The intimate relation between the extended Jaffe class and special spaces of typeS

It is shown that a natural but useful generalisation of Jaffe's mathematical results concerning strict localisability is just an easy consequence of Gelfand's and Shilov's work on spaces of typeS. Furthermore, proof is given for the statement that there is no minimal space of test functions with compact support, whereas every countable intersection of such spaces also contains test functions with compact support.     

Normal functional and spaces of weights

It is shown that the cone of positive normal functionals on a hypergraphA may be substantially larger than the cone of positive weights onA. For a semiclassical hypergraphA the two cones coincide if and only if the number of edges ofA of cardinality 2 is finite. This disproves an earlier statement of T. A. Cook.     

Binaural interference in the free field

In an anechoic chamber the minimum audible angle (MAA) was measured in seven normal-hearing adults for a narrow band of noise centered at 4000 Hz (target). In the absence of an interfering stimulus, the average MAA was 2.1°. When a low-frequency interferer (a narrow band of noise centered at 500 Hz) was pulsed on and off with the target from directly in front of the subject, the average MAA was significantly elevated (13.4°). However, if the interferer was continuously present, or if it consisted of two independent noises presented from ±90°, interference was much reduced. The interference effect was asymmetric: a high-frequency interferer did not result in elevation of MAA threshold for a low-frequency target. These results are similar to those that have been extensively reported for stimuli under headphones [Bernstein and Trahiotis (1995). J. Acoust. Soc. Am. 98, 155-163]. These data are consistent with the notion that interference from a spectrally remote low-frequency interferer occurs in the free field to the extent that the target and interferer are fused into a single perceptual object. If cues are provided that promote perceptual segregation (such as temporal onset differences or spatial location differences), the interference is reduced or eliminated.     

Entropic repulsion of the lattice free field

Consider the massless free field on thed-dimensional lattice ^d ,d3; that is the centered Gaussian field on with covariances given by the Green function of the simple random walk on ^d . We show that the probability, that all the spins are positive in a box of volumeN ^d , decays exponentially at a rate of orderN ^d–2 logN and compute explicitly the corresponding constant in terms of the capacity of the unit cube. The result is extended to a class of transient random walks with transition functions in the domain of the normal and -stable law.This research was partially supported by the foundation for promotion of research at the Technion.     

New explicit solutions in acoustics of closed spaces on the basis of divergent series

A new approach to the acoustics of closed spaces is developed that involves solutions for polygonal shapes in explicit form. It is shown that exact solutions can be constructed for polygonal geometries where all the interior angles are equal to pi/n (n is an integer). It is stated that the set of such polygons consists of the rectangle (known result) and three types of triangles. Some new explicit formulas are obtained for the eigenfrequencies of the triangles. It is demonstrated that the proposed technique also permits an exact representation of the impulse response function for the geometries described.     

Metrics on test function spaces for canonical field operators

In a canonical field theory, the field (f) and momentum (g) are assumed defined for test functionsf andg which are elements of linear vector spaces and, respectively. Generally, the continuity of the map onto the unitary Weyl operatorsU(f),V(g) is taken as ray continuity, the barest minimum to recover the field operators as their generators, i.e.,U(f)=e ^i(f) ,V(g)=e ^i(g) . This leaves open the question of whether any wider continuity properties follow and what form they would take. We show that much richer continuity properties do follow in a natural fashion for every cyclic representation of the canonical commutation relations. In particular, we show that the test function space may be taken as a metric space, that the space may be uniquely completed in this topology, and that the map into the unitary Weyl operators is strongly continuous in this topology. The topology induced by this metric is minimal in the sense that it is the weakest vector topology for which the mapsfU(f),gV(g) are strongly continuous. An expression for a suitable metric can easily be given in terms of a simple integral over a state on the Weyl operators.     

Quantization of scalar field in cosmic spaces

Equations of scalar field are constructed by the method of embedding in conformally planar cosmic spaces of the general relativity theory (GRT). The equations are linear relative to the scalar field, which, on the one hand, enables one to regard the permutation function as a four-dimensional radially symmetric solution of the equation of the scalar field, and on the other hand, as a commutator of the wave solutions of the field; in this way the quantization laws are determined for the Fourier amplitudes of the solutions of the equations for the meson field. The wave solution of the scalar meson field is found in the conformally planar GRT space, and the permutation function is obtained as their commutator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 75–79, March, 1977.     

