Optical properties of magnetic crystals

From symmetry considerations and using generalized Onsager relations, it is shown that 66 of the 90 magnetic classes, consisting of 29 single colour and 37 double colour ones, can exhibit what may be called the strain gyrotropic rotation. Similarly, 69 of the 90 magnetic classes, consisting of 21 single colour and 48 double colour ones, can exhibit what may be called the strain gyrotropic birefringence. A crystal in the class m3 or m3m is interesting as it can exhibit strain gyrotropic rotation despite its being cubic and incapable of exhibiting gyrotropic rotation in the unstressed state. Similarly, a crystal in the classm3m, is interesting as it can exhibit strain gyrotropic birefringence despite its being cubic and incapable of exhibiting gyrotropic birefringence in the unstressed state.     

Spectral properties of complex unit gain graphs

A complex unit gain graph is a graph where each orientation of an edge is given a complex unit, which is the inverse of the complex unit assigned to the opposite orientation. We extend some fundamental concepts from spectral graph theory to complex unit gain graphs. We define the adjacency, incidence and Laplacian matrices, and study each of them. The main results of the paper are eigenvalue bounds for the adjacency and Laplacian matrices.     

Mapping properties of analytic functions on the unit disk

Let be analytic on the unit disk with . In 1989, D. Marshall conjectured the existence of the universal constant such that whenever the area, counting multiplicity, of a portion of over is . Recently, P. Poggi-Corradini (2007) proved this conjecture with an unspecified constant by the method of extremal metrics. In this note we show that such a universal constant exists for a much larger class consisting of analytic functions omitting two values of a certain doubly-sheeted Riemann surface. We also find a numerical value, , which is sharp for the problem in this larger class but is not sharp for Marshall's problem.

     

Dependence of the properties of polycaproamide obtained in the presence of benzhydrazide on the symmetry type of the unit cell

The structure and properties of polycaproamide obtained in the presence of benzhydrazide have been studied. They are shown to depend on the duration of application of pressure in the mold. Under tensile deformation a transition from hexagonal to monoclinic polycaproamide takes place in the neck.Lugansk Machine-Building Institute. Institute of the Chemistry of High-Molecular Compounds, As UkrSSR, Kiev. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1125–1127, November–December, 1968.     

Residual properties of unit loops and augmentation ideals of alternative loop rings

In this paper we study the lattice of all preradicals on a ring R. We describe this lattice, we prove that it is an atomic and coatomic lattice and we describe the atoms and coatoms. We also give characterizations of simple Artinian, semisimple Artinian, and V-rings in terms of preradicals.     

Descriptive properties of families of autohomeomorphisms of the unit interval

Let H⊂C[0,1] stand for the Polish space of all increasing autohomeomorphisms of [0,1]. We show that the family of all strictly singular autohomeomorphisms is -complete. This confirms a suggestion of Graf, Mauldin and Williams. Some related results are also included.     

Optical properties of nanocrystalline silicon embedded in SiO2

Nanocrystalline silicon embedded SiO₂ matrix has been formed by annealing the a-SiO_x films fabricated by plasma enhanced chemical vapor deposition technique. Absorption and photoluminescence spectra of the films have been studied in conjunction with micro-Raman scattering spectra. It is found that absorption presents an exponential dependence of absorption coefficient to photon energy in the range of 1.5–3.0 eV, and a sub-band appears in the range of 1.0–1.5 eV. The exponential absorption is due to the indirect band-to-band transition of electrons in silicon nanocrys-tallites, while the sub-band absorption is ascribed to transitions between surfaces and/or defect states of the silicon nanocrystallites. The existence of Stokes shift between absorption and photoluminescence suggests that the phonon-assisted luminescence would be enhanced due to the quantum confinement effects.     

Dependence of thermooxidative aging parameters on composite properties

An analytical relationship between the thermooxidation rate constants and mechanical properties of composite materials under isothermal and dynamic conditions is obtained. With the example of epoxy-based composites, it is shown that the kinetic parameters of thermooxidation can be used to predict the internal stresses and breakdown voltage of coatings. The calculated drop in the impact toughness exceeds its experimental value by 30%, while the calculated relative breaking elongation is 1.5–2 times greater than the experimental one. A considerable decrease in these indices is observed at a loss of 0.1–1 wt.% of volatile products of thermooxidation. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 237–248, January–February, 2000.     

Descriptive properties of density preserving autohomeomorphisms of the unit interval

We prove that density preserving homeomorphisms form a Π ₁ ¹ -complete subset in the Polish space ? of all increasing autohomeomorphisms of unit interval.     

On properties of cell matrices

In this paper properties of cell matrices are studied. A determinant of such a matrix is given in a closed form. In the proof a general method for determining a determinant of a symbolic matrix with polynomial entries, based on multivariate polynomial Lagrange interpolation, is outlined. It is shown that a cell matrix of size n>1 has exactly one positive eigenvalue. Using this result it is proven that cell matrices are (Circum-)Euclidean Distance Matrices ((C)EDM), and their generalization, k-cell matrices, are CEDM under certain natural restrictions. A characterization of k-cell matrices is outlined.     

Asymptotic properties of the estimators of the Weibull distribution parameters

The properties of the maximum likelihood and moment estimators are investigated for the three-dimensional Weibull distribution in the case of arbitrary values of the shape parameter.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 166, pp. 9–16, 1988.     

Infrared absorption spectra of single crystals of glycine silver nitrate and monoglycine nitrate

The infrared absorption spectra of glycine silver nitrate (GAgNO₃) and glycine nitrate (GHNO₃) show that the glycine group exists completely in the zwitter ion form in the former and in both forms in the latter. The spectrum of GAgNO₃ at liquid air temperature did not reveal any striking change which can be attributed to a freezing of the rapid reorientation of the NH ₃ ⁺ group taking place at higher temperatures. The position of the COO^? stretching frequencies indicate that this group is co-ordinated only weakly to the Ag⁺ ion. The summation frequencies reported by Schroeder, Wier and Lippincott (1962) for AgNO₃ were not observed in the present study on GAgNO₃. It shows however that ferroelectricity in GAgNO₃ is in all probability due to the motion of the Ag⁺ ion in the oxygen co-ordination polyhedron and is not directly connected with the ordering of the hydrogen bonds below Curie point.     

Maximin efficiency robust test for multiple nuisance parameters and its statistical properties

We propose the maximin efficiency robust test (MERT) for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test. We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more. We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied. Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters.     

Geometric and approximation properties of a complex Post–Widder operator in the unit disk

The purpose of this work is to obtain Jackson-type estimates in approximation by a complex Post–Widder operator in the unit disk. In addition, these operators preserve some sufficient conditions for starlikeness and univalence of analytic functions.