Refinements of the results on partitions and overpartitions with bounded part differences

Recently, partitions with fixed or bounded differences between largest and smallest parts have attracted a lot of attention. In this paper, we first give a simple combinatorial proof of Breuer and Kronholm’s identity. Inspired by it, we construct a useful bijection to produce refinements of the results for partitions and overpartitions with bounded differences between largest and smallest parts. Consequently, we obtain Chern’s curious identity in a combinatorial manner.     

Objectifying the adjacent and opposite angles: a cultural historical analysis

The angle topic is central to the development of geometric knowledge. Two of the basic concepts associated with this topic are the adjacent and opposite angles. It is the goal of the present study to analyze, based on the cultural historical semiotics framework, how high-achieving seventh grade students objectify the adjacent and opposite angles’ concepts. We videoed the learning of a group of three high-achieving students who used technology, specifically GeoGebra, to explore geometric relations related to the adjacent and opposite angles’ concepts. To analyze students’ objectification of these concepts, we used the categories of objectification of knowledge (attention and awareness) and the categories of generalization (factual, contextual and symbolic), developed by Radford. The research results indicate that teacher's and students’ verbal and visual signs, together with the software dynamic tools, mediated the students’ objectification of the adjacent and opposite angles’ concepts. Specifically, eye and gestures perceiving were part of the semiosis cycles in which the participating students were engaged and which related to the mathematical signs that signified the adjacent and the opposite angles. Moreover, the teacher's suggestions/requests/questions included/suggested semiotic signs/tools, including verbal signs that helped the students pay attention, be aware of and objectify the adjacent and opposite angles’ concepts.     

Teichmüller curves in the space of two-genus double covers of flat tori

This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed.     

A new high accuracy finite difference discretization for the solution of 2D nonlinear biharmonic equations using coupled approach

In this article, using coupled approach, we discuss fourth order finite difference approximation for the solution of two dimensional nonlinear biharmonic partial differential equations on a 9‐point compact stencil. The solutions of unknown variable and its Laplacian are obtained at each internal grid points. This discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions. We require only system of two equations to obtain the solution and its Laplacian. The proposed fourth order method is used to solve a set of test problems and produce high accuracy numerical solutions. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Using power level difference for near field dual-microphone speech enhancement

In this contribution, a novel dual-channel speech enhancement technique is introduced. The proposed approach uses the dissimilarity between the power of received signals in the two channels as a criterion for speech enhancement and noise reduction. We claim that in near field conditions, where the distances between microphones and sound source are short, the difference in the received power levels at the two microphones is an estimate of the clean speech signal power. Then, apply this theory to present an optimum method for speech enhancement. Fortunately, the method has the ability to cope with problems such as transient noise and nearby microphones which are two of the main problems of the proposed dual-microphone speech enhancement techniques. Using objective speech quality measures and spectrogram analysis, we show that the proposed method results in improved speech quality.     

Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Critical Line between Ferroelectric and Disordered Phases

This is a continuation of the papers of Bleher and Fokin (Commun. Math. Phys., 268:223–284, 2006) and of Bleher and Liechty (Commun. Math. Phys., 286:777–801, 2009), in which the large n asymptotics is obtained for the partition function Z _n of the six-vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, respectively. In the present paper we obtain the large n asymptotics of Z _n on the critical line between these two phases. The first author is supported in part by the National Science Foundation (NSF) Grant DMS-0652005.     

一种性能稳定的新单元频率选择表面

通过对十字孔径单元的四个端点添加L形的孔径,给出了一种新单元的频率选择表面(FSS)设计,同时通过拆分,得到了相对应的拆分单元FSS.利用谱域法,对两种FSS结构从理论上进行了分析,在TE波入射时角度变化、大角度入射时极化变化对中心频率的影响以及通带带宽三个方面进行了研究,并采用镀膜和光刻技术制备了两种FSS结构的实验样件,在微波暗室中进行测试,得到的实验曲线与理论仿真曲线基本一致.结果表明：新单元的两种FSS结构的中心频率均能在TE波入射时实现角度稳定性和大角度入射时实现极化稳定性;拆分单元FSS的中心 关键词： 频率选择表面(FSS) 新单元 极化稳定性 角度稳定性     

Fluorescence Origin of 6,P-toluidinyl-naphthalene-2-sulfonate (TNS) Bound to Proteins

6,P-toluidinylnaphthalene-2-sulfonate (TNS) is a highly fluorescent molecule when dissolved in a low polarity medium or when bound to proteins. The aim of the present work is to explain origin of this fluorescence, to find out how the medium (solvent, protein matrix) affects fluorescence observables such as lifetimes and spectra and finally to put into evidence possible relation that exists between these observables and fluorophore structure. To achieve our goal we performed studies on TNS dissolved in ethanol, at high concentrations in water (aggregated form) and bound to proteins. Our experiments allowed us to find out that TNS in the three environments has different structures. Presence of three lifetimes observed in proteins and in water instead of one lifetime found in ethanol can be assigned to the high contact between TNS molecules. Our results are discussed in terms of solvent polarity and interaction within fluorophore molecules bound to proteins.     

Self-spectral calibration of a compound zero-order waveplate at blind rotation angles

A blind-angle calibration method is introduced for self-spectral calibration of a compound zero-order waveplate. By rotating the waveplate at blind detection angles, the wavelength-dependent retardance and the orientation of the effective fast axis can be determined through iterative least-squares calculations of the spectra measured by a multi-channel spectrometer. Excellent agreement between the experimental values and the theoretical values is achieved, indicating that the new method can be used as a reliable way to calibrate compound zero-order wave plates. Using the new method, there is no need to rotate the waveplate at specific detection angles. A high-precision waveplate holder or complex adjustment procedure is not required.     

单模辐射场作用下两二能级原子的Wigner-Yanse偏振信息

研究了与单模辐射场作用过程中两二能级原子的Wigner-Yanse信息.结果表明：两原子总Wigner-Yanse偏振信息依赖于处于基态|gg>, 第一激发态(|ge>+|eg>)/2^(1/2)和第二激发态|ee>的概率. 由于光场的作用, 总Wigner-Yanse偏振信息呈现出周期性的丢失与恢复现象, 但原子间的偶极-偶极相互作用对Wigner-Yanse信息的丢失有阻抗作用.