Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

A novel method for synthesizing diorganylphosphinous acids from red phosphorus and arylalkenes

The reaction of styrene and -methylstyrene with P in aprotic polar solvents in the presence of KOH affords diorganylphosphinous acids.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1680–1681, September, 1994.     

Tris(2,2''''-bipyridyl)ruthenium(Ⅱ) electrochemiluminescence (ECL) enhanced by rutin on platinum electrode

Ru(bpy)_(3~(2 )) electrochemiluminescence (ECL) was applied to determination of rutin. ECL intensity of Ru(bpy)_(3~(2 ))could be enhanced in the presence of rutin in basic solution on platinum electrode. At pH 9.9, light emission intensity was found to be linear with rutin in the range of 1-50 mmol/L.     

Das asymptotische Verhalten der Peanokerne einiger interpolatorischer Quadraturverfahren

Summary Interpolatory quadrature formulae consist in replacing by wherep _f denotes the interpolating polynomial off with respect to a certain knot setX. The remainder may in many cases be written as wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP _X (t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis.

     

Fields as Kolmogzrov flows

It is widely recognized that for highly unstable dynamical systems there exists a fundamental limitation on predictability and determinism. An important class of such highly unstable systems is the class of K-flow, which is further characterized by the existence of time-asymmetric objects in the form of K-partition. Our recent approach to the problem of irreversibility has shown that when the implications of the limitation on determinism arising from strong form of instability and those of the existence of K-partition are consistently taken into account, one is naturally led from the physically unrealizable deterministic evolution of phase points to an entropy-increasing stochastic Markovian evolution. Furthermore, this transition is not the result of extraneously imposed coarse graining and/or approximation schemes, but can be brought about by an invertible transformation whose existence and construction are determined by the nature of the instability of the dynamical system itself. After a brief review of this theory which also contains some relatively new remarks, we prove that classical Klein-Gordon field (both massive and massless) possess the structure of K-flow. This seems to provide the first examples of relativistic systems that are K-flows. Some of the implications of this result are briefly discussed. From a mathematical point of view, this seems to be a first step toward an ergodic theory of partial differential equations. In the process, we also provide an independant group-theoretic proof of the existence of incoming and outgoing subspaces of the scattering theory of Lax and Phillips for the wave equation.     

Why is space three-dimensional and how may groups be seen?

First we propose a model of visual perception essentially based on the Keldysh-Chernavsky-Sossinsky three-channel theorem, from which three-dimensionality of space follows. Second, we associate with a system of subgroups H ₁, ..., H_s of a given group G a geometric object, called a group crystal, in order to visualize G. How this notion works is illustrated via the Burnside problem.     

Darstellung und Strukturen einiger N-(Tri-t-butoxysilyl)anilin-Derivate

Formation and Structures of N-(tri-t-butoxysilyl)aniline Compounds Para-substituted N-(tri-t-butoxysilyl)anilines (t-BuO)₃SiNRC₄H₄X-p, R = H, CH₃, with substituents of high electron affinity (X = CN, NO₂) were prepared by a one-pot reaction of tri-t-butoxychlorsilane, potassium t-butanolate and substituted anilines. Corresponding compounds with substituents of low electron affinity (X = OMe, H) preferably were prepared by metalation of anilines with sodium amide. Four crystal structures were determined. N-(tri-t-butoxysilyl)-p-nitro-aniline, N-methyl-(N-tri-t-butoxysilyl)-p-nitroaniline and N-(tri-t-butoxysilyl)-p-cyanoaniline crystallize at 298 K monoclinically, N-(tri-t-butoxysilyl)aniline crystallizes orthorhombically.     

Tetragonal low-temperature structure of LiAl

The cubic face-centered structure of LiAl (, at ) transforms into a tetragonal body-centered structure (I4₁/amd, , at ). This first-order phase transition at about during heating is probably the reason for the so-called “ anomalies” in some physical properties like specific heat, electrical resistivity and nuclear-spin lattice relaxation. This transition seems to be correlated with the composition Li:Al of the alloy and the amount of Li vacancies.     

Paraquat guest induced hydrogen-bonding modes of a hydrazide-derived bis(meta-phenylene)-32-crown-10 host in the solid state

A hydrazide-derived bis(meta-phenylene)-32-crown-10 host showed a dimeric structure via quadruple N-H?O hydrogen bonds, but a polymeric structure via two N-H?O hydrogen bonds and two C-H?O hydrogen bonds at each knot in the presence of paraquat in the solid state, which led to a novel poly(taco complex) and ordering arrangement of the guest molecules indirectly.     

On semianalytic subsets of rigid analytic varieties

We show some topological properties of semianalytic subsets of rigid analytic varieties: curve selection lemma, the closure of a semianalytic subsetS is semianalytic, for every quasi-compact morphismf. As an application we show that a morphismf: X Y of rigid analytic varieties is open at a pointx X if and only if SpecO _X,x SpecO _Y,f(x) is surjective.