The number of roots of a polynomial outside a circle

We obtain a new criterion in terms of determinant inequalities that all the roots of a real polynomial should lie inside the unit circle, i.e., a criterion for the stability of periodic motions. In comparison with the Shur-Kon criterion, the number of determinants is halved.The results of this paper were published without proof in [2].Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 3–12, January, 1973.     

Raman mapping of coesite inclusions in garnet from the Kokchetav Massif (Northern Kazakhstan)

Coesite inclusions occur in a wide range of lithologies and coesite is therefore a powerful ultrahigh-pressure (UHP) indicator. The transformation of coesite to quartz is evidenced by three optically well identifiable characteristics (e.g. palisade textures, radial crack patterns, polycrystalline quartz pseudomorphs). Under overpressure monomineralic coesite (on an optical basis), lacking the above transformation characteristics may survive. Raman micro-spectroscopy was applied on monomineralic coesite inclusions in garnet porphyroblasts from diamond-bearing garnet-clinozoisite-biotite gneisses of the Barchi-Kol area (Kokchetav Massif, Northern Kazakhstan). These coesite inclusions are euhedral and display a characteristic anisotropic hallo. However, Raman maps and separate spectra of these inclusions display shifted bands for coesite and quartz. Microscopically undetectable, quartz shows on the Raman map as a thin shell around coesite inclusion. Shift of the main coesite band allows to estimate their overpressure: coesite inclusions record 0-2.4 GPa in garnet and zircon. The quartz shell remains under lower pressure 0-1.6 GPa. The possible application of coesite and quartz Raman geobarometers for UHP metamorphic rocks is discussed.     

Synthesis and Investigation of Magnesium–Aluminum Nanopowders and Ceramics Activated by Copper

Technical Physics - Nanopowders of two crystalline phases, magnesium–aluminum spinel (98 wt %), and cuprite (2 wt %) have been obtained by laser evaporation of a solid target, which...     

Magnetorefractive effect in manganites with a colossal magnetoresistance in the visible spectral region

The magnetotransmission, magnetoreflection, and magnetoresistance of the La_0.7Ca_0.3MnO₃ and La_0.9Ag_0.1MnO₃ epitaxial films have been investigated. It has been found that the films exhibit a significant magnetorefractive effect in the case of reflection and transmission of light in the fundamental absorption region both in the vicinity of the Curie temperature and at low temperatures. It has been shown that the magnetorefractive effect in the infrared spectral region of the manganites is determined by a high-frequency response to magnetoresistance, whereas the magnetorefractive effect in the visible spectral region of these materials is associated with a change in the electronic structure in response to a magnetic field, which, in turn, leads to a change in the electron density of states, the probability of interband optical transitions, and the shift of light absorption bands. The obtained values of the magnetotransmittance and magnetoreflectance in the visible spectral region are less than those observed in the infrared region of the spectrum, but they are several times greater than the linear magneto-optical effects. As a result, the magnetorefractive effect, which is a nongyrotropic phenomenon, makes it possible to avoid the use of light analyzers and polarizers in optical circuits.     

Brown diamonds from an eclogite xenolith from Udachnaya kimberlite, Yakutia, Russia

We have performed petrographic and spectroscopic studies of brown diamonds from an eclogite xenolith from the Udachnaya pipe (Yakutia, Russia). Brown diamonds are randomly intermixed with colorless ones in the rock and often located at the grain boundaries of clinopyroxene and garnet. Brown diamonds can be characterized by a set of defects (H4, N2D and a line at 490.7 nm) which are absent in colorless diamonds. This set of defects is typical for plastically deformed diamonds and indicates that diamonds were likely annealed for a relatively short period after deformation had occurred. Excitation of brown colored zones with a 632.8 nm He-Ne laser produced the typical diamond band plus two additional bands at 1730 cm(-1) and 3350 cm(-1). These spectral features are not genuine Raman bands, and can be attributed to photoluminescence at ～710 nm (1.75 eV) and ～802 nm (1.54 eV). No Raman peak corresponding to graphite was observed in regions of brown coloration. Comparison with previous reports of brown diamonds from eclogites showed our eclogitic sample to have a typical structure without signs of apparent deformation. Two mechanisms with regard to diamond deformation are proposed: deformation of eclogite by external forces followed by subsequent recrystallization of silicates or, alternatively, deformation by local stress arising due to decompression and expansion of silicates during ascent of the xenolith to surface conditions.     

Domestic Developments of IR Optical Materials Based on Solid Solutions of Silver Halogenides and Monovalent Thallium

Optics and Spectroscopy - A review of the current progress in fiber optics for the mid-infrared range of the spectrum (2.0–50.0 µm) is performed. The problem in development of infrared...     

Elastic properties of the Ta–V system: bcc Ta0.33V0.67 and C15 TaV2

Resonant ultrasound spectroscopy was used to measure the elastic constants of bcc Ta_0.33V_0.67 over the temperature range 3.5–300?K; the results were compared to earlier measurements on C15 TaV₂. The temperature dependence of the polycrystalline shear modulus is completely different in the two phases; that of the bcc phase decreases with temperature whereas that of the C15 phases increases in an anomalous fashion. This difference is consistent with a model involving doubly-degenerate levels at the X point of the Brillouin zone in the C15 phase with the Fermi level lying near the doubly degenerate level. This model accounted for the unusual behaviour of the C15 phase. Debye temperatures were determined from the ultrasonic measurements: 295?K for the C15 phase and 315?K for the bcc phase.     

Synthesis and crystal structures of [K(H<Subscript>2</Subscript>O)(Piv)]<Subscript>∞</Subscript> and [K<Subscript>2</Subscript>(Phen)(H<Subscript>2</Subscript>O)<Subscript>2</Subscript>(Piv)<Subscript>2</Subscript>]<Subscript>∞</Subscript>

A method for the synthesis of potassium pivalates (trimethylacetates) from potassium tert-butoxide and pivalic acid was proposed. The complexes of the formulas [K(H₂O)(Piv)]_∞(I) and [K₂(Phen)(H₂O)₂(Piv)₂]_∞ (II) (Piv denotes the pivalate anion and Phen denotes 1,10-phenanthroline) were obtained and characterized by elemental analysis and IR and ¹H NMR spectroscopy. The crystal structures of complexes I and II were determined using X-ray diffraction. Crystal structure I has a layered motif with two nonequivalent K atoms (C.N.s 5 + 2 and 6). The coordination of phenanthroline in II gives rise to a ribbon motif, the structure containing three nonequivalent K atoms (C.N.s 6, 6 + 1, and 8).     

Critical behavior of the heat capacity of the manganite La<Subscript>0.87</Subscript>K<Subscript>0.13</Subscript>MnO<Subscript>3</Subscript>

The heat capacity of the manganite La_0.87K_0.13MnO₃ has been measured in the temperature range 80–350 K. The nature of the ferromagnetic phase transition and the critical properties of heat capacity near the Curie temperature have been studied. The regularities of variations in the universal critical parameters near the phase transition point have been established. The calculated critical exponent and amplitudes of the heat capacity with allowance for corrections on the scaling (α = −0.13 and A ⁺/A ⁻ = 1.178) correspond to the critical behavior of the 3D Heizenberg model.