On the positive nonoscillatory solutions of the difference equation Xn＋1=α＋（xn-k/xn-m）^p

The aim of this paper is to show that the following difference equation：Xn＋1=α＋（xn-k/xn-m）^p, n=0,1,2,…,
where α 〉 -1, p 〉 O, k,m ∈ N are fixed, 0 ≤ m 〈 k, x-k, x-k＋1,…,x-m,…,X-1, x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α＋1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.     

On the permanent of random Bernoulli matrices

We show that the permanent of an n×n matrix with iid Bernoulli entries ±1 is of magnitude with probability 1−o(1). In particular, it is almost surely non-zero.     

Network evolution model: thermodynamics consistency,parameter identification and finite element implementation

In this contribution, the previously proposed network evolution model [1] for carbon black filled elastomers is further studied. First, we show that the model does not contradict the second law of thermodynamics and is thus thermodynamically consistent. On the basis of new experimental data the influence of filler concentration on the material parameters is further examined. Accordingly, this influence concerns only three material parameters and is approximated by phenomenological relations. These relations enable one to simulate rubbers based on the same compound with various filler concentrations. Finally, the model is implemented into the FE-Software ABAQUS and illustrated by a number of numerical examples. The examples demonstrate good agreement with experimental results with respect to the Mullins-Effect, permanent set and induced anisotropy. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

High-efficiency single and tandem fullerene solar cells with asymmetric monofluorinated diketopyrrolopyrrole-based polymer

Design and synthesis of low bandgap(LBG) polymer donors is inevitably challenging and their processability from a non-halogenated solvent system remains a hurdle to overcome in the area of highperformance polymer solar cells(PSCs).Due to a high aggregation tendency of LBG polymers,especially diketopyrrolopyrrole(DPP)-based polymers coupled with bithiophenes in the polymer backbones,their widespread adoption in non-ha logena ted solvent-processed PSCs has been limited.Herein,a novel LBG DPP-based...     

Hyers–Ulam stability for boundary value problem of fractional differential equations with κ-Caputo fractional derivative

The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) via the concept of Caputo fractional derivative with respect to another function with the order $\alpha \in (\mathrm{1,2})$. The existence and uniqueness results of a solution for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. We also provide new sufficient conditions to guarantee the Hyers-Ulam stability and the Hyers–Ulam–Rassias stability of BVP-FDEs. Furthermore, some concrete examples to consolidate the obtained results are also considered.     

Physical Interpretation of Mixed Ionic-electronic Conductive Polymer-coated Electrodes by a Simple Universal Impedance Model

A simple equivalent electrical circuit is used to obtain the physical parameters of electrical circuit elements from measured electrochemical impedance spectra. This model consists of four circuit elements with a clear physical meaning for each of the elements. Compared to complex models with multiple constant phase elements or Warburg impedances, our model is suitable for extracting physical values for important electrode parameters with low errors. The feasibility of the model was shown by investigating pure metal or polymer-coated electrodes. Here, gold electrodes were coated either with Poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT : PSS), Polypyrrole:poly(styrenesulfonate) (PPy : PSS), or (PEDOT/PPy) : PSS by means of electropolymerization. The model could demonstrate the ionic-electronic differences such as the ion accessibility of the differently coated electrodes. To prove the correctness of the model, the obtained results were compared to the literature.     

Regularity of powers of Stanley–Reisner ideals of one-dimensional simplicial complexes

Let Δ be a one-dimensional simplicial complex. Let $I_{\mathrm{\Delta }}$ be the Stanley–Reisner ideal of Δ. We prove that for all $s\ge 1$ and all intermediate ideals J generated by $I_{\mathrm{\Delta }}^s$ and some minimal generators of $I_{\mathrm{\Delta }}^{(s)}$, we have $$regJ=reg{I}_{\mathrm{\Delta }}^s=reg{I}_{\mathrm{\Delta }}^{(s)}.$$