DETERMINISTIC ALGORITHMS FOR MATCHING AND PACKING PROBLEMS BASED ON REPRESENTATIVE SETS

In this work, we study the well-known r-DIMENSIONAL k-MATCHING ((r, k)-DM), and r-SET k-PACKING ((r, k)-SP) problems. Given a universe U := U-1 ... U-r and an r-uniform family F subset of U-1 x ... x U-r, the (r, k)-DM problem asks if F admits a collection of k mutually disjoint sets. Given a universe U and an r-uniform family F subset of 2(U), the (r, k)-SP problem asks if F admits a collection of k mutually disjoint sets. We employ techniques based on dynamic programming and representative families. This leads to a deterministic algorithm with running time O(2.851((r-1)k) .vertical bar F vertical bar. n log(2)n . logW) for the weighted version of (r, k)-DM, where W is the maximum weight in the input, and a deterministic algorithm with running time O(2.851((r-0.5501)k).vertical bar F vertical bar.n log(2) n . logW) for the weighted version of (r, k)-SP. Thus, we significantly improve the previous best known deterministic running times for (r, k)-DM and (r, k)-SP and the previous best known running times for their weighted versions. We rely on structural properties of (r, k)-DM and (r, k)-SP to develop algorithms that are faster than those that can be obtained by a standard use of representative sets. Incorporating the principles of iterative expansion, we obtain a better algorithm for (3, k)-DM, running in time O(2.004(3k).vertical bar F vertical bar . n log(2)n). We believe that this algorithm demonstrates an interesting application of representative families in conjunction with more traditional techniques. Furthermore, we present kernels of size O(e(r)r(k-1)(r) logW) for the weighted versions of (r, k)-DM and (r, k)-SP, improving the previous best known kernels of size O(r!r(k-1)(r) logW) for these problems.

Asymptotic behavior and interpretation of virtual states: The effects of confinement and of basis sets

A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations. (C) 2016 AIP Publishing LLC.

Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Practical Criterion for Universal Laws and Practical Methods for Construction of Co-variance Sets

给出相对论力学中普遍定律的实用判别法和协变集的实用构造法,还给出实现非普遍定律的“可导出性”的一种实用方法．

Immunosensor Interface Based on Physical and Chemical Immunogylobulin G Adsorption onto Mixed Self-Assembled Monolayers

An immunosensor interface based on mixed hydrophobic self-assembled monolayers (SAMs) of methyl and carboxylic acid terminated thiols with covalently attached human Immunoglobulin G (hIgG), is investigated. The densely packed and organised SAMs were characterised by contact angle measurements and cyclic voltammetry. The effect of the non-ionic surfactant, Tween 20, in preventing nonspecific adsorption is addressed by ellipsometry during physical and covalent hIgG immobilization on pure and mixed SAMs, respectively. It is clearly demonstrated that nonspecific adsorption due to hydrophobic interactions of hIgG on methyl ended groups is totally inhibited, whereas electrostatic/hydrogen bonding interactions with the exposed carboxylic groups prevail in the presence of surfactant. Results of ellipsometry and Atomic Force Microscopy, reveal that the surface concentration of covalently immobilized hIgG is determined by the ratio of COOH/CH3-terminated thiols in SAM forming solution. Moreover, the ellipsometric data demonstrates that the ratio of bound anti-hIgG/hIgG depends on the density of hIgG on the surface and that the highest ratio is close to three. We also report the selectivity and high sensitivity achieved by chronoamperometry in the detection of adsorbed hIgG and the reaction with its antibody.

Adsorption of human serum albumin onto gold: a combined electrochemical and ellipsometric study

Human serum albumin adsorption onto gold surfaces was investigated by electrochemical and ellipsometric methods. Albumin adsorption onto gold was confirmed by the change of the open circuit potential of gold and by the ellipsometric parameter variation during albumin immobilization. In both experiments the parameters reached stable values within 10-15 min. The albumin adsorption layer thickness measured with the ellipsometer was about 1.5 nm. The adsorption of albumin Under applied potential was also investigated and it was found that both positive and negative applied potential promote albumin adsorption. Changes in the optical parameters of bare gold and albumin adsorbed onto gold surface under applied potential were investigated with in Situ ellipsometry. The similarity and reversibility of the optical changes showed that adsorbed albumin was stable on the gold surface Under the applied potential range (-200-600 mV). The cyclic voltammograms of K3Fe(CN)(6) on the modified gold surface showed that albumin Could partly block the oxidation and reduction reaction. (C) 2004 Elsevier Inc. All rights reserved.