The Integral Mean of the Discrepancy of the Sequence (nα)

 For a real number x let be the fractional part of x and for any set M let c _M be the characteristic function of M. For and a positive integer N let

Calculation of Improper Integrals Using (nα)-Sequences

 We give a necessary and sufficient condition for the relation to hold as . Here α is an irrational number, denotes the fractional part of x and f is from a suitable class of functions with the property that or for a finite set of rational . Received 11 January 2001; in revised form 10 August 2001     

A decomposition theorem for neutrices

Neutrices are convex additive subgroups of the nonstandard space R^k, most of them are external sets. Because of the convexity and the invariance under some translations and multiplications, external neutrices are models for orders of magnitude. One dimensional neutrices have been applied to asymptotics, singular perturbations, and statistics. This paper shows that in R^k, with standard k, every neutrix is the direct sum of k neutrices of R. These components may be chosen to be orthogonal.     

Highway games on weakly cyclic graphs

A highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices, a cost function on the edges of the graph and a set of players, each in need of constructing a connection between a specific entry and exit vertex. Mosquera (2007) introduce highway problems and the corresponding cooperative cost games called highway games to address the problem of fair allocation of the construction costs in case the underlying graph is a tree. In this paper, we study the concavity and the balancedness of highway games on weakly cyclic graphs. A graph G is called highway-game concave if for each highway problem in which G is the underlying graph the corresponding highway game is concave. We show that a graph is highway-game concave if and only if it is weakly triangular. Moreover, we prove that highway games on weakly cyclic graphs are balanced.     

Evaluation of German parties and coalitions by methods of the mathematical theory of democracy

The paper continues author’s studies on applications of the mathematical theory of democracy. Five German leading parties and their coalitions are evaluated with indices of popularity and universality to show how well they represent the electorate. The evaluation goes beyond the information on election results and uses an operational representation of party manifestos.     

Bulk Heterojunction Solar Cells with Ternary Mixed PTB7:PCDTBT:PC71BM Active Layers

We report on bulk-heterojunction solar cells fabricated based on ternary mixed solutions of two donors of poly[[4,8-bis[(2-ethylhexyl)oxy]benzo [1,2-b:4,5-b’] dithiophene-2, 6-diyl] [3-fluoro-2- [(2-ethylhexyl) carbonyl]thieno[3,4-b]-thiophenediyl] (PTB7) and [N-9’-heptadecanyl-2,7-carbazole-alt-5,5-(4’,7’-di-2-thienyl-2’,1’,3’-benzothiadiazole)] (PCDTBT), and an accepter of [6,6]-phenyl C₇₁ butyric acid methyl ester (PC₇₁BM). The solar cells had a glass/ITO/NiO/PTB7:PCDTBT:PC₇₁BM/LiF/Al structure. Solar cells containing a 1-2% PCDTBT weight fraction showed a noticeable improvement in short circuit current density (J_sc), fill factor (FF), and power conversion efficiency (PCE). Solar cells with a 2% PCDTBT weight fraction exhibited an open circuit voltage (V_oc) of 0.77 V, J_sc of 13 mA/cm², FF of 0.42, and PCE of 4.23%. Possible mechanisms for the solar cell performance improvement by the introduction of the small amount of PCDTBT in the PTB7:PC₇₁BM active layer was discussed based on the active layer morphology changes and carrier transport mechanisms.     

Optical nonlinearity of CdS

The discovery and investigation of optically nonlinear behavior of CdS is reviewed. The development is described from nonlinear anti-Stokes excitation via the characterization of inelastic light scattering processes and the identification of high-density phenomena like biexciton creation, excitonic collisions, and electron-hole plasma generation towards very recent time-resolved gain, light-induced grating, and in particular optical bistability experiments. CdS is thus shown to allow for an extremely wide variety of different optically nonlinear processes and may be regarded as a model material for this field. Possible applications show up for several of the described phenomena.     

On 1-convexity and nucleolus of co-insurance games

The insurance situation in which an enormous risk is insured by a number of insurance companies is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we present certain conditions on the parameters of the model that guarantee the 1-convexity property of co-insurance games which in turn ensures the nonemptiness of the core and the linearity of the nucleolus as a function of the variable premium. Further we reveal conditions when a co-insurance game is representable in the form of a veto-removed game and present an efficient final algorithm for computing the nucleolus of a veto-removed game.     

On Banach spaces whose norm-open sets are -sets in the weak topology

We investigate non-separable Banach spaces whose norm-open sets are countable unions of sets closed in the weak topology and a narrower class of Banach spaces with a network for the norm topology which is σ-discrete in the weak topology. In particular, we answer a question of Arhangel'skii exhibiting various examples of non-separable function spaces C(K) with a σ-discrete network for the pointwise topology and (consistently) we answer some questions of Edgar and Oncina concerning Borel structures and Kadec renormings in Banach spaces.