Convergence of interval-type algorithms for generalized fractional programming

The purpose of this paper is to analyze the convergence of interval-type algorithms for solving the generalized fractional program. They are characterized by an interval [LB _k , UB _k ] including*, and the length of the interval is reduced at each iteration. A closer analysis of the bounds LB _k and UB _k allows to modify slightly the best known interval-type algorithm NEWMODM accordingly to prove its convergence and derive convergence rates similar to those for a Dinkelbach-type algorithm MAXMODM under the same conditions. Numerical results in the linear case indicate that the modifications to get convergence results are not obtained at the expense of the numerical efficiency since the modified version BFII is as efficient as NEWMODM and more efficient than MAXMODM.This research was supported by NSERC (Grant A8312) and FCAR (Grant 0899).     

Analysis of a class of fractional programming problems

We propose a solution strategy for fractional programming problems of the form max _xx g(x)/ (u(x)), where the function satisfies certain convexity conditions. It is shown that subject to these conditions optimal solutions to this problem can be obtained from the solution of the problem max _xx g(x) + u(x), where is an exogenous parameter. The proposed strategy combines fractional programming andc-programming techniques. A maximal mean-standard deviation ratio problem is solved to illustrate the strategy in action.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Generalized Brownian motion and elasticity

We introduce a family of stochastic processes which are a natural extension of Brownian motion to a tensor form. This allows us to solve a Dirichlet problem of linear elasticity obeying Lamé's equation, [1–(d– 1)]²V(x)+ [·V(x)]=0.     

The interface of the Ising model and the Brownian sheet

We study the limit theorem related to the interface of the three-dimensional Ising model. Dobrushin proved that the interface does not fluctuate and becomes rigid for sufficiently large. We define the random fieldX ^L (t, s), 0t, s1, on the interface, and prove that X^L(t, s) converges to the Brownian sheet as L for sufficiently large, whereL denotes the size of the system. This result does not mean that the interface itself converges to the Brownian sheet.     

Note on the fractal dimension of hard sphere trajectories

Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations.     

分数级反应热动力学研究—丙烯酰胺聚合反应动力学

应用n级等摩尔浓度反应的热动力学理论,在30℃和40℃下研究了丙烯酰胺在水溶液中和CTAB胶束溶液中由亚硫酸钠引发的聚合反应动力学.讨论了引发剂和CTAB的浓度对聚丙烯酰胺分子量的影响。     

Fraktionierte Kristallisation von Ammonium- und Magnesiumdoppelnitraten der Ceriterden; Bestimmung der Trennfaktoren und Vergleich der Trennwirkung

Summary The Separation Factors for Pr/La, Nd/Pr, and Sm/Nd, characterizing the crystallization of ammonium and magnesium double nitrates under practical conditions, were determined analytically and are discussed. They confirm that La and Pr can be separated better by fractional crystallization of ammonium double nitrates, whereas in the presence of Sm the magnesium double nitrates are preferable.

     

Conformational Transformation Exhibited by the Peptide Extracted from Crystalline Region of Bombyx mori Silk Fibroin in Solid and Solution States

The conformational transformation of a 30-residue peptide H（Ala-Gly-Ser-Gly-AIa-Gly）5OH, i.e., （AGSGAG）5, extracted from highly crystalline region of Bombyx mori （B. mori） silk fibroin was described by using the high resolution solid state 13^C NMR, and CD spectroscopies. Based on the conformation-dependent 13^C NMR chemical shifts of the Ala, Gly and Ser residues and the line-shape analysis of the conformation sensitive Ala Cβ resonance, the peptide revealed a strong preference for silk Ⅱ structural form, i,e,, an antiparallel fl-sheet structure （φ= - 140±20°and ψ= 135±20°） in solid state. On the contrary, the CD spectra of this peptide in the two non-native hexafluorinated fibre spinning solvents, hexafluoroisopropanol （HFIP） and hexafluoroacetone （HFA）, exhibited the existence of an unusual tightly-folded conformation resembling 310-helix （φ=- 60±20° and ψ=-30±20°）, as judged from the R ratio of [θ]222/[θ]203 in HFIP solution, whereas a dynamically averaged unordered structure in HFA, Taken together, the information inclined to hypothesis that the primary structure of the highly crystalline regions of B. mori silk fibroin may be easily accessible to the large conformational changes, which in turn may be critical for facilitating the structural transformation from unprocessed silk fibroin （silk I form） to processed silk fiber （silk Ⅱform）.     

Triple Positive Solutions of Boundary Value Problems for High-order Fractional Differential Equation at Resonance with Singularities

In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.