An analysis of the conditions for the formation of an internal interface and their effect on the freezing point of zinc

The effect of the conditions for the formation of an internal interface on the freezing point of zinc of 99.9999% purity for different intensities of the removal of heat from the zinc in the thermometer channel is investigated. Comparative measurements without the formation of an internal interface were carried out. The difference between the maximum values of the measured temperatures reached approximately 1 mK. The reasons for these differences are considered.Translated from Izmeritelnaya Tekhnika, No. 11, pp. 43–45, November, 2004.     

Secondary ion emission of Fe-Ni alloys in the temperature range including the Curie point

The temperature dependence of secondary ion emission was investigated for Fe-Ni ferromagnetic alloys with different Curie points T_c and elemental composition: 35% Ni 65% Fe (T_c=240°C), 40% Ni 60% Fe (T_c=360°C), and 50% Ni 50% Fe (T_c=530°C). The alloy 79% Ni 16% Fe 5% Mo (T_c=345°C) was also studied. The spatial distribution of Ni⁺ and Fe⁺ secondary ions emitted from the (1 1 1) face of invar and permalloy single crystals was shown to be anisotropic with pronounced ion-yield maximum for both components in the 〈1 1 0〉 directions. The shape of the energy distribution of Ni⁺ and Fe⁺ ions was found to be virtually identical for all the alloys under investigation with a most probable energy at 7 eV and a width at half-maximum of 12 eV. The temperature dependence of the Ni⁺ and Fe⁺ emission has a maximum near the Curie point of the investigated alloys and another maximum at the Curie point of nickel which may indicate the precipitation of nickel into microscopic islands on the surface as a result of heating and sputtering. Auger analysis of the surface composition in the surface layers showed a variation in concentration of oxygen and carbon atoms when Fe-Ni alloys pass from the ferromagnetic to the paramagnetic state and this must affect also the secondary ion emission of alloy components.     

Perspective as a Symmetry Transformation

From the quattrocento to the end of the nineteenth century perspective has been the main tool of artists aiming to paint a naturalistic representation of our environment. In painters’ perspective we find a combination of affine projection and similitude. We recognise the original object in the painting because perspective is a symmetry transformation preserving certain features. The subject of the transformation, in the case of perspectival representation, is visible reality, and the transformed object is the artwork. The application of symmetry transformations developed from the origin of perspective through the centuries to the present day. The single vanishing point could be moved (translated), and even doubled, developments that made it possible to represent an object from different points of view. In the twentieth century, the application of topological symmetry combined with similitude resulted in new ways of seeing, new tools for artists such as cubists and futurists.     

Critical Light Scattering in Pure Liquids

Light-scattering experiments near the critical point (T _c, _c) in fluid systems and, in particular, the central Rayleigh peak in the frequency spectrum are reviewed. Within a nonasymptotic renormalization-group theory, the crossover function is calculated between several regions: (i) from the background to the asymptotic region, (ii) from the hydrodynamic region (wave lengthcorrelation length) to the critical region (wave lengthcorrelation length), and (iii) from critical densities to noncritical densities. Contrary to the mode-coupling expression, the appropriate scaling function is well defined in all limits of its arguments. At T _c the crossover in the wave-vector dependence of the linewidth is also considered. Theoretical results are compared with experiments for pure liquids. Nonuniversal parameters are chosen consistent with the transport coefficients (i.e., the shear viscosity) for the same substance which can be evaluated within the same formalism.     

A Fat Boundary Method for the Poisson Problem in a Domain with Holes

We consider the Poisson equation with Dirichlet boundary conditions, in a domain , where ⁿ , and B is a collection of smooth open subsets (typically balls). The objective is to split the initial problem into two parts: a problem set in the whole domain , for which fast solvers can be used, and local subproblems set in narrow domains around the connected components of B, which can be solved in a fully parallel way. We shall present here a method based on a multi-domain formulation of the initial problem, which leads to a fixed point algorithm. The convergence of the algorithm is established, under some conditions on a relaxation parameter . The dependence of the convergence interval for upon the geometry is investigated. Some 2D computations based on a finite element discretization of both global and local problems are presented.     

