed in the nonuniform field of submicron ferromagnetic particles are reviewed.     

On Osgood theorem in Banach spaces

Let X be a real Banach space, ω : [0, +∞) → ? be an increasing continuous function such that ω(0) = 0 and ω(t + s) ≤ ω(t) + ω(s) for all t, s ∈ [0, +∞). According to the infinite dimensional analog of the Osgood theorem if ∫¹₀ (ω(t))^?1 dt = ∞, then for any (t₀, x₀) ∈ ?×X and any continuous map f : ?×X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all t ∈ ?, x, y ∈ X, the Cauchy problem (t) = f(t, x(t)), x(t₀) = x₀ has a unique solution in a neighborhood of t₀. We prove that if X has a complemented subspace with an unconditional Schauder basis and ∫¹₀ (ω(t))^?1 dt < ∞ then there exists a continuous map f : ? × X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all (t, x, y) ∈ ? × X × X and the Cauchy problem (t) = f(t, x(t)), x(t₀) = x₀ has no solutions in any interval of the real line.     

On continuity points of Gateaux differentiable mappings

Moscow. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp., 176–185, September–October, 1992.     

Multiplicative Spectra of Banach Spaces

The multiplicative spectrum of a complex Banach space X is the class (X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X, *) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with unity. Properties of multiplicative spectra are studied. In particular, we show that (X ⁿ ) consists of countable compact spaces with at most n nonisolated points for any separable, hereditarily indecomposable Banach space X. We prove that (C[0, 1]) coincides with the class of all metrizable compact spaces. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 14, Algebra, 2004.     

Genesis of phase composition in Fe?Mn catalysts for synthesis of olefins from CO and H2 under catalytic conditions in situ

Genesis of the phase composition in oxide Fe–Mn catalysts for olefin synthesis under close to catalytic conditions has been studied in a high temperature X-ray chamber.

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, , Fe–Mn .

     

A weighted bilateral shift with cyclic square is supercyclic

It is shown, for a bounded weighted bilateral shift T actingon _p(), and for 1p2, that supercyclicity of T, weak supercyclicityof T, cyclicity of T T and cyclicity of T² are equivalent. Anew sufficient condition for cyclicity of a weighted bilateralshift is proved, which implies, in particular, that any compactweighted bilateral shift is cyclic.     

Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator $f(z)\stackrel{T_{\lambda }}{?}f(z+\lambda )$ acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of $C_0$-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that $(T,T^2)$ is not d-mixing.     

Spectral theory of Volterra-composition operators

Given a Lebesgue measurable self-map of the interval [0, 1], the Volterra- composition operator is defined as We develop the spectral theory of these operators. In particular, for a class of natural symbols , finiteness of the spectrum is characterized and formulae for the trace and the convergence exponent of eigenvalues are provided. The positivity of the spectrum as well as the analyticity of the eigenfunctions are also treated. The theory of entire functions as well as solving some Cauchy Problems will play a fundamental role in this theory. We also supply some examples of symbols to which the theory can be applied and, in particular, eigenvalues and eigenfunctions are computed explicitly. Partially supported by Plan Nacional I+D+I grant no. MTM2006-09060, Junta de Andalucía FQM-260 and P06-FQM-02225.