Super-edge-graceful Labelings of Some Cubic Graphs

The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994.However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-graceful. A conjecture is proposed.     

Bare-State Time-Evolving Operator Solution to Raman Model in A Configuration

We derive exact analytical expressions of time-evolving bare-state operators of level occupation numbers and the photon numbers for a composite system consisting of a three-level atom interacting with two modes of a quantized electromagnetic field in A configuration. These results demonstrate the oscillations with three-family frequencies for a nonzero detuning, which dramatically differ from the previous results showing only single-family Rabi oscillations.     

具有梯形结构钴(Ⅱ)配位聚合物的合成及晶体结构

Co(NO₃)₂, N-carbazolyacetic acid and 4,4′-bipyridyl can give rise to a novel coordination polymer [CO₂(Cabo)₂(NO₃)₂(4,4′-bipy)₂]_n using a fritted U-tube. Single crystal X-ray diffraction displays in the complex, each Co(Ⅱ) is six-coordinated by two N atoms from different 4,4′-bipyridyl ligands, two O atoms of the bridge from two N-carbazolyacetic acid and two O atoms of one nitrate anion to form a distorted octahedral. Two O atoms of the carboxyl group act as bridge to link two Co(Ⅱ) atoms. The resulting structure is a ladder polymer. CCDC: 211713.     

Dye-free protein molecular weight markers

Protein molecular weight markers are widely used in sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and Western blotting. Here, we describe novel protein molecular weight markers in which a prestaining procedure is no longer needed. Green fluorescent protein (GFP) is stable and resistant to denaturing agents/conditions. Various histidine-tagged GFP fusion proteins were overexpressed in Escherichia coli and purified by metal affinity chromatography. The minimal amount of each protein marker needed for analysis in SDS-PAGE and Western blot under visible light was 62.5 and 125 ng, respectively. Under ultraviolet (UV) ray, the minimal amount of each protein marker needed for analysis in SDS-PAGE and Western blot was half of those amounts used under visible light, respectively. Collectively, the accuracy, sensitivity, ease, economy, and flexibility of our strategy may reinforce the application of GFP in molecular biology.     

Parameter-dependent renewal theorems with applications

Let ₁, ₂, ... be a sequence of i.i.d. random variables with positive mean and finite variance and letr(b), b0, be real numbers tending to 0 asb . Definings _n=₁+...+_n andS _n=S_n(b)=s_n+r(b)n, the stopping time =(b)=inf {n>/1:S_n >b} whereb=b(b) , will be considered with special regard to the excess over the boundaryR _b=s+r(b)–b. It turns out that the limiting distribution ofR _b is the same as in the caser(b)0 for allb. Proving this, Blackwell's renewal theorem and its integral version have to be established first in the above stated situation. Finally, an expansion ofE to vanishing terms asb will be provided and applied to some examples arising in economics.

---

Zusammenfassung Seien ₁, ₂, ... unabhängige identisch verteilte Zufallsgrößen mit positivem Erwartungswert und endlicher Varianz sowier(b), b0, reelle Zahlen mitr(b)0 für b. Sei ferners ₁, s₂, ... der zugehörige Summenprozeß,S _n= S_n(b)=s_n+r(b)n fürn1 und =(b)=inf {n1: S_n>b, wobeib=b(b) fürb . Es wird gezeigt, daß die asymptotische Verteilung des ExzessesR _b=s +r(b) –b mit der im Fallr(·)0 übereinstimmt. Dazu werden sowohl das Blackwellsche Erneuerungstheorem als auch seine Integralversion in der vorher beschriebenen parameterabhängigen Situation geeignet formuliert und bewiesen. Als Folgerung ergibt sich dann eine asymptotische Entwicklung vonE(b) fürb bis zu Termen o(1). Anh- and einiger Beispiele aus dem ökonomischen Bereich wird schließlich noch aufgezeigt, wo Approximationen fürE(b) von Interesse sein können.

     

On the linear dispersion-linear potential quantum oscillator

We solve the bi-linear quantum oscillator H = v|p| + F|x| both quasi-classically and numerically.     

构造阶梯算符的定量及其应用

给出一个基本定理，提供了构造二阶线性常微分算符相应的阶梯算符的普遍适用的方法，利用这个定理得到量子力学中常见的本征问题的解。     

A copula based Bayesian approach for paid–incurred claims models for non-life insurance reserving

Our article considers the class of recently developed stochastic models that combine claims payments and incurred losses information into a coherent reserving methodology. In particular, we develop a family of hierarchical Bayesian paid–incurred claims models, combining the claims reserving models of Hertig (1985) and Gogol (1993). In the process we extend the independent log-normal model of Merz and Wüthrich (2010) by incorporating different dependence structures using a Data-Augmented mixture Copula paid–incurred claims model.In this way the paper makes two main contributions: firstly we develop an extended class of model structures for the paid–incurred chain ladder models where we develop precisely the Bayesian formulation of such models; secondly we explain how to develop advanced Markov chain Monte Carlo sampling algorithms to make inference under these copula dependence PIC models accurately and efficiently, making such models accessible to practitioners to explore their suitability in practice. In this regard the focus of the paper should be considered in two parts, firstly development of Bayesian PIC models for general dependence structures with specialised properties relating to conjugacy and consistency of tail dependence across the development years and accident years and between Payment and incurred loss data are developed. The second main contribution is the development of techniques that allow general audiences to efficiently work with such Bayesian models to make inference. The focus of the paper is not so much to illustrate that the PIC paper is a good class of models for a particular data set, the suitability of such PIC type models is discussed in Merz and Wüthrich (2010) and Happ and Wüthrich (2013). Instead we develop generalised model classes for the PIC family of Bayesian models and in addition provide advanced Monte Carlo methods for inference that practitioners may utilise with confidence in their efficiency and validity.     

微波场作用下三能级原子系统的无反转光放大

研究了外加微波场作用下三能级原子系统的无粒子数反转放大特性. 通过求解系统的密度矩阵方程得到其探测吸收谱. 结果表明, 介质对探测场的吸收呈现多峰结构, 并且在强微波驱动场的作用下, 特定范围内出现了明显的负吸收(即光放大). 进一步定量分析各能级粒子数布居随作用场强度的变化, 揭示出该三能级原子系统呈现无粒子数反转光放大的规律. 最后, 采用缀饰态理论对探测吸收特性做出了准确的解释.