Uniform Translations Research Articles

Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equation

We consider a class of Gibbs measures defined with respect to increments {ω(t)−ω(s)}s<t of d-dimensional Wiener measure, with the underlying Hamiltonian carrying interactions of the form H(t−s,ω(t)−ω(s)) that are invariant under uniform translations of paths. In such interactions, we allow long-range dependence in the time variable (including power law decay up to t↦(1+t)−(2+ε) for ε>0) and unbounded (singular) interactions (including singularities of the form x↦1/|x|p in d≥3 or x↦δ0(x) in d=1) attached to the space variables. These assumptions on the interaction seem to be sharp and cover quantum mechanical models like the Nelson model and the polaron problem with ultraviolet cut off (both carrying bounded spatial interactions with power law decay in time) as well as the Fröhlich polaron with a short range interaction in time but carrying Coulomb singularity in space. In this set up, we develop a unified approach for proving a central limit theorem for the rescaled process of increments for any coupling parameter and obtain an explicit expression for the limiting variance, which is strictly positive. As a further application, we study the solution of the multiplicative-noise stochastic heat equation in spatial dimensions d≥3. When the noise is mollified both in time and space, we show that the averages of the diffusively rescaled solutions converge pointwise to the solution of a diffusion equation whose coefficients are homogenized in this limit.

Uma abordagem reflexiva de ensino de prática de tradução (semi-)automatizada para formação de tradutores

A adoção de sistemas de memória tem promovido transformações definitivas no desenvolvimento e nos critérios de contratação de traduções de textos em formato eletrônico. Com o objetivo de examinar a influência do uso dessas ferramentas na produção de tradutores em formação, este trabalho apresenta um estudo que propõe uma abordagem reflexiva de análise da produção tradutória de estudantes em treinamento acadêmico. Para tanto, oito participantes do terceiro ano de um curso de graduação em Tradução foram convidados a traduzirem três contratos do inglês para o português com e sem o uso do sistema Worfast Classic (versão 6.0). Os resultados da análise da produção dos estudantes indicam que aqueles que utilizaram a ferramenta produziram traduções mais uniformes, com alto índice de semelhança entre elas, o que pode ser indicativo da influência da memória no trabalho de tradução. Considerando a escassez de pesquisas voltadas à análise da maneira como tradutores se relacionam com as ferramentas que empregam em seu trabalho e o modo como são afetados por elas, espera-se contribuir para um melhor entendimento das possíveis implicações envolvidas na associação entre o tradutor e tecnologias como os sistemas de memória no trabalho de tradução.

Microbubble translation in plane-wave ultrasound transmission

Primary radiation force is capable of translating microbubbles in the focal region of single-element and array ultrasound probes. This effect can be harnessed to enhance the contact between ligand-bearing microbubbles and targeted endothelium for applications in targeted drug delivery and ultrasound molecular imaging. In this study, displacements of lipid-coated microbubbles associated with plane-wave transmission are investigated using the multi-gate Doppler approach, and compared with focused-wave transmission at equivalent peak negative pressures. In plane wave transmission, the radiation force is nearly uniform over the field of view and therefore allows for a more uniform translation of microbubbles compared to focused wave. Statistically determined median displacements are in good agreement with the axial and lateral ultrasound beamplots both in plane-wave and focused-wave transmissions, while peak microbubble displacements reveal a number of discrepancies. Distinct size-isolated microbubble populations (diameters 1–2 μm, 3–4 μm, 4–5 μm, 5–8 μm, and polydisperse) were tested, showing important differences in their displacements and a strong driving frequency dependence thereof. These findings help tune the ultrasound transmission parameters for uniform and size-selective microbubble translations.

An algebraic approach to the design of compilers for object-oriented languages

Abstract In this paper we describe an algebraic approach to construct provably correct compilers for object-oriented languages; this is illustrated for programs written in a language similar to a sequential subset of Java. It includes recursive classes, inheritance, dynamic binding, recursion, type casts and test, assignment, and class-based visibility, but a copy semantics. In our approach, we tackle the problem of compiler correctness by reducing the task of compilation to that of program refinement. Compilation is identified with the reduction of a source program to a normal form that models the execution of object code. The normal form is generated by a series of correctness-preserving transformations that are proved sound from the basic laws of the language; therefore it is correct by construction. The main advantages of our approach are the characterisation of compilation within a uniform framework, where comparisons and translations between semantics are avoided, and the modularity and extensibility of the resulting compiler.

