Fibre bundle formulation of nonrelativistic quantum mechanics. III. Pictures and integrals of motion

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. It's evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. In this third part of our series we investigate the bundle analogues of the conventional pictures of motion. In particular, there are found the state sections and bundle morphisms corresponding to state vectors and observables respectively. The equations of motion for these quantities are derived too. Using the results obtained, we consider from the bundle view-point problems concerning the integrals of motion. An invariant (bundle) necessary and sufficient conditions for a dynamical variable to be an integral of motion are found.Comment: 19 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. New references and comments are added. Minor style chages. Continuation of quant-ph/9803083, quant-ph/9803084 and quant-ph/9804062. For continuation of the series view http://www.inrne.bas.bg/mathmod/bozhome

Phonons and Magnetic Excitations in Mott-Insulator LaTiO3_3

The polarized Raman spectra of stoichiometric LaTiO$_3$ (T$_N = 150$ K) were measured between 6 and 300 K. In contrast to earlier report on half-metallic LaTiO$_{3.02}$, neither strong background scattering, nor Fano shape of the Raman lines was observed. The high frequency phonon line at 655 cm$^{-1}$ exhibits anomalous softening below T$_N$: a signature for structural rearrangement. The assignment of the Raman lines was done by comparison to the calculations of lattice dynamics and the nature of structural changes upon magnetic ordering are discussed. The broad Raman band, which appears in the antiferromagnetic phase, is assigned to two-magnon scattering. The estimated superexchange constant $J = 15.4\pm0.5$ meV is in excellent agreement with the result of neutron scattering studies.Comment: 4 pages, 5 figure

Smrtnost od akutnih otrovanja u području Plovdiva u Bugarskoj

The severe recession in Bulgaria which followed the collapse of the totalitarian regime in 1989 had an unfavourable impact on the health status of the population. Systematic studies of acute poisoning mortality rate in the transitional period (1990-98) are scarce in the post-totalitarian Eastern European countries and are lacking in Bulgaria. This retrospective study analysed 1,150 deaths due to acute poisoning in Plovdiv Region for the period 1961-98. Acute poisoning mortality rate was moderately high in the period between 1990 and 1998 with respect to the average of 4.99 per 100,000 a year. It grew steadily during rapid socialist industrialization (1961-90) and showed a trend of slight decrease during transition (1991-1998). The decrease may largely be accounted for by the foundation of the regional toxicological centre and to a certain degree by a drop in industrial and agricultural production and exposure to hazards.Nakon pada totalitarnog režima 1989. godine, socioekonomska kriza što je zahvatila zemlju odrazila se negativno na zdravstveno stanje populacije. Sustavna praćenja akutnih otrovanja tijekom tranzicijskog razdoblja u Istočnoj Europi su oskudna, a u Bugarskoj ih nije ni bilo. U ovom se radu retrospektivno analizira 1150 slučajeva akutnih smrtnih otrovanja u području Plovdiva, i to u razdoblju 1961-1990. u vrijeme intenzivne industrijalizacije. U tom je razdoblju stopa smrtnosti od akutnih otrovanja stalno rasla dosegnuvši maksimum između 1986. i 1989., a nakon toga je počela lagano opadati. U razdoblju između 1990. i 1998. smrtnost od akutnih otrovanja iznosila je 4,99 na 100.000 stanovnika. Spomenuti trend opadanja smrtnosti pripisuje se osnivanju regionalnoga toksikološkog centra, kao i usporavanju industrijske i poljoprivredne aktivnosti s posljedicom smanjenja ekspozicije toksičnim tvarima. U smanjivanju stope smrtnosti od akutnih otrovanja posebnu ulogu imaju dobro planirane i provođene preventivne mjere

Raman and Infrared-Active Phonons in Hexagonal HoMnO3_3 Single Crystals: Magnetic Ordering Effects

Polarized Raman scattering and infrared reflection spectra of hexagonal HoMnO$_3$ single crystals in the temperature range 10-300 K are reported. Group-theoretical analysis is performed and scattering selection rules for the second order scattering processes are presented. Based on the results of lattice dynamics calculations, performed within the shell model, the observed lines in the spectra are assigned to definite lattice vibrations. The magnetic ordering of Mn ions, which occurs below T$_N$=76 K, is shown to effect both Raman- and infrared-active phonons, which modulate Mn-O-Mn bonds and, consequently, Mn exchange interaction.Comment: 8 pages, 6 figure

