Effects of structure and electronic properties of D-π-A organic dyes on photovoltaic performance of dye-sensitized solar cells

Herein,we examine the performance of dye-sensitized solar cells containing five D-π-A organic dyes designed by systematic modification of π-bridge size and geometric structure.Each dye has a simple push-pull structure with a triarylamino group as an electron donor,bithiophene-4,4-dimethyl-4 H-cyclopenta 1,2-b:5,4-b’]dithiophene(M11),4,4-dimethyl-4 H-cyclopenta[1,2-b:5,4-b’]dithiophenethiophene(M12),thiophene-4,4-dimethyl-4 H-cyclopenta[1,2-b:5,4-b’]dithiophene(M13),4,4-dimethyl-4 H-cyclopenta[1,2-b:5,4-b’]dithiophene-benzene(M14),and 4,4-dimethyl-4 H-cyclopenta[1,2-b:5,4-b’]dithiophene(M15)units asπ-bridges,and cyanoacrylic acid as an electron acceptor/anchor.The extension of theπ-bridge linkage favors wide-range absorption but,because of the concomitant molecular volume increase,hinders the efficient adsorption of dyes on the TiO₂ film surface.Hence,higher loadings are achieved for smaller dye molecules,resulting in(i)a shift of the TiO₂ conduction band edge to more negative values,(ii)a greater photocurrent,and(iii)suppressed charge recombination between the photoanode and the redox couple in the electrolyte.Consequently,under one-sun equivalent illumination(AM 1.5 G,100 mW/cm²),the highest photovoltage,photocurrent,and conversion efficiency(η=7.19%)are observed for M15,which has the smallest molecular volume among M series dyes.     

Biases in the prime number race of function fields

We derive a formula for the density of positive integers satisfying a certain system of inequality, often referred as prime number races, in the case of the polynomial rings over finite fields. This is a function field analog of the work of Feuerverger and Martin, who established such formula in the number field case, building up on the fundamental work of Rubinstein and Sarnak.     

Signature invariants of covering links

We apply the theory of signature invariants of links in rational homology spheres to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, we derive an explicit formula to compute signature invariants of their covering links. Using the formula, we produce fused boundary links that are positive mutants of ribbon links but are not concordant to boundary links. We also show that for any finite collection of patterns, there are homology boundary links that are not concordant to any homology boundary links admitting a pattern in the collection.

     

L2‐signatures,homology localization,and amenable groups

Aimed at geometric applications, we prove the homology cobordism invariance of the L²‐Betti numbers and L²‐signature defects associated to the class of amenable groups lying in Strebel's class D(R), which includes some interesting infinite/finite non‐torsion‐free groups. This result includes the only prior known condition, that Γ is a poly‐torsion‐free abelian group (or a finite p‐group). We define a new commutator series that refines Harvey's torsion‐free derived series of groups, using the localizations of groups and rings of Bousfield, Vogel, and Cohn. The series, called the local derived series, has versions for homology with arbitrary coefficients and satisfies functoriality and an injectivity theorem. We combine these two new tools to give some applications to distinct homology cobordism types within the same simple homotopy type in higher dimensions, to concordance of knots in three manifolds, and to spherical space forms in dimension 3. © 2012 Wiley Periodicals, Inc.     

Bounds to optimal burn‐in and optimal work size

Burn‐in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we consider the problem of determining the optimal burn‐in time and optimal work size maximizing the long‐run average amount of work saved per time unit in the computer applications. Assuming that the underlying lifetime distribution of the computer has an initially decreasing or/and eventually increasing failure rate function, an upper bound for the optimal burn‐in time is derived for each fixed work size and a uniform (with respect to the burn‐in time) upper bound for the optimal work size is also obtained. Furthermore, it is shown that a non‐trivial lower bound for the optimal burn‐in time can be derived if the underlying lifetime distribution has a large initial failure rate. Copyright © 2005 John Wiley & Sons, Ltd.     

An inverse backward problem for degenerate parabolic equations

This work studies the inverse problem of reconstructing an initial value function in the degenerate parabolic equation using the final measurement data. Problems of this type have important applications in the field of financial engineering. Being different from other inverse backward parabolic problems, the mathematical model in our article may be allowed to degenerate at some part of boundaries, which may lead to the corresponding boundary conditions missing. The conditional stability of the solution is obtained using the logarithmic convexity method. A finite difference scheme is constructed to solve the direct problem and the corresponding stability and convergence are proved. The Landweber iteration algorithm is applied to the inverse problem and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown initial value is recovered very well.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1900–1923, 2017     

On generalized shock models for deteriorating systems

Standard assumptions in shock models are that failures of items are related either to the cumulative effect of shocks (cumulative models) or that they are caused by shocks that exceed a certain critical level (extreme shocks models). In this paper, we present useful generalizations of this setting to the case when an item is deteriorating itself, for example, when the boundary for the fatal shock magnitude is decreasing with time. Three stochastic failure models describing different impacts of shocks on items are considered. The cumulative effect of shocks is modeled in a way similar to the proportional hazards model. Explicit formulas for the corresponding survival functions are derived and several simple examples are considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Stochastic modeling of quality of systems operating in a heterogeneous environment

We consider systems that are subject to an external mixed Poisson shock process. Each shock can result in a failure of a system with a given probability and is survived with the complementary probability. Each shock additionally decreases the quality function that describes the performance of a system, thus forming the corresponding stochastic process. Expectations (unconditional and conditional on survival) and relevant variability characteristics for the stochastic quality function are derived. Some monotonicity properties of the conditional quality function are investigated and the future values of this function are derived.     

Deformations of Charged Axially Symmetric Initial Data and the Mass–Angular Momentum–Charge Inequality

We show how to reduce the general formulation of the mass–angular momentum–charge inequality, for axisymmetric initial data of the Einstein–Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass, angular momentum, and charge. This extends previous work by the authors (Cha and Khuri, Ann Henri Poincaré, doi: 10.1007/s00023-014-0332-6, arXiv:1401.3384, 2014), in which the role of charge was omitted. Lastly, we improve upon the hypotheses required for the mass–angular momentum–charge inequality in the maximal case.     

飞机舱音记录器背景声的联合时频分析研究

飞机舱音记录器记录的舱音主要是由话语音、噪声和具有不同物理意义的背景声组成的复杂混合体,用传统的辨听和分析方法难以获取较多的舱音特征参数。本文以一个舱音记录器记录的主告警声为例,针对传统短时傅立叶变换在舱音辨听、分析的不足,将联合时频分析引入到飞机舱音分析中,扩展了舱音分析方法。对比分析结果表明:时频分布及其重排,在时频分辨率、时频凝聚性、交叉项干扰的抑制上各有所长,都适合分析非平稳舱音背景声,从而为飞行事故调查提供一种值得采用的方法。