Parametrizing Equivalence Classes of Invariant Star Products

Let (M,,) be a symplectic manifold endowed with a symplectic connection . Let Symp(M,) be the group of symplectic transformations of (M,) and Aff(M,) be the group of affine transformations of the affine manifold (M, ). In this Letter, we show that, for any subgroup G of Symp(M,) Aff(M,), the set of G-equivalence classes of G-invariant star products on (M,) is canonically parametrized by the set of sequences of elements belonging to the second de Rham cohomology space of the G-invariant de Rham complex on M.     

Die Theorie der Vernichtung der Exzitonen,die von einem Entstehen von Störungen eines neuen Types und von Stromträgern begleitet ist

Zusammenfassung Es wird der Prozeß der Vernichtung von Exzitonen an Vakanzen und Zentren des F-Typs in Ionenkristallen studiert, der vom Entstehen eines Zentrums neuen Typs und der Stromträger begleitet ist. Es werden die allgemeinen Ausdrücke für die betreffenden Wirkungsquerschnitte in quasiklassischer Annäherung abgeleitet und diskutiert.

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The dependence of the uniaxial magnetic anisotropy in evaporated films on the angle of incidence

The method of local ferromagnetic resonance and direct torsional measurements were used to measure the dependence of the magnetic anisotropy in permalloy films on the angle of incidence in a broad range of such angles. It was found that this dependence is not monotonous and that at larger angles of incidence the easy axis of magnetization is rotated. An interpretation of this phenomenon is proposed.

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In conclusion the authors wish to thank J. Grolmus for performing some of the measurements, members of the mechanics workshop of the Institute of Physics, Czechoslovak Academy of Sciences, for carefully preparing the apparatus, and particularly K. Schaffner for accurately making the resonance cavity. We thank J. Kaczér and V. Janovec for carefully reading this paper and for a number of valuable remarks.     

Non-isovalent alkali metal “substitution” in YBa2Cu3O7−y granular ceramics

The aim of this paper is to study the influence of non-isovalent doping in YBa₂Cu₃O_7–y in particular on its synthesis conditions and on the resistive properties both with and without a magnetic field. We concentrate on the study of possible alkali ions (Na, K, Cs) substitution at the barium sites. A low temperature sintering process is used in order to induce a reactive liquid phase. The final chemical composition is discussed as a function of the amount of the liquid phase. No alkali ion is substituted. Carbonate layers are present. However, this (lack of) substitution leads to induced vacancies and improved electrical transport properties which are as good as in highly pure materials. For conciseness the case of Na substitution only is illustrated. The use of such data in order to probe the microstructure is emphasized.     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

Inertial frames of reference: Mass coupling to space and time

We consider a new expression for the dependence of mass on velocity, more general than the corresponding law of the special theory of relativity (STR). The deviations from the STR become large with increasing rest mass. One should therefore measure the dependence of mass on velocity for objects with a large rest mass. The theory predicts that particles with real mass can travel with hyperlight velocities. The space-time picture discussed here is close to Mach's conception: It is assumed that the dynamical behavior of a particle in uniform translational motion is due to the action of all the other masses in the universe. Space-time is eliminated as an active cause and, in contrast to the STR, is not absolute within the theory discussed here. It turns out that effects based on the new transformation formulas (from the coordinates and time in a stationary frame to the coordinates and time in a moving frame) are identical to those expected from the Lorentz transformations. For example, it is known that rapidly moving mesons decay with a longer half-life than stationary mesons and the STR describes this effect quantitatively. However, there is no strong evidence for the validity of the STR because the theory given in this paper predicts the same result.     

The 1/N F expansion of the γ and β functions in Q.E.D.

The Callan-Symanzik- and-functions are calculated analytically for Q.E.D. in the limit of a large number of leptons (N _F) up to terms of order 1/N _F inclusive. We give closed analytic expressions for the coefficients of these terms in their series expansion in powers ofK N _F/. We have been able to sum these series and to obtain some striking results.     

