Corrections to cluster-radius scaling for branched polymers and percolation

We report analyses of series enumerations for the mean radius of gyration for isotropic and directed lattice animals and for percolation clusters, in two and three dimensions. We allow for the leading correction to the scaling behaviour and obtain estimates of the leading correction-to-scaling exponent . We find -0.640±0.004 and =0.87±0.07 for isotropic animals in 2d, and =0.64±0.06 in 3d. For directed lattice animals we argue that the leading correction has= or= ; we also estimate =0.82±0.01 and 0.69 ±0.01 ind=2, 3 respectively. For percolation clusters at and abovep _c, we find (p _c) =0.58±0.06 and (p>p _c)=0.84±0.09 in 2d, and (p _c)=0.42±0.11 and (p>p _c)=0.41 ±0.09 in 3d.     

Parametric dependence of the properties of pulsed-laser-deposited diamond-like carbon films

The properties of Pulsed-Laser-Deposited Diamond-Like Carbon (PLD DLC) films are studied as functions of the power density and the wavelength of the laser beam, and the incident angle of the beam relative to the normal of the target surface. All the films have a similar structure consisting of graphite particulates embedded in a continuous matrix, so the macroscopic performance of the films is determined by the overall contributions of the particulates and the matrix. The use of higher, shorter, or larger leads to an enhancement of the diamond-like characteristics and a simultaneous increase of the particulate density. These two effects give opposite contributions to the electrical conductivity _R, leading to the following results. (i) _R drops with increasing in the low range (region I) due to the stronger diamond-like nature of the matrix, but increases sharply after has exceeded a threshold _min as a result of the rapid increase in particulate density. (ii) In region I, the use of shorter or larger leads to a more diamond-like matrix, and this overwhelms the degradation effect caused by the slight increase in particulate density. The samples thus become more insulating. In the high region (region II), however, the use of shorter or larger gives rise to higher particulate density, thereby increasing the electrical conductivity.     

The Einstein 3-form Gα and its Equivalent 1-form Lα in Riemann–Cartan Space

We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L ^*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.     

Multiple coherent scattering of γ-radiation

Conclusions Multiplying (5) by 2d and integrating over angle, we get the relationship between the total flux and depth in the form , where .A similar result is obtained from integration of (11) over the angles and integration of (12) over the plane z = const. It thus follows that if we are interested in the angular distribution for in the first two cases and in the radial distribution for z in the third case, we can make an approximate estimate of the coherent scattering by eliminating the appropriate term from. This approach has been used in [15 etc.] but no indications were given of the conditions under which this is permissible.For problems in which small angles or small distances from the axis of a collimated source are important, allowance for the coherent scattering can change the result by an order of magnitude or more. For angles and it is possible to consider only the coherent scattering and to use (5), (11), and (12). For angles >gh and scattering >z, the contribution from coherent and incoherent scattering can be comparable. The kinetic equation must then be solved with allowance for both effects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 129–132, May, 1973.     

On the existence of a local Hamiltonian in the Galilean invariant Lee Model

It is shown that there exists a selfadjoint Hamilton operator in the limit of local coupling for the Galilean invariant Lee Model. We discuss the scattering theory of this Hamilton operator in theV —N sector.     

Gravity on a Parallelizable Manifold. Exact Solutions

The wave type field equation^a =^a, where ^ais a coframe field on a space-time, was recentlyproposed to describe the gravity field. This equationhas a unique static, spherically symmetric, asymptotically flat solution, whichleads to the viable Yilmaz–Rosen metric. We showthat the wave type field equation is satisfied by thepseudo-conformal frame if the conformal factor isdetermined by a scalar 3D-harmonic function. This functioncan be related to the Newtonian potential of classicalgravity. So we obtain a direct relation between thenon-relativistic gravity and the relativistic model: every classical exact solution leads to asolution of the field equation. With this result weobtain a wide class of exact, static metrics. We showthat the theory of Yilmaz relates to thepseudo-conformal sector of our construction. We derive also aunique cosmological (time dependent) solution of thedescribed type.     

Spin-orbit coupling in the chlorobenzene molecule

The possible ways of drawing of the intensity of the S₀ T* transition in the chlorobenzene molecule are investigated. The effective spin-orbit coupling of either S* or S* states with the T* state leads to the out-of-plane polarized component of phosphorescence in the chlorobenzene. The in-plane polarized component cannot be explained by the mechanism under consideration — by drawing of intensity of the S₀ S₀* transitions through spin-orbit coupling of first order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 134–138, August, 1974.     

A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.     

Unevenness of the sandwich cathode and its influence upon distributions of emitted electrons

The influence of the cathode surface unevenness on the angular and energy distributions of electrons emitted from MIM structures is studied. First, the structure of the surface of sandwich cathodes prepared by various technological processes is found with the help of optical and stylus methods for irregularities greater than several thousand Å. The exact expressions and their simplifications correcting the angular and normal energy distributions are derived for arbitrary relief of the cathode described by the surface distribution functiona (). The comparison of these expressions with experimental electron distributions shows that the surface unevenness disturbs only the central part of the angular distribution and that the error is roughly 5 per cent. The correction of the normal energy distribution is much smaller, and the total energy distribution does not depend on the structure of cathode surface at all.Ke Karlovu 5, Praha 2, Czechoslovakia.The author wishes to thank Dr. A. Ryska from TESLA Lankroun, for his help which enabled us to measure the cathode surface with the stylus method.     

