On the Error of the Optical Response Approximation in Chiral Media

We study the equations modelling the evolution of electromagnetic fields in chiral media with dispersion. We prove existence and uniqueness of solutions of these equations and provide estimates for the error of the optical response approximation for chiral media.     

The numerical evaluation of the error term in Gaussian quadrature rules

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.     

Hochschild cohomology of partial relation extensions

We show how to compute the low Hochschild cohomology groups of a partial relation extension algebra.     

Group decision making based on intuitionistic multiplicative aggregation operators

Preference relations are the most common techniques to express decision maker’s preference information over alternatives or criteria. To consistent with the law of diminishing marginal utility, we use the asymmetrical scale instead of the symmetrical one to express the information in intuitionistic fuzzy preference relations, and introduce a new kind of preference relation called the intuitionistic multiplicative preference relation, which contains two parts of information describing the intensity degrees that an alternative is or not priority to another. Some basic operations are introduced, based on which, an aggregation principle is proposed to aggregate the intuitionistic multiplicative preference information, the desirable properties and special cases are further discussed. Choquet Integral and power average are also applied to the aggregation principle to produce the aggregation operators to reflect the correlations of the intuitionistic multiplicative preference information. Finally, a method is given to deal with the group decision making based on intuitionistic multiplicative preference relations.     

On the conditional increments of degradation processes

Recently, Wang and Xu (2010) developed an efficient EM algorithm for the semiparametric inference of the inverse Gaussian (IG) process. In the presence of missing degradation data, the algorithm needs to compute the mean of the IG increment during some time interval [_s1,_s2]$[s_1,s_2]$ conditional on that the process is tied down on two points before _s1$s_1$ and after _s2$s_2$, respectively. This study derives the conditional distribution of this increment and gives the expectation of the increment and of the reciprocal of the increment. The results simplify the implementation of the EM algorithm for the IG process. In a similar vein, we further derive distributions for the conditional increments of the Wiener process and the Gamma process, respectively.     

The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology

One of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this study, we consider a row of n plants in which m are infected. We then develop a rigorous mathematical approach to investigate the total number of ways to obtain k isolated individuals among m infected plants. We give a recurrence relation in three parameters that describes the problem, then we find a closed-form solution, and give two different approaches to tackle the proof. Finally, we find interesting formulae for the expectation and variance of the random variable that represents the number of infected and isolated plants.