Phase transitions of the q-state Potts model on multiply-laced Sierpinski gaskets

We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered phase at any q>=1. Multicriticality is observed in the presence of a symmetry-breaking field. Exact renormalization group analysis yields the phase diagram of the model and a complete set of critical exponents at various transitions.Comment: 6 pages, 6 figures; figures correcte

Impulsive problems for fractional differential equations with boundary value conditions

AbstractWe consider impulsive problems for a fractional differential equation with boundary value conditions. Natural formulae of a solution for our problem are introduced, which can be regarded as a novelty item. Some related new existence results are established by applying fixed point methods via a generalized singular Gronwall inequality. Examples are given to illustrate the results

Characteristic Functions of L1-Spherical and L1-Norm Symmetric Distributions and Their Applications

AbstractIn this article we obtain the characteristic functions (c.f.'s) for L1-spherical distributions and simplify that of the L1-norm symmetric distributions to an expression of a finite sum. These forms of c.f.'s can be used to derive the probability density functions (p.d.f.'s) of linear combinations of variables. We shall show that this gives a unified approach to the treatment of the linear function of i.i.d. random variables and their order statistics associated with double-exponential (i.e., Laplace), exponential, and uniform distributions. Some applications in reliability prediction, random weighting, and serial correlation are also shown

Bounding the inefficiency of logit-based stochastic user equilibrium

Bounding the inefficiency of selfish routing has become an emerging research subject. A central result obtained in the literature is that the inefficiency of deterministic User Equilibrium (UE) is bounded and the bound is independent of network topology. This paper makes a contribution to the literature by bounding the inefficiency of the logit-based Stochastic User Equilibrium (SUE). In a stochastic environment there are two different definitions of system optimization: one is the traditional System Optimum (SO) which minimizes the total actual system travel time, and the other is the Stochastic System Optimum (SSO) which minimizes the total perceived travel time of all users. Thus there are two ways to define the inefficiency of SUE, i.e. to compare SUE with SO in terms of total actual system travel time, or to compare SUE with SSO in terms of total perceived travel time. We establish upper bounds on the inefficiency of SUE in both situations

Structural damage detection based on cloud model and Dempster-Shafer evidence theory

Cloud model and D-S theory have been widely used in uncertainty reasoning. Meanwhile, modal strain energy and Inner Product Vector are also utilized as damage-sensitive features to detect structural damage. In this paper, a new structural damage identification approach is proposed based on Dempster-Shafer theory and cloud model. Cloud models were created to make uncertainty reasoning in damage structures by modal strain energy and the Inner Product Vector of acceleration. Then the results of the two methods were combined by using the Dempster-Shafer theory. Due to the classical D-S theory involves counter – intuitive behavious when the high conflicting evidences exists, the distance function was introduced to correct the conflict factor K and combine the evidences. Moreover, a model of simple beam was created to verify the feasibility and accuracy for the single-damage and the multiple-damage. The effects of noise on damage detection were investigated simultaneously. The results show that the method has strong anti-noise ability and high accuracy

Photoelectrochemical Sensors for the Rapid Detection of DNA Damage Induced by Some Nanoparticles

Photoelectrochemcal sensors were developed for the rapid detection of oxidative DNA damage induced by titanium dioxide and polystyrene nanoparticles. Each sensor is a multilayer film prepared on a tin oxide nanoparticle electrode using layer- by-layer self assembly and is composed of separate layer of a photoelectrochemical indicator, DNA. The organic compound and heavy metals represent genotoxic chemicals leading two major damaging mechanisms, DNA adduct formation and DNA oxidation. The DNA damage is detected by monitoring the change of photocurrent of the indicator. In one sensor configuration, a DNA intercalator, Ru(bpy)2 (dppz)2+ [bpy=2, 2′ -bipyridine, dppz=dipyrido( 3, 2-a: 2′ 3′-c) phenazine], was employed as the photoelectrochemical indicator. The damaged DNA on the sensor bound lesser Ru(bpy)2 (dppz)2+ than the intact DNA, resulting in a drop in photocurrent. In another configuration, ruthenium tris(bipyridine) was used as the indicator and was immobilized on the electrode underneath the DNA layer. After oxidative damage, the DNA bases became more accessible to photoelectrochemical oxidation than the intact DNA, producing a rise in photocurrent. Both sensors displayed substantial photocurrent change after incubation in titanium dioxide / polystyrene solution in a time – dependent manner. According to the data, damage of the DNA film was completed in 1h in titanium dioxide / polystyrene solution. In addition, the titanium dioxide induced much more sever damage than polysterene. The results were verified independently by gel electrophoresis and UV-Vis absorbance experiments. The photoelectrochemical reaction can be employed as a new and inexpensive screening tool for the rapid assessment of the genotoxicity of existing and new chemicals