An Invariant Formulation of Special Relativity, or the “True Transformations Relativity,” and Comparison with Experiments

Different formulations of special relativity (SR) are briefly theoretically discussed. In the first formulation SR is understood as the theory of a four-dimensional (4D) spacetime with the pseudo-Euclidean geometry. It is an invariant formulation of SR, which we call the true transformations (TT) relativity. There a physical quantity in the 4D spacetime is mathematically represented either by a true tensor (when no basis has been introduced) or equivalently by a coordinate-based geometric quantity comprising both components and a basis (when some basis has been introduced). This invariant formulation is compared with the usual covariant formulation, which mainly deals with the basis components of tensors in a specific, i.e., Einstein's coordinatization of the chosen inertial frame of reference. The third formulation is the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rather quantities from 3+1 space and time, e.g., the synchronously determined spatial length. This formulation is called the apparent transformations (AT) relativity. Some of the well-known experiments: the muon experiment, the Michelson–Morley type experiments, the Kennedy–Thorndike type experiments, and the Ives–Stilwell type experiments are analyzed using the nonrelativistic theory and the mentioned different formulations of SR. It is shown that all the experiments (when they are complete from the TT relativity viewpoint) are in agreement with the TT relativity but not always with the AT relativity.     

Relativistic Spin Operator for Dirac Particles

It is shown that a relativistic spin operator,obeying the required SU(2) commutation relations, may bedefined in terms of the Pauli-Lubanski vectorW. In the case of Dirac particles, thisoperator reduces to the Foldy-Wouthuysen mean-spinoperator for states of positive energy.     

Fluctuating hydrodynamics and principal oscillation pattern analysis

Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series x_i(t) produced by systems whose dynamics are described by a linear Markov process x=Bx + . The matrixB gives the deterministic feedback and is a white noise vector with covariances (t) _j (t*Q _ij (t–t. The POP method is applied to data from a direct simulation Monte Carlo program. The system is a dilute gas with 50,000 particles in a Rayleigh-Bénard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrixB) and the stochastic fluxes (in the matrixQ) as given by Landau-Lifschitz fluctuating hydrodynamics. Using this method, we find the Landau-Lifschitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Bénard convection.     

Cosmological Relativity: Determining the Universe by the Cosmological Redshift as Infinite and Curved

Using cosmological relativity theory, we derive the formula for the cosmological redshift written explicitly in terms of 1 – , where = /_c is the ratio of the average mass density to the critical closure density. Based on the present day data of observed redshifts, we conclude that < 1, which means the universe is infinite and curved, and expands forever.     

Invariant simultaneity

The concept of the relativity of simultaneity, as a consequence of the Lorentz transformations, is shown to be an unproven inference based on the implicit idea that simultaneity can be determined only on the basis of synchroneity. The Lorentz transformations do imply, by interpretive inference, a relativity of synchroneity whereby a moving system of synchronized clocks appears to be nonsynchronous, with constant nonzero time invariant phases among the clocks that depend only on their relative fixed distances from each other. It does not seem to have been recognized that such an array of uniformly running nonsynchronous clocks, described as isochronous, can also lead to the unambiguous determination of simultaneity. The important significance of the relative temporal phases, namely the relativity of synchroneity, entailed by the Lorentz transformations is that certain alleged logical inconsistencies, asserted by both proponents and opponents of the special theory of relativity, can be readily resolved. The relativity of synchroneity does, however, raise certain other consequences that merit attention and careful consideration.     

Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.     

Special relativistic gravitational theory

Based on special relativity, we introduce a way to develop a new field theory from (1) the relativistic property of the particle coupling coefficient with the field, and (2) the field due to a static point source. As an example, we discuss a theory of electromagnetic and gravitational fields. The results of this special relativistic gravitational theory for the redshift and the deflection of light are the same as those deduced from general relativity. The results of experiments on the planetary perihelion procession shift and on an additional short-range gravity are more favorable to the special relativistic gravitational theory than to general relativity. We put forward a new idea to test experimentally whether the equivalence principle of general relativity is correct.Plovdiv University Paissii Hilendarskii.Moscow Institute of Railway Transport Engineers.     

