A Novel Fiber Taper for Efficient Optical Interconnection

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｅｒｃｏｎｎｅｃｔｉｏｎｓｏｆｏｐｔｉｃａｌｗａｖｅｇｕｉｄｅｃｏｍｐｏｎｅｎｔｓｗｉｔｈｄｉｆｅｒｅｎｔｍｏｄａｌｓｐｏｔｓｉｚｅｓ，ｐａｒｔｉｃｕｌａｒｌｙｆｏｒｔｈｅｃｏｎｎｅｃｔｉｏｎｏｆ（１）ｌａｓｅｒｓｏｕ...     

最佳的潜艇搜索模型

对直线式逃跑的潜艇被捕获的必然性进行了证明,并为驱逐舰给出了一个最佳的搜索模型.     

树的Nordhaus-Gaddum类型谱半径的排序

给出了n阶树的Nordhaus-Gaddum类型谱半径即图及其补图的谱半径之和的可达上界:ρ(T) ρ(Tc)≤■ n-2,等号成立当且仅当T K1,n-1,其中Tc为T的补图,K1,n-1为n阶星图.同时证明了对于n阶双星图S(a,b)的Nordhaus-Gaddum类型谱半径随a的值单调上升,其中[n-1/2]≤a≤n-3.     

Effects of Density-Dependent Bag Constant and Strange Star Rotation

With the emphasis on the effects of the density-dependent bag constant and the rotation of strange star the limiting mass of strange star is calculated. The obtained results show that the limiting mass and the corresponding radius of strange star increase as the rotation frequency increases, and tend to be lowered when the density-dependent bag constant is considered.     

电子束参量对轫致辐射照射量角分布的影响

本文研究了电子束半径,发射度及能量等参量对闪光X射线照射量在1m处角分布的影响。求得了使中心照射量最大,束半径与发射度之间应满足的拟合关系,表明了电子束能量越高,发射度越小,那么中心照射量就越大,照射量的空间分布就越理想。对电子细束入射位置和入射方向使用了解析法和随机抽样法求出,两种方法的数值计算所得的照射量分布符合得比较好。     

Maximum principle for functional equations in the space of discontinuous functions of three variables

The paper is devoted to the maximum principles for functional equations in the space of measurable essentially bounded functions. The necessary and sufficient conditions for validity of corresponding maximum principles are obtained in a form of theorems about functional inequalities similar to the classical theorems about differential inequalities of the Vallee Poussin type. Assertions about the strong maximum principle are proposed. All results are also true for difference equations, which can be considered as a particular case of functional equations. The problems of validity of the maximum principles are reduced to nonoscillation properties and disconjugacy of functional equations. Note that zeros and nonoscillation of a solution in a space of discontinuous functions are defined in this paper. It is demonstrated that nonoscillation properties of functional equations are connected with the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Simple sufficient conditions of nonoscillation, disconjugacy and validity of the maximum principles are proposed. The known nonoscillation results for equation in space of functions of one variable follow as a particular cases of these assertions. It should be noted that corresponding coefficient tests obtained on this basis cannot be improved. Various applications to nonoscillation, disconjugacy and the maximum principles for partial differential equations are proposed.     

实四元数矩阵的数值半径

本文定义了实四元数矩阵的数值半径,并讨论了它与矩阵迹、谱范数的关系,得到了一些等式与不等式.     

Structural changes in β-lactoglobulin by conjugation with three different kinds of carboxymethyl cyclodextrins

β-Lactoglobulin-carboxymethyl cyclodextrin (β-LG-CMCyD) conjugates were prepared by using water soluble carbodiimide. Three kinds of CMCyDs differing in molecular mass were used to investigate the effects of different CMCyD contents, net charge and hydrophobicity on the structural changes in β-lactoglobulin. The effect of CMCyDs on the structure of β-lactoglobulin was utilized to investigate the contribution of hydrophobic interactions to the stability of the protein. Spectroscopic studies suggested that the conformation around had not changed in either conjugate but the α-helix content of β-LG-CMCyD conjugates had markedly increased as compared with that of β-lactoglobulin. The differential scanning calorimetry technique confirmed that the addition of one glucose unit in β-LG-CMCyD conjugates, enthalpy change of calorimetry decreased and the denaturation temperature of each conjugate was higher than that of native β-lactoglobulin. The heat contents agreed well with the conformational transition measured by molar ellipticity at 222 nm ([θ]₂₂₂) and Stoke's radius (R_S) values. Therefore, hydrophobic forces play an important role in stabilizing and shielding of the β-LG-CMCyD conjugates.     

Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets

Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed.     

The numerical range of a nonnegative matrix

We offer an almost self-contained development of Perron–Frobenius type results for the numerical range of an (irreducible) nonnegative matrix, rederiving and completing the previous work of Issos, Nylen and Tam, and Tam and Yang on this topic. We solve the open problem of characterizing nonnegative matrices whose numerical ranges are regular convex polygons with center at the origin. Some related results are obtained and some open problems are also posed.