The form factors of the decays π− → e−¯veγ and K− → e−¯veγ

In the special type of the quark model we obtain the ratio=h _A/h_V of the axial (h_A) and vector (h_V) form factors for the decays ^– e^– ¯v_e and K^– e^–¯v_e different from unity. The low-energy theorem, relating the electric polarizability of the charged pion with the ratio, is analyzed. It is shown that < 1 corresponds to , calculated by accounting the contribution of the scalar meson(700) into the amplitude of the Compton effect on the pion. In the absence of the(700) contribution we have=1.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

The contrast gain in a guest-host nematic display due to a periodic boundary condition

The mean square tilt angle of a nematic slab with finite anchoring energy and periodic boundary conditions has been theoretically investigated, as a function of the slab geometry and of the reduced extrapolation length. If the anchoring strength is free-surfacelike, the contrast is affected by a loss 10% at room temperature if the ratio between the anchoring pitch and the cell thickness is 0.5.Glossary anchoring pitch - h cell thickness - /h - ( = x/, = y/h) reduced coordinates - (, ) local tilt angle - elastic constant - w_a anchoring energy anisotropy - b=/w _a de Gennes-Kleman extrapolation length - B=b/h reduced extrapolation length - T _NI nematic-isotropic transition temperature - :=(T/T _NI ) – 1 reduced temperature - easy axis direction - _MAX - _± ² mean square tilt angle along the boundary - () absorbance coefficients of the p-dye - r /: dichroic ratio - c contrast - G contrast gain - S order parameter     

A finite size analysis of the structure factor in the antiferromagnetic Heisenberg (AFH) model

From a finite size analysis we extract the structure factorS(p, N=) of the one dimensional AFH-model in the groundstate: The gross structure is well described byL (p) = –ln(1– ^p ). The fine structure which only contributes a few percent reveals a pronounced non-linear behavior inL(p) with a maximum atp=0.20 and a minimum atp=0.82.     

General tachyon absorption by Kerr-Newman black holes: Thermodynamic consequences

Following the analyses of B. Carter and J. V. Narlikar, the nature of the incomplete, spacelike trajectories about a charged, rotating black hole is described. The study concentrates on those paths which a charged tachyon would follow, incident from off the equatorial plane (on which=/2). The effect of the absorption upon the black hole is calculated and it is concluded that for _i /2 only certain charged tachyons will reduce its entropy. However, a sustained bombardment by such particles could cause the singularity to be exposed.     

A theoretical study of the spectra of ketones,acids, and esters

The long-wave * transitions and weak n * transitions are discussed for several compounds of practical importance. Wave functions are presented for aliphatic ketones, acids, and esters.     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).     

Dynamics of a rigid test body in curved space-time

A covariant canonical formulation of the motion of a rigid test body in a curved space-time is obtained from a suitable Cartan form on the tangent bundleT of the bundle of Lorentz frames over the space-time manifoldV. The form (essentially equivalent to a Lagrangean) is chosen in close analogy to the corresponding 1-form in the classical Newtonian model of a rigid body and is very simple in terms of the natural geometrical structure of . The presymplectic manifold (T,d) then serves as evolution manifold of the system. One obtain the equations of motion and also a uniquely defined Poisson bracket on the set of observables defined as real valued functions on the manifold of motions. The rigid body interacts with the space-time curvature only via its spin in the same way as a spinning particle. Quadrupole and higher multiple interactions with the space-time curvature are not considered in this model.Supported in part by the National Research Council of Canada.     

The low energy scattering for slowly decreasing potentials

For the radial Schrödinger equation with a potentialq(x) decreasing at infinity asq ₀ q ^–, (0, 2), the low energy asymptotics of spectral and scattering data is found. In particular, it is shown that forq ₀>0 the spectral function vanishes exponentially as the energyk ² tends to zero. On the contrary, there is always a zero-energy resonance forq ₀<0. These results determine the local asymptotics of solutions of the time-dependent Schrödinger equation for large timest. Specifically, for positive potentials its solutions decay as exp(–₀ t ^(2–)/(2+), ₀>0,t. In the case (1, 2) it is shown that for ±q ₀>0 the phase shift tends to ± ask0 and its asymptotics is evaluated.     

Semimodularity and the logic of quantum mechanics

If (, ,P, ) is an event-state-operation structure, then the events form an orthomodular ortholattice (, , ) and the operations, mappings from the set of states into , form a Baer *-semigroup (S, , *, ). Additional axioms are adopted which yield the existence of a homomorphism from (S, , *, ) into the Baer *-semigroup (S(), , *, ) of residuated mappings of (, , ) such thatx S maps states while _x S () maps supports of states. If (, , ) is atomic and there exists a correspondence between atoms and pure states, then the existence of provides the result: (, , ) is semimodular if and only if every operationx S is a pure operation (maps pure states into pure states).Supported in part by the United States Atomic Energy Commission and in part by the Fonds National Suisse.     

Statistical phase properties in a coherent state

The wave function of a harmonic oscillator is investigated under the assumption that the phase plays the role of a generalized coordinate. This wave function makes it possible to obtain all possible statistical information concerning the phase in a coherent state (moments of all orders). It is particularly simple to calculate cos and sin .Odessa State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 748–760, July, 1991.     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.