Test Method for Boom Suspension Influence on Spray Distribution, Part I: Experimental Study of Pesticide Application under a Moving Boom

The quality of pesticide spraying depends on boom movement. A conveyor with a shaking platform was built to analyse the influence of boom movements on spray distribution. It is able to generate uniform translations and rotational movements of a small boom under laboratory conditions. The overall ground spray distributions were studied using image analysis. Suitable representations and mathematical tools were considered to analyse the unevenness of ground spray distributions and to compare accurately spray patterns. The effects of boom height, boom speed and nozzle type on dynamic spray distributions were analysed and compared with stationary distributions. The effects of yaw and roll movements were also considered. Measurements of droplet size and velocity made with a phase Doppler analyser were added to complete the dynamic effect study. Tests were repeatable but some fluctuations were obtained when boom height increased. Static and dynamic distributions have the same overall unevenness but this unevenness is more important in dynamic conditions due to turbulence effects. Roll and yaw increase unevenness. For roll movements, changes in nozzle heights explain the variations. For yaw movements, over-dosed areas are observed where the nozzles have a small horizontal velocity.

Wilson-like functions on von Neumann lattices

An orthonormal set of functions is defined on a von Neumann lattice in phase space. There is one function assigned to each unit cell of area h. The functions are of the Wilson type in that in the x-direction they are obtained from one another by uniform translations, while in the p-direction they are double-peaked, and cannot be obtained by translations. A similar construction is also carried out with the x- and p-axes interchanged. The results apply to any dimension. An explicit example is worked out for the ground state of a harmonic oscillator, and a relation to coherent states is pointed out.

Lines and dots: characteristics of the motion integration process

Local motion detectors can only provide the velocity component perpendicular to a moving line that crosses their receptive field, leading to an ambiguity known as the ‘aperture problem’. This problem is solved exactly for rigid objects translating in the screen plane via the intersection of constraints (IOC). In natural scenes, however, object motions are not restricted to fronto-parallel translations, and several objects with distinct motions may be present in the visual space. Under these conditions the usual IOC construction is no longer valid, which raises questions as its use as a basis for spatial integration and selection of motion signals in uniform and non-uniform velocity fields. The influence of the motion of random dots on the perceived direction of a horizontal line grating was measured, when dots and lines are seen through different apertures. The random dots were mapped on a plane that translates in a fronto-parallel plane (uniform 2D translation) or in depth (3D, corresponding to a non-uniform projected velocity field, either expanding or contracting). The grating was either moving rigidly with the dots or in the opposite direction. Subjects’ responses show that the direction of line grating movement was reliably influenced only in conditions consistent with rigid motion; where there was a reliable influence, the perceived direction was consistent with the dot motion pattern. This finding points to the existence of a motion-based selection mechanism that operates prior to the disambiguation of the line movement direction. Disambiguation could occur for both uniform and non-uniform velocity fields, even though in the last case none of the individual dots indicated the proper direction in 2D velocity space. Finally, the capture by non-uniform motion patterns was less robust than that by uniform 2D translations, and could be disrupted by manipulations of the shape and size of the apertures.

General thermostatistical formalisms, invariance under uniform spectrum translations, and Tsallis q-additivity

The recent proposal by Tsallis of a generalized thermostatistics devised to treat systems endowed with long-range interactions, long-range memory effects, or a fractal-like relevant phase space, has raised interesting and profound issues concerning the properties of general thermostatistical formalisms. In the present paper we identify families of thermostatistical formalisms that share some fundamental characteristics. The canonical ensemble's invariance under uniform translations of the Hamiltonian's energy spectrum is shown to be a universal property verified by any thermostatistical formalism based upon linear mean energy constraints. We also provide multiparametric families of entropies exhibiting Tsallis q-additivity law.

Hertz's Special Relativity and Physical Reality

Einstein’s Special Relativity (ESR), in its original formulation1, is limited to inertial motions only, while an insight into real - world shows that the motions are non - inertial. It is hard to accept that the launching of a rocket implies a succession of inertial motions. Similalry, during the re - entry of a satellite in the Earth’s atmosphere, its continuously decaying angular momentum and the violations of the Lorentz - Poincare symmetries, are then evident. From the view - point of kinematics, defined as the science of pure motion, apart from causes, the motion may be either inertial or non - inertial. Since a motion cannot be, at the same time, either a uniform translation or a non - uniform motion, then they form a pair of complementary kinematic concepts, mutually exclusive. If the gravitational effects are neglected, ESR assumes uniform translations, while under similar circumstances (regarding the neglecting of the space curvature) to the best of our knowledge, nothing is known in the literature to take into consideration non - inertial motions. As a consequence, we shall denote by Special Relativity that branch of physics where by neglecting the gravitational effects, the motion may be either inertial or noninertial, called in this paper permissible motions. As a consequence, the following chart of complementarities:

