The structure and expression of power group

With the application of the topological upgrade, more and more experts are interested in the problems concerning the mathematical structure’s upgrade to its power set. This paper is a further study on the structure and interrelationship of a power group. By revealing the nature of relationship between the power group and a regular one, the present paper proves some theorems of the structure of the power group and constructs some theorems on its homomorphism and isomorphism as well, proposing an expression form and isomorphism replacement construct methods of the power group.     

(<Emphasis Type="Italic">δ</Emphasis>,<Emphasis Type="Italic">δ</Emphasis>′)-continuity on generalized topological spaces

We introduce the notion of (δ,δ′)-continuous functions on generalized topological spaces and investigate characterizations for such functions. We study the relationship between (δ,δ′)-continuity and several types of continuity on generalized topological spaces.     

Imaging of periodic dielectrics

We consider imaging of periodic penetrable structures from measurements of scattered electromagnetic waves. The importance of this problem stems from the decreasing size of periodic structures in photonic devices, together with an increasing demand in fast non-destructive testing. This demand makes qualitative inverse scattering techniques particularly attractive since they do not use time consuming optimization techniques for reconstruction but rather directly transform measured data into a picture of the scattering object. We present the Factorization method as an algorithm for imaging of a special class of periodic dielectric structures known as diffraction gratings. Our sampling method computes a picture of the shape of the periodic structure from measured near-field data in a rapid way. We provide numerical examples illustrating this imaging technique.     

On the Asymptotic Behavior of Solutions of the Heat Equation with a Random,Long-Range Correlated Potential

In this note we investigate the asymptotic behavior of the solutions of the heat equation with random, fast oscillating potential

A lower bound on convergence rates of nonadaptive algorithms for univariate optimization with noise

This paper considers complexity bounds for the problem of approximating the global minimum of a univariate function when the function evaluations are corrupted by random noise. We take an average-case point of view, where the objective function is taken to be a sample function of a Wiener process and the noise is independent Gaussian. Previous papers have bounded the convergence rates of some nonadaptive algorithms. We establish a lower bound on the convergence rate of any nonadaptive algorithm.     

Sequences of bias-adjusted covariance matrix estimators under heteroskedasticity of unknown form

The linear regression model is commonly used by practitioners to model the relationship between the variable of interest and a set of explanatory variables. The assumption that all error variances are the same, known as homoskedasticity, is oftentimes violated when cross sectional data are used. Consistent standard errors for the ordinary least squares estimators of the regression parameters can be computed following the approach proposed by White (Econometrica 48:817–838, 1980). Such standard errors, however, are considerably biased in samples of typical sizes. An improved covariance matrix estimator was proposed by Qian and Wang (J Stat Comput Simul 70:161–174, 2001). In this paper, we improve upon the Qian–Wang estimator by defining a sequence of bias-adjusted estimators with increasing accuracy. The numerical results show that the Qian–Wang estimator is typically much less biased than the estimator proposed by Halbert White and that our correction to the former can be quite effective in small samples. Finally, we show that the Qian–Wang estimator can be generalized into a broad class of heteroskedasticity-consistent covariance matrix estimators, and our results can be easily extended to such a class of estimators.     

Hubbing and routing in postal delivery systems

We consider the combined hubbing and routing problem in postal delivery systems and develop an iterative two-stage solution procedure for the problem. In the first stage, hub locations are determined and postal offices are multiply allocated to the hubs. The second stage gives the routes in hub regions that alter the distances between points used in the hub-location problem. The procedure then iterates between two stages by updating the distances used in hubbing in order to produce a route-compatible hub configuration. Computational experience is reported for the test problems taken from the literature. For a case study Turkish postal delivery system data are utilized. As the case study is applied on a road network, a final stage, seeking improvements based on special structures in the routed network, is appended to the two-stage solution procedure.     

Equity portfolio construction and selection using multiobjective mathematical programming

A multi-objective mixed integer programming model for equity portfolio construction and selection is developed in this study, in order to generate the Pareto optimal portfolios, using a novel version of the well known ε-constraint method. Subsequently, an interactive filtering process is also proposed to assist the decision maker in making his/her final choice among the Pareto solutions. The proposed methodology is tested through an application in the Athens Stock Exchange.     

To the theory of operator monotone and operator convex functions

We prove that a real function is operator monotone (operator convex) if the corresponding monotonicity (convexity) inequalities are valid for some normal state on the algebra of all bounded operators in an infinite-dimensional Hilbert space. We describe the class of convex operator functions with respect to a given von Neumann algebra in dependence of types of direct summands in this algebra. We prove that if a function from ℝ⁺ into ℝ⁺ is monotone with respect to a von Neumann algebra, then it is also operator monotone in the sense of the natural order on the set of positive self-adjoint operators affiliated with this algebra.     

Möbius and triangle semigroups

The purpose of this paper is to describe the structures of the Möbius semigroup induced by the Möbius transformation group (?, SL(2,?)). In particular, we study stabilizer subsemigoups of Möbius semigroup via the triangle semigroup. In this work, we obtained a geometric interpretation of the least contraction coefficient function of the Möbius semigroup via the triangle semigroup and investigated an extension of stabilizer subsemigoups of the Möbius semigroup. Finally, we obtained a factorization of our stabilizer subsemigoups of the Möbius semigroup.