Frames of reference in spaces with affine connections and metrics

A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to the vector field sub space, (c) an affine connection and the related to it covariant differential operator determining a transport along the given non-null vector filed. On the grounds of this definition other definitions related to the notions of accelerated, inertial, proper accelerated and proper inertial frames of reference are introduced and applied to some mathematical models for the space-time. The auto-parallel equation is obtained as an Euler-Lagrange's equation. Einstein's theory of gravitation appears as a theory for determination of a special frame of reference (with the gravitational force as inertial force) by means of the metrics and the characteristics of a material distribution. PACS numbers: 0490, 0450, 1210G, 0240VComment: 17 pages, LaTeX 2

Smrtnost od akutnih otrovanja u području Plovdiva u Bugarskoj

The severe recession in Bulgaria which followed the collapse of the totalitarian regime in 1989 had an unfavourable impact on the health status of the population. Systematic studies of acute poisoning mortality rate in the transitional period (1990-98) are scarce in the post-totalitarian Eastern European countries and are lacking in Bulgaria. This retrospective study analysed 1,150 deaths due to acute poisoning in Plovdiv Region for the period 1961-98. Acute poisoning mortality rate was moderately high in the period between 1990 and 1998 with respect to the average of 4.99 per 100,000 a year. It grew steadily during rapid socialist industrialization (1961-90) and showed a trend of slight decrease during transition (1991-1998). The decrease may largely be accounted for by the foundation of the regional toxicological centre and to a certain degree by a drop in industrial and agricultural production and exposure to hazards.Nakon pada totalitarnog režima 1989. godine, socioekonomska kriza što je zahvatila zemlju odrazila se negativno na zdravstveno stanje populacije. Sustavna praćenja akutnih otrovanja tijekom tranzicijskog razdoblja u Istočnoj Europi su oskudna, a u Bugarskoj ih nije ni bilo. U ovom se radu retrospektivno analizira 1150 slučajeva akutnih smrtnih otrovanja u području Plovdiva, i to u razdoblju 1961-1990. u vrijeme intenzivne industrijalizacije. U tom je razdoblju stopa smrtnosti od akutnih otrovanja stalno rasla dosegnuvši maksimum između 1986. i 1989., a nakon toga je počela lagano opadati. U razdoblju između 1990. i 1998. smrtnost od akutnih otrovanja iznosila je 4,99 na 100.000 stanovnika. Spomenuti trend opadanja smrtnosti pripisuje se osnivanju regionalnoga toksikološkog centra, kao i usporavanju industrijske i poljoprivredne aktivnosti s posljedicom smanjenja ekspozicije toksičnim tvarima. U smanjivanju stope smrtnosti od akutnih otrovanja posebnu ulogu imaju dobro planirane i provođene preventivne mjere

Apolarity, Hessian and Macaulay polynomials

A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth hypersurface g=0, then b is just equal to the degree of the Hessian polynomial of g. In this paper we investigate the relationship between f and the Hessian polynomial of g.Comment: 12 pages. Improved exposition, minor correction

Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces

Conditions for the existence of flows with non-null shear-free and expansion-free velocities in spaces with affine connections and metrics are found. On their basis, generalized Weyl's spaces with shear-free and expansion-free conformal Killing vectors as velocity's vectors of spinless test particles moving in a Weyl's space are considered. The necessary and sufficient conditions are found under which a free spinless test particle could move in spaces with affine connections and metrics on a curve described by means of an auto-parallel equation. In Weyl's spaces with Weyl's covector, constructed by the use of a dilaton field, the dilaton field appears as a scaling factor for the rest mass density of the test particle. PACS numbers: 02.40.Ky, 04.20.Cv, 04.50.+h, 04.90.+eComment: 20 pages, LaTeX, to appear in Classical and Quantum Gravity. arXiv admin note: substantial text overlap with arXiv:gr-qc/001104