基于伽辽金级数的空间电荷场计算模型

利用局部伽辽金矩量法,建立了电子注空间电荷场的2.5维计算模型. 将空间电荷场在径向展开为各个模式的叠加,利用伽辽金级数表示,通过求解其系数方程组, 最终求得空间电荷场.利用本文的模型,计算分析了电子注空间电荷场的特性, 并研究了模型中仿真参量对空间电荷场计算结果的影响.本文的空间电荷场计算模型利用粒子模拟基本方法, 可以应用到速调管注波互作用计算模型中.     

Theory of density functional gradient series

It is shown how a reformulation of a density functional gradient expression optimises the convergence of this series.     

Twistor flag spaces as phase spaces of conformal particles

This paper contains a kinematic interpretation of certain open orbits of conformal group on twistor flag spaces. In a particular case, the complexified Minkowski space IM _inf4c ^supc becomes the phase space of massive scalar conformal particle.This research has been supported by M. Skodowska-Curie Found.,-Grant No. OIP 74-01416.     

Probability measures on distribution spaces and quantum field theoretical models

It is well known that there is a close connection between (Abelian) fields and probability measures on distribution space, or more generally, on infinite-dimensional vector spaces, and their associated random processes. We establish general criteria for mutual singularity of such measures and apply them to quantum fields. In particular, it is shown that a kind of generalized clustering implies singularity. Then a condition for singularity is given in terms of a natural metric introduced previously. It is used to show that the translate of a measure by a linear functional which is not continuous for this metric is singular to the untranslated measure. The results are applied to processes with independent values at each point, corresponding to the ultra-local model. It is shown that each such measuris singular to any of its translates although its finite-dimensional projections may be equivalent to Lebesgue measure.     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

The upper critical magnetic field of lead as a function of the mean free path of the electrons

The transition curves of quenched lead films are measured in a perpendicular magnetic field as a function of the field strength. We vary the mean free path of the electrons by different condensation temperatures and by the annealing of the films. An influence of the edge of the film on the resistance measurement is suppressed by the superposition of iron onto the lead film. We will show, that the measured critical fieldB _{c ⊥} of the film is the upper critical fieldB _c2 of a bulk superconductor with the sameeffective mean free path. As a result of the measurements we obtain ?B _c2/?T as a function of the degree of disorder (the mean free path of the electrons) of the films. The results are compared with the theory of Gor'kov for the weak coupling superconductor and the theory of Eilenberger and Ambegaokar for the strong coupling superconductor. They disagree with both theories. From the magnetic measurement we can determine the coherence length of lead. An independent determination at the same film is given by the proximity effect of the system Pb/Fe. The results of both methods are compared.     

Generalized coulomb gauges for the free photon field

We point out that the classical notion of gauge transformations can be interpreted in two different ways in the quantum theory. Beside the transformation of the field operator appearing in the Gupta-Bleuler theory, the gauge transformations can be viewed as acting on the wave functions in a generalization of the Coulomb gauge.     

半自由声场的全息重建和预测实验研究

半自由声场环境下的声源重建和声场预测研究对声全息技术走向实际应用具有非常重要的意义.在提出基于分布源边界点法的半自由声场全息重建和预测方法的基础上，对此展开了实验研究.并将重建和预测的结果与常规方法重建和预测的结果进行了比较和讨论，说明了重建预测过程中反射声压的影响和考虑反射声压的必要性，证明了所提出方法在解决半自由声场环境下存在地面反射时的声源重建和声场预测时的有效性和准确性.还提出了采用奇异值截断滤波和Tikhonov正则化方法来削弱测量误差的影响，从而进一步优化了重建结果，提高了全息成像的可信度. 关键词： 声全息 半自由场 边界点 声辐射 反射声     

The Markoff property of the free Euclidean electromagnetic field

We show the Markoff property for the free Euclidean electromagnetic field in terms ofF ^ij.     

On the linearization of source free gauge field equations

A scheme for linearizing the source free Yang-Mills field equations is given. An infinite parameter invariance group of the gauge field equations is discovered.     

自由场结构体声辐射研究

结构体振动与其辐射的噪声之间存在着一种定量关系.本文从自由场结构体声辐射的理论公式──自由场Helmholtz积分方程入手,然后采用边界元法(BEM)离散积分方程,通过任意形状结构体表面弹性振动的速度场,来计算其向外辐射的声场,从而达到有效地预测其声场特性的目的.