Mach-Einstein doctrine and general relativity

It is argued that, under the assumption that the strong principle of equivalence holds, the theoretical realization of the Mach principle (in the version of the Mach-Einstein doctrine) and of the principle of general relativity are alternative programs. That means only the former or the latter can be realized—at least as long as only field equations of second order are considered. To demonstrate this we discuss two sufficiently wide classes of theories (Einstein-Grossmann and Einstein-Mayer theories, respectively) both embracing Einstein's theory of general relativity (GRT). GRT is shown to be just that degenerate case of the two classes which satisfies the principle of general relativity but not the Mach-Einstein doctrine; in all the other cases one finds an opposite situation.These considerations lead to an interesting complementarity between general relativity and Mach-Einstein doctine. In GRT, via Einstein's equations, the covariant and Lorentz-invariant Riemann-Einstein structure of the space-time defines the dynamics of matter: The symmetric matter tensor T_tk is given by variation of the Lorentz-invariant scalar densityL _mat, and the dynamical equations satisfied by T_ik result as a consequence of the Bianchi identities valid for the left-hand side of Einstein's equations. Otherwise, in all other cases, i.e., for the Mach-Einstein theories here under consideration, the matter determines the coordinate or reference systems via gravity. In Einstein-Grossmann theories using a holonomic representation of the space-time structure, the coordinates are determined up to affine (i.e. linear) transformations, and in Einstein-Mayer theories based on an anholonomic representation the reference systems (the tetrads) are specified up to global Lorentz transformations. The corresponding conditions on the coordinate and reference systems result from the postulate that the gravitational field is compatible with the strong equivalence of inertial and gravitational masses.     

On the Foundation of the Principle of Relativity

The relation of the special and the general principle of relativity to the principle of covariance, the principle of equivalence and Mach's principle, is discussed. In particular, the connection between Lorentz covariance and the special principle of relativity is illustrated by giving Lorentz covariant formulations of laws that violate the special principle of relativity: Ohm's law and what we call Aristotle's first and second laws. An Aristotelian universe in which all motion is relative to absolute space is considered. The first law: a free particle is at rest. The second law: force is proportional to velocity. Ohm's law: the current density is proportional to the electrical field strength. Neither of these laws fulfills the principle of relativity. The examples illustrate, in the context of Lorentz covariance and special relativity, Kretschmann's critique of founding Einstein's general principle of relativity on the principle of general covariance. A modification of the principle of covariance is suggested, which may serve as a restricted criterium for a physical law to satisfy Einstein's general principle of relativity. Other objections that have been raised to the validity of Einstein's general principle of relativity are based upon the preferred state of inertial frames in the general, as well as in the special theory, the existence of tidal effects in true gravitational fields, doubts as to the validity of Mach's principle, whether electromagnetic phenomena obey the principle, and, finally, the anisotropy of the cosmic background radiation. These objections are reviewed and discussed.     

Канал кратковременн ого силъноточного электрического разр яда

, ( 10² sec, , 10⁴ A), .

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Channel of short-time high-intensity electric discharge

By the spatial expansion of the radial cross-section of the channel of the given type of discharge (duration 10² sec and maximum intensity smaller than 10⁴ A)and by measuring some of its electrical quantities information was obtained on its channel and the influences bringing about the forming process.

     

Локалъная чувствите лъностъ фотокатодов фотоумножителей

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The local sensitivity of photo-multiplier photo-cathodes

The influence of the non-uniform distribution of the sensitivity of a photo-multiplier photo-cathode on the spectrum shape of the output pulses from a scintillation detector is studied. Methods of scanning the local sensitivity and determining its distribution function are described. The theory was compared qualitatively with measurement on a slow-neutron detector from a mixture of zinc sulphate and boric acid.

     

ФОТОЯДЕРНЫЙ ЭФФЕКТ Н А НИКЕЛЕ, МЕДИ И ЦИНКЕ

, - 17,6 , . , (8±4)·10^–23, (7±4)·10^–23 (4±2)·10^{–23 2}. , - .     

Lévy walks for turbulence: A numerical study

We present a numerical study of enhanced diffusion, for which the mean-squared displacement follows asymptotically r ²(t) t , > 1. We simulate continuous time random walks with waiting-time distributions which couple the spatial and temporal parameters; this gives rise to Lévy-walks. Our results confirm the theoretically predicted long-time behavior and demonstrate its temporal regime of validity. Furthermore, the simulations document the appearance of (parameter-dependent) transitions between regular and enhanced diffusion regimes.