Two-Phase Isochoric Heat Capacity Measurements for Nitrogen Tetroxide in the Critical Region and Yang–Yang Relation

The two-phase isochoric heat capacity of nitrogen tetroxide was measured in the temperature range from 261.74 K to the critical temperature (431.072 K) at densities between 201.21 and 1426.5 kg·m^–3 using a high-temperature and high-pressure adiabatic calorimeter. The measurements were performed in the two-phase region for 26 isochores (15 liquid and 11 vapor densities) including the coexistence curve and critical region. Uncertainties of the measurements are estimated to be 2%. The original temperatures and C _V data were converted to the ITS-90. The liquid and vapor two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from experimental data for each measured isochore. From measured (T _S, _S, C _V2, C _V2) data, the values of second temperature derivatives of vapor-pressure d ² P _S/dT ² and chemical potential d ² /dT ² were derived using the Yang–Yang relation. The results were compared with values calculated from other vapor-pressure equations. The values of saturated densities and critical parameters derived in calorimetric experiments were compared with literature data. The unusual temperature behavior of d ² P _S/dT ² and d ² /dT ² was found at low temperatures around 351 K and near the critical point.     

一种GF(2m)上椭圆曲线点运算的混合坐标系

椭圆曲线密码体制(ECC)是一种基于代数曲线的公钥密码体制。椭圆曲线上点运算是该密码体制核心运算，而坐标系的选取决定了点运算速度。为了提高椭圆曲线标量乘速度，在对已有仿射坐标系、Standard投影坐标系、Jacobian投影坐标系和Lopez & Dahab投影坐标系研究的基础上，提出了一种Lopez & Dahab投影坐标系扩展形式，并基于此构建了一种混合坐标系。算法复杂度分析表明，在该混合坐标系下，椭圆曲线标量乘运算时间复杂度比已有坐标系下运算时间复杂度要小。     

Reconstruction of Piecewise Smooth Functions from Non-uniform Grid Point Data

Spectral series expansions of piecewise smooth functions are known to yield poor results, with spurious oscillations forming near the jump discontinuities and reduced convergence throughout the interval of approximation. The spectral reprojection method, most notably the Gegenbauer reconstruction method, can restore exponential convergence to piecewise smooth function approximations from their (pseudo-)spectral coefficients. Difficulties may arise due to numerical robustness and ill-conditioning of the reprojection basis polynomials, however. This paper considers non-classical orthogonal polynomials as reprojection bases for a general order (finite or spectral) reconstruction of piecewise smooth functions. Furthermore, when the given data are discrete grid point values, the reprojection polynomials are constructed to be orthogonal in the discrete sense, rather than by the usual continuous inner product. No calculation of optimal quadrature points is therefore needed. This adaptation suggests a method to approximate piecewise smooth functions from discrete non-uniform data, and results in a one-dimensional approximation that is accurate and numerically robust.      

Vision-Based SLAM: Stereo and Monocular Approaches

Building a spatially consistent model is a key functionality to endow a mobile robot with autonomy. Without an initial map or an absolute localization means, it requires to concurrently solve the localization and mapping problems. For this purpose, vision is a powerful sensor, because it provides data from which stable features can be extracted and matched as the robot moves. But it does not directly provide 3D information, which is a difficulty for estimating the geometry of the environment. This article presents two approaches to the SLAM problem using vision: one with stereovision, and one with monocular images. Both approaches rely on a robust interest point matching algorithm that works in very diverse environments. The stereovision based approach is a classic SLAM implementation, whereas the monocular approach introduces a new way to initialize landmarks. Both approaches are analyzed and compared with extensive experimental results, with a rover and a blimp.     

<Emphasis Type="Italic">k</Emphasis>-Nearest-Neighbor Clustering and Percolation Theory

Let P be a realization of a homogeneous Poisson point process in ℝ ^d with density 1. We prove that there exists a constant k _d , 1<k _d <∞, such that the k-nearest neighborhood graph of P has an infinite connected component with probability 1 when k≥k _d . In particular, we prove that k ₂≤213. Our analysis establishes and exploits a close connection between the k-nearest neighborhood graphs of a Poisson point set and classical percolation theory. We give simulation results which suggest k ₂=3. We also obtain similar results for finite random point sets. Part of the work was done while S.-H. Teng was at Xerox Palo Alto Research Center and MIT. The work of F.F. Yao was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 1165/04E].