Operations that preserve total dual integrality

There are many useful operations, such as adding slack variables, taking scalar multiples of inequalities, and applying Fourier-Motzkin elimination, that can be performed on a linear system such that if the system defines an integer polyhedron then so does the derived system. The topic dealt with here is whether or not these operations also preserve total dual integrality of linear systems.     

Work function of metals: Relation between theory and experiment

Theoretical approaches to calculation of work function within jellium model and the problem of extension of this model to include the lattice corrections to the work function are briefly discussed. Lattice corrections to the work function obtained from the experiment are estimated and compared with those calculated theoretically.

It is found that the mean value of the experimental lattice correction <δψ_hkl>_hkl compared to the mean work function is negligible. It is stated that the mean work function can be treated as a material constant characterizing a given metal, such as, e.g., binding energy.An expression for the dependence of jellium work function on r_s, valid in a metallic range of r_s, is given. A comparison between then theoretical and experimental results is presented and the role of correlation energy is examined. It is shown that more accurate approximations of the correlation energy than that given by Wigner's formula lead to a better agreement with experiment. A simple model is presented for explanation of work function changes on single crystal planes. Some recent results concerning the thermal dependence of work function are given. The dependence of the work function on the degree of coverage is discussed both for alkali and non-alkali atoms adsorption. Theoretical models are briefly reviewed and comparison between theory and experiment is made. A simple model is presented for explanation of the work function variation on rough planes in metallic non-alkali atoms chemisorption.     

Degree of approximation to function of bounded variation by Bézier variant of MKZ operators

Guo (Approx. Theory Appl. 4 (1988) 9-18) introduced the integral modification of Meyer-Konig and Zeller operators and studied the rate of convergence for functions of bounded variation. In this paper we introduce the Bézier variant of these integrated MKZ operators and study the rate of convergence by means of the decomposition technique of functions of bounded variation together with some results of probability theory and the exact bound of MKZ basis functions. Recently, Zeng (J. Math. Anal. Appl. 219 (1998) 364-376) claimed to improve the results of Guo and Gupta (Approx. Theory Appl. 11 (1995) 106-107), but there is a major mistake in the paper of Zeng. For special case our main theorem gives the correct estimate on the rate of convergence, over the result of Zeng.     

Liouville—Ttype Theorems for Conformal Gaussian Curvature Equations in R^2

In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions.     

Leading and higher twists in proton,neutron and deuteron unpolarized structure functions F<Subscript>2</Subscript>

We summarize the results of a recent global analysis of proton and deuteron F₂ structure function world data performed over a large range of kinematics, including recent measurements done at JLab with the CLAS detector. From these data the lowest moments (n≤10) of the unpolarized structure functions are determined with good statistics and systematics. The Q² evolution of the extracted moments is analyzed in terms of an OPE-based twist expansion, taking into account soft-gluon effects at large x. A clean separation among the leading- and higher-twist terms is achieved. By combining proton and deuteron measurements the lowest moments of the neutron F₂ structure function are determined and its leading-twist term is extracted. Particular attention is paid to nuclear effects in the deuteron, which become increasingly important for the higher moments. Our results for the non-singlet, isovector (p-n) combination of the leading-twist moments are used to test recent lattice simulations. We also determine the lowest few moments of the higher-twist contributions, and find these to be approximately isospin independent, suggesting the possible dominance of ud correlations over uu and dd in the nucleon.     

Calculation of triaxial superdeformation in <Superscript>174</Superscript>Hf

A two-dimensional Total Routhian Surface (TRS) calculation with the fixed hexadecapole deformation ε4 = 0.03 was carried out for several configurations of 174Hf. Results indicate that the shell corrections have an important contribution to the formation of triaxial superdeformation in 174Hf and some possible configuration assignments are made to the 4 TSD bands experimentally found in 174Hf.     

Structural analysis of Si(1 1 1)-√21 × √21-(Ag, Au) surface by using reflection high-energy positron diffraction

The Au adsorption induced √21 × √21 super-lattice structure on the Si(1 1 1)-√3 × √3-Ag structure has been investigated using reflection high-energy positron diffraction. The height of the Au adatom was determined to be 0.59 Å from the underlying Ag layer from the rocking curve analysis with the dynamical diffraction theory. The adatoms were preferentially situated at the center of the large Ag triangle of the inequivalent triangle structure of the Si(1 1 1)-√3 × √3-Ag substrate. From the intensity distribution in the fractional-order Laue zone, the in-plane coordinate of the Au adatoms was obtained.     

Surface structure of In/Si(1 1 1) studied by reflection high-energy positron diffraction

We have investigated a quasi-one-dimensional structure of In/Si(1 1 1) surface using reflection high-energy positron diffraction (RHEPD), which is sensitive to the topmost surface structure under the total reflection condition. From the rocking curves, we found that In atoms are located at two different vertical positions, i.e., 0.99 Å and 0.55 Å from the Si zigzag chain in both 4 × 1 (210 K) and 8 × 2 (60 K) phases.     

Fast TV Regularization for 2D Maximum Penalized Likelihood Estimation

Total Variation-based regularization, well established for image processing applications such as denoising, was recently introduced for Maximum Penalized Likelihood Estimation (MPLE) as an effective way to estimate nonsmooth probability densities. While the estimates show promise for a variety of applications, the nonlinearity of the regularization leads to computational challenges, especially in multidimensions. In this article we present a numerical methodology, based upon the Split Bregman L1 minimization technique, that overcomes these challenges, allowing for the fast and accurate computation of 2D TV-based MPLE. We test the methodology with several examples, including V-fold cross-validation with large 2D datasets, and highlight the application of TV-based MPLE to point process crime modeling. The proposed algorithm is implemented as the Matlab function TVMPLE. The Matlab (mex) code and datasets for examples and simulations are available as online supplements.     

Radiation attenuation and nuclear properties of high density concrete made with steel aggregates

Abstract

The fast neutron and gamma ray spectra measured behind different thickness of steel scrap concrete with density of 4 g/cm³ have been studied. The mix proportions by weight of this type of concrete were 1 cement: 6.89 steel scrap: 2.9 sand and 0.5 Water. Comparison with a standard ordinary concrete of density 2.3 g/cm³ have been carried out. The measurements were made using a collimated beam of both gamma rays and neutrons emitted from one of the horizontal channel of the Egyptian Research Reactor-1. A fast neutron and gamma ray spectrometer with a stilbene crystal was used to measure the spectra of fast neutrons and gamma rays. Pulse shape discrimination using the zero cross over technique was used to separate the photon pulses from the electron pulses. The equation due to Schmidt has been modified and applied for determining the neutron effective removal cross sections (～_R) for steel scrap, ordinary, hematite–serpentine, ilmenite–limonite and ilmenite concretes. This equation gives results which are in good agreement with the measured values. The derived empirical equation in a previous work to calculate the neutron integral flux behind different thicknesses of different types of concretes, gives good results for steel scrap concrete under investigation comparing with the corresponding experimental data. Total neutron macroscopic cross sections, linear attenuation coefficients for gamma rays and the half-value layers for both radiations at different energies have been obtained for steel scrap concrete and comparing with the corresponding values of ordinary concrete. The results show that steel scrap concrete is better than ordinary, hematite–serpentine, ilmenite–limonite and ilmenite concretes from the radiation shielding point of view.