The limiting semigroup of the Bernstein iterates: degree of convergence

Summary We study the degree of approximation of the iterated Bernstein operators to the members (T(t)) _{t ≧0}, of their limiting semigroup. This yields a full quantitative version of an earlier convergence result by Karlin and Ziegler.     

Roots of mappings on nonorientable surfaces¶and equations in free groups

Let f:M ₁→M ₂ be a continuous map and c:M ₁→M ₂ a constant map between closed (not necessarily orientable) surfaces. By definition the pair (f,c) has the Wecken property if f can be deformed into a map f' such that the number of coincidence points of (f',c) is the same as the number of essential coincidence classes of (f,c) and, hence, every essential coincidence class consists of exactly one point. When both surfaces are orientable the problem to determine all maps which have the Wecken property was solved in [14]. Let A(f) denote the absolute degree as defined in [6] or [15] and . Here we show that a map f has the Wecken property iff either the Euler characteristic or . In free groups there are solved certain quadratic equations closely related to the root problem. Received: Received: 18 January 2001 / Revised version: 27 November 2001     

Sensitivity analysis in fuzzy linear programming

In this paper we propose a certain interpretation of a partially fuzzy LP-Problem. This LP-is dualized and the corresponding variables of the Dual are analyzed and an economic interpretation is given.     

On finding compromise solutions in multicriteria problems using the fuzzy min-operator

This paper presents an application of fuzzy approaches to the linear vectormaximum problem. It shows that using the fuzzy min-operator together with linear as well as special nonlinear membership functions the obtained solutions are always compromise solutions of the original multicriteria problem.     

Overcoming Kinetic Limitations of Electron Injection in the Dye Solar Cell via Coadsorption and FRET

A new, extremely simple concept for the use of energy transfer as a means to the enhancement of light absorption and current generation in the dye solar cell (DSC) is presented. This model study is based upon a carboxy‐functionalized 4‐aminonaphthalimide dye (carboxy‐fluorol) as donor, and (NBu₄)₂[Ru(dcbpy)₂(NCS)₂] (N719) as acceptor chromophores. A set of three different devices is assembled containing either exclusively carboxy‐fluorol or N719, or a mixture of both. This set of transparent devices is characterized via IV‐measurements under AM1.5G and monochromatic illumination and their light‐harvesting and external quantum efficiencies (LHE and EQE, respectively) are determined as well. It is shown that the device containing only the donor chromophore has a marginal power conversion efficiency, thus indicating that carboxy‐fluorol is a poor sensitizer for the DSC. Cyclovoltametric measurements show that the poor sensitization ability arises from the kinetic inhibition of electron injection into the TiO₂ conduction band. Comparing the spectral properties of the DSCs assembled presently, however, demonstrates that light absorbed by carboxy‐fluorol is almost quantitatively contributing to the photocurrent if N719 is present as an additional sensitizer. In this case, N719 acts as a catalyst for the sensitization of TiO₂ by carboxy‐fluorol in addition to being a photosensitizer. Evaluation of the maximum output power under blue illumination shows that the introduction of an energy‐donor moiety via coadsorption, leads to a significant increase in the monochromatic maximum output power. This result demonstrates that energy transfer between coadsorbed chromophores could be useful for the generation of current in dye‐sensitized solar cells.     

Efficient determination of accurate atomic polarizabilities for polarizeable embedding calculations

We evaluate embedding potentials, obtained via various methods, used for polarizable embedding computations of excitation energies of para‐nitroaniline in water and organic solvents as well as of the green fluorescent protein. We found that isotropic polarizabilities derived from DFTD3 dispersion coefficients correlate well with those obtained via the LoProp method. We show that these polarizabilities in conjunction with appropriately derived point charges are in good agreement with calculations employing static multipole moments up to quadrupoles and anisotropic polarizabilities for both computed systems. The (partial) use of these easily‐accessible parameters drastically reduces the computational effort to obtain accurate embedding potentials especially for proteins. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Enhancing dominant modes in nonstationary time series by means of the symbolic resonance analysis

We present the symbolic resonance analysis (SRA) as a viable method for addressing the problem of enhancing a weakly dominant mode in a mixture of impulse responses obtained from a nonlinear dynamical system. We demonstrate this using results from a numerical simulation with Duffing oscillators in different domains of their parameter space, and by analyzing event-related brain potentials (ERPs) from a language processing experiment in German as a representative application. In this paradigm, the averaged ERPs exhibit an N400 followed by a sentence final negativity. Contemporary sentence processing models predict a late positivity (P600) as well. We show that the SRA is able to unveil the P600 evoked by the critical stimuli as a weakly dominant mode from the covering sentence final negativity.     

Controlling Internal Pore Sizes in Bicontinuous Polymeric Nanospheres

Complex polymeric nanospheres were formed in water from comb‐like amphiphilic block copolymers. Their internal morphology was determined by three‐dimensional cryo‐electron tomographic analysis. Varying the polymer molecular weight (MW) and the hydrophilic block weight content allowed for fine control over the internal structure. Construction of a partial phase diagram allowed us to determine the criteria for the formation of bicontinuous polymer nanosphere (BPN), namely for copolymers with MW of up to 17 kDa and hydrophilic weight fractions of ≤0.25; and varying the organic solvent to water ratio used in their preparation allowed for control over nanosphere diameters from 70 to 460 nm. Significantly, altering the block copolymer hydrophilic–hydrophobic balance enabled control of the internal pore diameter of the BPNs from 10 to 19 nm.