GENERALIZED ANALYTIC MAPPINGS AND FLAT-SPACE MODELS OF HAWKING RADIATION

We generalize the approach to Q.F.T. in accelerated frames based on analytic mappings in a way which stresses further the comparison between the flat and curved space-time situations. Combined linear acceleration with uniform and nonuniform translations or rotations, and nonanalytic but asymptotically analytic mappings are included. A density matrix formulation is given for quantum states at global and asymptotic thermal equilibrium, and the role of the PCT symmetry is discussed. Flat space models of rotating and charged black holes are investigated, together with their surface gravity, chemical potentials, Hawking radiation and superradiance properties.

Random linear systems and temporal homogeneity

The class of random linear systems having stochastic Green’s functions whose moments are invariant under arbitrary uniform translations of all time variables is defined and investigated. It is pointed out that this class is very broad, including, for example, virtually all treatments of wave propagation through a random medium. Proceeding by analogy with quantum field theory the quantities 𝒢 and M, related to the first and second moments of the stochastic Green’s function, are defined. Various properties of 𝒢 and M (which in quantum field theory correspond respectively to a propagator and an elastic scattering amplitude) are discussed, and it is shown that they may be conveniently used to describe the principal physical effects induced by transmission through a randomly fluctuating system. Specific examples are given in which these quantities are explicitly calculated and used to illustrate the general results.

Periodic Reticle for Optical Classification*

We deal here with a specific type of linear filter in which the input is a spatially limited nonnegative intensity such as that which appears on the image plane of an optical system having a finite field of view. This intensity is passed through a mask, or reticle, having a transmittance with two-dimensional periodicity. The transmitted intensity is detected so as to produce a voltage output which varies with time as the mask is moved. For a discrete set of uniform translations of the mask, the filter codes linear combinations of the Fourier transform of the input at certain spatial frequencies into the Fourier coefficients of the output.For certain input classes of images, characterized by dominant spatial frequencies, the reticle as well as its motion can be chosen in an optimum manner so as to “best distinguish” these classes by their outputs.There is an interesting analogy between this linear filter and that of a crystalline material irradiated with a plane monochromatic X ray. The reticle has a two-dimensional primary and reciprocal lattice corresponding to the three-dimensional ones of a crystal. Just as certain positions of the crystal, specified by its reciprocal lattice, give rise to Bragg reflections, so do certain translations of the reticle, specified by its primary lattice, give rise to the “coded voltage waveforms.”

Towards a Quantum Many-Body Theory of Lattice Dynamics. I. Time-Dependent Hartree Approximation

The phonon is discussed as an example of a collective mode which restores a symmetry property (in this case, translational invariance) to a system whose Hamiltonian is invariant under the symmetry operation, but in whose ground state the symmetry is broken. The crystal lattice is first studied within the time-independent Hartree approximation. It is then shown that allowing small time-dependent changes in the Hartree field generates an equation for the normal modes of vibration. The three k=0 modes with $\ensuremath{\omega}=0$ are shown to represent uniform translations of the solid, as expected. The $\mathbf{k}\ensuremath{\ne}0$ modes are analyzed to extract those three which may be identified as one-phonon modes, and the contribution of these modes to the free energy is computed. The recent theory of Brout is found to be equivalent to the Hartree approximation with the further assumption that the atoms are infinitely heavy. No restrictions are made here on the interatomic potential other than that a hard core is absent. The reduction of the present theory to well-known results in the case of harmonic forces is demonstrated. An extension to include hard cores, analogous to the Brueckner theory, is discussed.

Physics

THIS, the last, volume of Lorentz's “Lectures on Theoretical Physics” contains a translation of two courses, namely, “Maxwell's Theory”, edited in the Dutch by H. Bremekamp and published in Leyden in 1925, and “The Principle of Relativity for Uniform Translations”, edited by A. D. Fokker and published in 1922. Lectures on Theoretical Physics delivered at the University of Leiden. By H. A. Lorentz. Authorised translation by Dr. L. Silberstein and A. P. H. Trivelli Vol. 3: Maxwell's Theory, edited by Dr. A. D. Bremekamp; The Principle of Relativity for Uniform Translations, edited by Dr. A. D. Fokker. Pp. xi + 326. (London: Macmillan and Co., Ltd., 1931.) 21s. net.