Three elementary proofs of the goldberg-straus theorem on numerical radii

Three elementary proofs of the positive definiteness of the A-numerical radius, as defined by Goldberg and Straus, are given and a stronger result concerning exterior powers is conjectured     

The dirichlet problem in a domain whose boundary is partly degenerated

Summary In this paper we bring a formulation of the Dirichlet problem for strongly elliptic equations in domains vhose boundaries may include manifolds of different dimensions. It is shown that, under certain regularity conditions, this problem is equivalent to the generalized Dirichlèt problem, with respect to existence and uniquennes of solutions. This paper represents part of a thesis submitted to the Senate of the Technion, Israel Institute of Technology, in partial fulfillment of the requirements for the degree of Doctor of Science. The author wishes to tank ProfessorS. Agmon for his gudance and help in the preparation of this work.     

Phase separation and crystallization in amorphous Pd-Si-Sb

It is found that replacing some of the Si in a Pd-Si-Sb glass with Sb can make it more resistant to crystallization than the pure binary material. This is shown by the calorimetric results, in which the crystallization temperature increases and the glass temperature decreases with increasing Sb substitution, and also by the finding that certain alloys, such as Pd_80.5 Si_16.5Sb₃ may be quenched into amorphous rods (by the gradient-quench method) up to 0.5 mm thick.

Calorimetry and small-angle X-ray scattering data show that certain alloys in this system phase separate in the amorphous state. The two phases thus produced independently crystallize. Isothermal measurements indicate that the rate of crystallization of one of the phases is interface-limited, with most nuclei initially present. The other crystallization process does not fit an Avrami law, possibly due to a transformation of the crystalline phase.

A method called “gradient-quenching” (GQ) was used to prepare samples from the melt in such a way that the quench-rate was non-uniform, so all stages of crystallization in slowly-quenched alloys are displayed. Nucleation was frequently found to take place on voids and inclusions.

The use of the calorimetric and GQ methods in conjunction to gather information about crystallization processes in metallic glasses is discussed.     

Minimal models of theories of one function symbol

IfT ₁ is a theory of one function symbol andT ₁ has a minimal model which is not prime, thenT ₁ has 2^No non-isomorphic minimal models. This paper is part of the author’s doctoral dissertation prepared at the Hebrew University under the supervision of Professor Haim Gaifman.     

The blue bronze K0.3MoO3: A new one-dimensional conductor

The optical reflectivity of the blue bronze K_0.3MoO₃ has been measured on single crystals for photon energies between 0.03 and 12 eV at temperatures from 10 to 300 K using polarized light. The data are interpreted that this compound is a one-dimensional conductor for temperatures above 180 K and that the metal-semiconductor transition at 180 K is due to a Peierls type transition, leading to a gap of 0.15 eV in the density of states.     

Zur Methodik der Elementspezies-Analytik in Lebensmitteln

Summary Potentiometry with an ion-selective electrode as well as a cation-chelate-exchange procedure (combined with AAS) are presented as useful methods for the determination of stabilities of element species, for example of calcium in milk. The cation-exchange procedure is also applicable to other metals (e.g., magnesium) and other foodstuffs (e.g., meat extracts). New results of Ca- and Mg-extractabilities by the use of different aqueous extraction solutions (including enzymic solutions) are reported. Ultrafiltration, dialysis and gel-chromatography are further methods especially for the separation and analysis of protein-containing element species. Unoccupied binding fields can be detected after addition of Cu(II) ions by combination of gel chromatography and UV/VIS spectroscopy, as shown by example of rape-flour. The experiences gained in the analysis of element species in foodstuffs are combined to a strategy of analysis.     

Polarized neutron study of the RA12 compound: I. Magnetization density in NdA12

The magnetization density of the ferromagnet NdA1₂ has been studied by diffraction of polarized neutrons on single crystals. The data have been treated as well in direct space using Fourier transformation techniques as in reciprocal space with the tensor operator method. The two treatments give the same result: besides the localized magnetization due to the 4f electrons of Nd, and corresponding to 2.61 μ_B, there exist another magnetization, opposite to the first one, which fluctuates throughout the cell with a pronounced extremum around the Nd atoms. Its integrated value is -0.14 μ_B/ND. The 4f electron wave function corresponding to the localized magnetization has been determined.     

Cost and sensitivity of restricted active‐space calculations of metal L‐edge X‐ray absorption spectra

The restricted active‐space (RAS) approach can accurately simulate metal L‐edge X‐ray absorption spectra of first‐row transition metal complexes without the use of any fitting parameters. These characteristics provide a unique capability to identify unknown chemical species and to analyze their electronic structure. To find the best balance between cost and accuracy, the sensitivity of the simulated spectra with respect to the method variables has been tested for two models, [FeCl₆]^3– and [Fe(CN)₆]^3–. For these systems, the reference calculations give deviations, when compared with experiment, of ≤1 eV in peak positions, ≤30% for the relative intensity of major peaks, and ≤50% for minor peaks. When compared with these deviations, the simulated spectra are sensitive to the number of final states, the inclusion of dynamical correlation, and the ionization potential electron affinity shift, in addition to the selection of the active space. The spectra are less sensitive to the quality of the basis set and even a double‐ζ basis gives reasonable results. The inclusion of dynamical correlation through second‐order perturbation theory can be done efficiently using the state‐specific formalism without correlating the core orbitals. Although these observations are not directly transferable to other systems, they can, together with a cost analysis, aid in the design of RAS models and help to extend the use of this powerful approach to a wider range of transition metal systems. © 2015 Wiley Periodicals, Inc.