Scale Invariance Properties in the Simulated Annealing Algorithm

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.     

Zinn und Antimon in Legierungen

Ohne Zusammenfassung     

Maximin share and minimax envy in fair-division problems

For fair-division or cake-cutting problems with value functions which are normalized positive measures (i.e., the values are probability measures) maximin-share and minimax-envy inequalities are derived for both continuous and discrete measures. The tools used include classical and recent basic convexity results, as well as ad hoc constructions. Examples are given to show that the envy-minimizing criterion is not Pareto optimal, even if the values are mutually absolutely continuous. In the discrete measure case, sufficient conditions are obtained to guarantee the existence of envy-free partitions.     

Analysis of Static Simulated Annealing Algorithms

Generalized hill climbing (GHC) algorithms provide a framework for modeling local search algorithms to address intractable discrete optimization problems. This paper introduces a measure for determining the expected number of iterations to visit a predetermined objective function level, given that an inferior objective function level has been reached in a finite number of iterations. A variation of simulated annealing (SA), termed static simulated annealing (S²A), is analyzed using this measure. S²A uses a fixed cooling schedule during the algorithm execution. Though S²A is probably nonconvergent, its finite-time performance can be assessed using the finite-time performance measure defined in this paper.     

Mechanisms of ion-beam-enhanced diffusion in amorphous silicon

We have investigated ion-beam-enhanced diffusion of Au in undoped and B doped amorphous Si. The diffusion coefficients depend linearly on ion flux and exibit an Arrhenius-like temperature dependence with an activation energy of 0.37 eV in the temperature range 200–350° C. Moreover the diffusivity is enhanced by a factor of 5 by B-doping at a concentration of 1×10²⁰ atoms/cm³. A similar enhancement is observed in thermal diffusion of Au which has an activation energy of 1.5 eV. On the basis of these results a model for the ion-beam-enhanced diffusion of Au is proposed where the high density of defects present in amorphous Si act as traps for the fast moving interstitial Au atoms. The effectiveness of this trapping process can be changed by the high concentration of mobile defects generated by the beam and also by a change in the charge state of the traps induced by the presence of B.     

Neighborhood unions and the cycle cover number of a graph

For several years, the study of neighborhood unions of graphs has given rise to important structural consequences of graphs. In particular, neighborhood conditions that give rise to hamiltonian cycles have been considered in depth. In this paper we generalize these approaches to give a bound on the smallest number of cycles in G containing all the vertices of G. We show that if for all x, y ? V(G), |N(x) ∩ N(y)| ≧ 2n/5 + 1, then V(G) is coverable by at most two cycles. Several related results and extensions to t cycles are also given.     

Influence of the reaction temperature and ph on the coordination modes of the 1,4-benzenedicarboxylate (BDC) ligand: a case study of the Ni(II)(BDC)/2,2'-bipyridine system

Three new Ni(BDC)/2,2'-bipy compounds, Ni2(BDC)(HBDC)2(2,2'-bipy)2 (2), Ni3(BDC)3(2,2'-bipy)2 (3), and Ni(BDC)(2,2-bipy)2.2H2O (5), in addition to the previously reported Ni(BDC)(2,2'-bipy).0.75H2BDC (1) and Ni(BDC)(2,2'-bipy)(H2O) (4) [BDC = 1,4-benzenedicarboxylate; 2,2'-bipy = 2,2'-bipyridine], have been synthesized by hydrothermal reactions. A systematic investigation of the effect of the reaction temperature and pH resulted in a series of compounds with different compositions and dimensionality. The diverse product slate illustrates the marked sensitivity of the structural chemistry of polycarboxylate aromatic ligands to synthesis conditions. Compound 1, which has a channel structure containing guest H2BDC molecules, is formed at the lowest pH. The guest H2BDC molecules are connected by hydrogen bonds and form extended chains. At a slightly higher pH, a dimeric molecular compound 2 is formed with a lower number of protonated carboxylate groups per nickel atom and per BDC ligand. Reactions at higher temperature and the same pH lead to the transformation of 1 and 2 into the two-dimensional, layered trinuclear compound 3. As the pH is increased, a one-dimensional polymer 4 is formed with a water molecule coordinated to Ni2+. Bis-monodentate and bischelating BDC ligands alternate along the chain to give a crankshaft rather than a regular zigzag arrangement. A further increase of the pH leads to the one-dimensional chain compound 5, which has two chelating 2,2'-bipy ligands. Crystal data: 2, triclinic, space group P, a = 7.4896(9) angstroms, b = 9.912(1) angstroms, c = 13.508(2) angstroms, alpha = 86.390(2) degrees , beta = 75.825(2) degrees, gamma = 79.612(2) degrees, Z = 2; 3, orthorhombic, space group Pbca, a = 9.626(2) angstroms, b = 17.980(3) angstroms, c = 25.131(5) angstroms, Z = 4; 5, orthorhombic, space group Pbcn, a = 14.266(2) angstroms, b = 10.692(2) angstroms, c = 17.171(2) angstroms, Z = 8.