Inequalities for a unified family of Voigt functions in several variables

The classical Voigt functions occur frequently in a wide variety of problems in astrophysical spectroscopy, emission, absorption and transfer of radiation in heated atmosphere, and plasma dispersion, and indeed also in the theory of neutron reactions. Here, in the present paper, by applying several known upper bounds for the first-kind Bessel function J _ν (x) given recently by (for example) Landau, Olenko and Krasikov, sharp bounding inequalities are obtained for the unified multivariable Voigt function V _μ,ν (x; y) in terms of the confluent Fox-Wright function ₁ψ₀ and its incomplete variant ₁ψ₀. Connections of the unified multivariable Voigt function V _μ,ν (x; y) with other unifications and generalizations of the classical Voigt function are also briefly pointed out.     

Shadowing with multidimensional time in Banach spaces

We study linear dynamical systems with multidimensional time in Banach spaces. Using Taylor functional calculus we prove that under additional assumptions hyperbolic systems have shadowing property.     

Algebraic models of smooth manifolds

Research supported by the NSF Grant DMS-8602672     

Separation of Monovinyl and Divinyl Protochlorophyllides Using C30 Reverse Phase High Performance Liquid Chromatography Column: Analytical and Preparative Applications

A new, high performance liquid chromatography method has been developed for the separation of monovinyl- and divinyl-protochlorophyllides, using commercially available, C₃₀ reverse phase column and isocratic elution. This method can be used both for analytical applications and preparative scale purification of monovinyl- and divinyl-protochlorophyllides using the same column where submilimolar concentrations of the crude protochlorophyllide extract can be separated in one run. The purity of the obtained protochlorophyllides was demonstrated by spectroscopic methods, as well by the formation of aggregates in toluene.     

Multiple recurrence and nilsequences

Aiming at a simultaneous extension of Khintchine(X,X,m,T)(X,\mathcal{X},\mu,T) and a set A ? XA\in\mathcal{X} of positive measure, the set of integers n such that A T^2nA T^knA)(A)^k+1-\mu(A{\cap} T^{n}A{\cap} T^{2n}A{\cap} \ldots{\cap} T^{kn}A)>\mu(A)^{k+1}-\epsilon is syndetic. The size of this set, surprisingly enough, depends on the length (k+1) of the arithmetic progression under consideration. In an ergodic system, for k=2 and k=3, this set is syndetic, while for kòf(x)f(Tⁿx)f(T²ⁿx)? f(T^knx)  dm(x)\int{f(x)f(T^{n}x)f(T^{2n}x){\ldots} f(T^{kn}x) \,d\mu(x)} , where k and n are positive integers and f is a bounded measurable function. We also derive combinatorial consequences of these results, for example showing that for a set of integers E with upper Banach density d^*(E)>0 and for all {n ? \mathbbZ\colon d^*(E?(E+n)?(E+2n)?(E+3n)) > d^*(E)⁴-e}\big\{n\in\mathbb{Z}{\colon} d^*\big(E\cap(E+n)\cap(E+2n)\cap(E+3n)\big) > d^*(E)^4-\epsilon\big\}     

Temperature dependence of the iron hyperfine field distribution in amorphous Fe-rich Fe-Zr alloys

The temperature dependence of the iron hyperfine field distribution is reported in melt-quenched amorphous Fe-Zr alloys. The most remarkable feature is the compositinal change in the shape of the average hyperfine field versus temperature curves. The unusual increase in the average hyperfine field below about 85 K is a characteristic feature of the RSG systems; however, no anomaly is observed in the width of the hyperfine field distribution as a function of temperature. The results cannot be properly explained in the framework of the existing spin glass models.     

Paraxial designing of planar waveguide variable-index focusing elements: Part 2—lenses of elliptical symmetry

A paraxial ray-optics formalism proposed for designing radially symmetric variable-index lenses is extended to the case of lenses of elliptical symmetry of the index profile.     

Thickness dependence of the magnetic anisotropy of Fe layers separated by Al

Magnetic multilayers of ⁵⁷Fe with nominal thickness, T _nom, between 0.4 and 1.0 nm separated by 3.0 nm Al spacer layers were prepared by alternate deposition of the constituents in high vacuum. The samples were investigated at 4.2 K in external magnetic field. A fraction of Fe atoms corresponding to about 0.3 nm equivalent Fe-thickness was found to mix into the Al spacer. The extremely strong magnetic anisotropy observed for T _nom < 0.8 nm is attributed to Fe layers of approximately two atomic planes thick. The anisotropy decreases considerably after the building up of the third Fe atomic layer starts at T _nom = 0.8 nm, but full saturation was not achieved even for T _nom = 1 nm and 3 T magnetic field applied perpendicularly to the sample plane.     

A combinatorial property of points and ellipsoids

For eachd1 there is a constantc _d>0 such that any finite setXR ^d contains a subsetYX, |Y|[1/4d(d+3)]+1 having the following property: ifEY is an ellipsoid, then |E X|c _d |X|.On leave from the Mathematical Institute of the Hungarian Academy of Sciences, 1364 Budapest, P.O. Box 127, Hungary. Supported by a research fellowship from the Science and Engineering Research Council, U.K., and by Hungarian National Foundation for Scientific Research Grant No. 1812.