On a new class of multiplicative pseudo-random number generators

In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x _{0 1} ⁱ /p} on [0, 1] fori=0, 1,..., (p–1)p^–1–1, i.e. in current terminology, generators given byx _{n+1 1} x _n mod p wheren=0, 1,..., (p–1)p ^–1–1,p is any odd prime, (x ₀,p)=1, ₁ is a primitive root modp ², and 1 is any positive integer.We derive the expectationsE(X, ),E(X ², ),E(X _nX_n+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of ₁ for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.     

激光-钨靶耦合效应的二维模拟研究

利用二维ESCL-CASTOR磁流体力学三温激光靶程序,对激光-钨靶进行了计算机模拟研究。得到了密度、温度(T_e,T_i,T_R)和速度的空间分布以及随时间的变化规律;特别是得到了临界面的运动规律、辐射谱和X光转换效率等结果,并与实验结果进行了比较。     

The maximum covering/shortest path problem: A multiobjective network design and routing formulation

In this paper the authors introduce the maximum covering/shortest path problem and the maximum population/shortest path problem, a special case of the former model. Both models are formulated as two objective integer programs. A summary of the results of a sample problem for the latter formulation is given. Possible modifications to, and extensions and applications of both models are also presented. With these formulations the authors extend the concept of ‘coverage’ from facility location analysis to network design and routing analysis.     

Single particle SU(3) parentage coefficients

The single particle SU(3) parentage coefficients are calculated for the case of leading SU(3) representation in the highest orbital symmetry partition, using the method suggested by Hecht. Tabulations are given for all possible cases of identical nucleons in η=3 and η=4 shells.     

Thermodynamics of aqueous sodium sulfate

The activity coefficient of saturated aqueous Na₂SO₄ is calculated from the properties of the solid and the infinitely dilute solution as well as the solubility. These values are compared with those given by the equation of Rogers and Pitzer which is based on the measured dependence of heat capacity upon molality together with other solution properties at low temperature. Excellent agreement is found from 30 to 280°C. Consequently the equation of Rogers and Pitzer is given an extended range of validity to saturated molality and to 280°C. The trend of solubility with temperature is discussed in relation to the C_p of solution.     

Thermodynamics of electrolytes. X. Enthalpy and the effect of temperature on the activity coefficients

Heat of dilution and of solution data are fitted to the form of equation corresponding to that used successfully for activity and osmotic coefficients over a wide range of concentrations. The resulting parameters give the change with temperature of the activity and osmotic coefficients. Results are reported for 84 electrolytes of 1-1, 2-1, 3-1, and 2-2 valence types.     

Determination of diffusion coefficients of Cu(I) ions in concentrated perchlorate solutions

The diffusion coefficients of Cu(I) ions in concentrated aqueous Ca(ClO₄)₂ solutions have been determined from the limiting currents of anodic oxidation at the rotating disc electrode.

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Zur Bestimmung der Diffusionskoeffizienten von Cu(I)-Ionen in konzentrierten Perchloratlösungen (Kurze Mitteilung)

Zusammenfassung Diffusionskoeffizienten von Cu(I)-Ionen in konzentrierten wäßrigen Ca(ClO₄)₂-Lösungen wurden durch Messung der anodischen Grenzströme an der rotierenden Scheibenelektrode bestimmt.

     

Resolution enhancement of a.c. polarographic peaks by deconvolution using the fast fourier transform

A method for resolution enhancement of a.c. polarograms (voltammograms) is presented. The method is based on deconvolution using fast Fourier transforms. Overlapped a.c. polarograms are mathematically narrowed and sharpened, retaining the peak position and linear proportionality of the sharpened peak height with concentration. The advantages and limitations of the method are demonstrated on simulated and experimental a.c. polarograms. The same approach is applicable to related techniques such as. differential pulse and square-wave polarography.     

Macro-Scale Dynamic Effects in Homogeneous and Heterogeneous Porous Media

It is known that the classical capillary pressure-saturation relationship may be deficient under non-equilibrium conditions when large saturation changes may occur. An extended relationship has been proposed in the literature which correlates the rate of change of saturation to the difference between the phase pressures and the equilibrium capillary pressure. This linear relationship contains a damping coefficient, \tau, that may be a function of saturation. The extended relationship is examined at the macro-scale through simulations using the two-phase simulator MUFTE-UG. In these simulations, it is assumed that the traditional equilibrium relationship between the water saturation and the difference in fluid pressures holds locally. Steady-state and dynamic numerical experiments are performed where a non-wetting phase displaces a wetting phase in homogeneous and heterogeneous domains with varying boundary conditions, domain size, and soil parameters. From these simulations the damping coefficient can be identified as a (non-linear) function of the water saturation. It is shown that the value of increases with an increased domain size and/or with decreased intrinsic permeability. Also, the value of for a domain with a spatially correlated random distribution of intrinsic permeability is compared to a homogeneous domain with equivalent permeability; they are shown to be almost equal.     

Refinable bivariate quartic -splines for multi-level data representation and surface display

In this paper, a second-order Hermite basis of the space of -quartic splines on the six-directional mesh is constructed and the refinable mask of the basis functions is derived. In addition, the extra parameters of this basis are modified to extend the Hermite interpolating property at the integer lattices by including Lagrange interpolation at the half integers as well. We also formulate a compactly supported super function in terms of the basis functions to facilitate the construction of quasi-interpolants to achieve the highest (i.e., fifth) order of approximation in an efficient way. Due to the small (minimum) support of the basis functions, the refinable mask immediately yields (up to) four-point matrix-valued coefficient stencils of a vector subdivision scheme for efficient display of -quartic spline surfaces. Finally, this vector subdivision approach is further modified to reduce the size of the coefficient stencils to two-point templates while maintaining the second-order Hermite interpolating property.