Spectral analysis for the Gauss problem on continued fractions

We present a new derivation of the formula appearing in Babenko (1978) and Mayer and Roepstorff (1987) that gives the probability distribution of τ⁻ⁿ${\tau }^{-n}$ in terms of the eigenvalues of a symmetric operator. Here τ$\tau$ is the well-known Gauss-map.     

Solving Ck/Cm/1/N queues by using characteristic roots in matrix analytic methods

In this paper, we study a C_k/C_m/1/N open queueing system with finite capacity. We investigate the property which shows that a product of the Laplace Stieltjes Transforms of interarrival and service times distributions satisfies an equation of a simple form. According to this equation, we present that the stationary probabilities on the unboundary states can be written as a linear combination of vector product-forms. Each component of these products is expressed in terms of roots of an associated characteristic polynomial. As a result, we carry out an algorithm for solving stationary probabilities in C_k/C_m/1/N systems, which is independent of N, hence greatly reducing the computational complexity.     

窗口Fourier变换反演公式的级数表示——献给陆善镇教授75华诞

本文研究连续窗口Fourier变换的反演公式.与经典的积分重构公式不同,本文证明当窗函数满足合适的条件时,窗口Fourier变换的反演公式可以表示为一个离散级数.此外,本文还研究这一重构级数的逐点收敛及其在Lebesgue空间的收敛性.对于L^2空间,本文给出重构级数收敛的充分必要条件.     

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.     

The asymmetrical fractional Fourier transforms and its optical implement

Compared with the symmetrical lens system, the structure which contains double cylindrical lenses is also the basic units of a complex system and implement practical asymmetrical fractional Fourier transforms. Based on the theory of scalar diffraction and on the Fourier optics, we implement several kinds of asymmetrical fractional Fourier transforms and make the different mathematical manipulation at the corresponding coordinates, while the symmetrical system cannot. Meanwhile, the simulation experiment shows that such system not only makes the two perpendicular coordinates to be independently operated, but also increases the flexibility of the optical setup. All these characteristics make it flexible to application domain in optics.     

On axisymmetrical problem of layer with temperature dependent properties

The paper deals with the axisymmetrical problem of thermoelastic layer with mechanical properties dependent on temperature. The boundary planes of the body are kept at constant but different temperatures. Moreover, the layer is assumed to be ideal fixed to a rigid foundation. The upper boundary plane is loaded by normal forces dependent on the radius. The considered stationary problem is solved according with the following scheme: (1⁰) firstly the distribution of temperature is found, (2⁰) secondly, assuming that the Young modulus is a power function of temperature and Poisson ratio is constant, the displacements and stress are calculated from adequate boundary value problem. The obtained results in the form of Hankel integrals are analysed numerically for the case of linear dependence of Young modulus on the temperature.     

Uniqueness of Gaussian quadrature formula for computed tomography

This note answers positively a question raised by B. Bojanov and G. Petrova. Namely, the Gaussian quadrature formula for computed tomography among the given type is unique.     

两种D III型有界对称域的逆ABEL变换

利用bc     

On the Duals of Segre Varieties

The reflexivity, the (semi-)ordinariness, the dimension of dual varieties and the structure of Gauss maps are discussed for Segre varieties, where a Segre variety is the image of the product of two or more projective spaces under Segre embedding. A generalization is given to a theorem of A. Hefez and A. Thorup on Segre varieties of two projective spaces. In particular, a new proof is given to a theorem of F. Knop, G. Menzel, I. M. Gelfand, M.M. Kapranov and A. V. Zelevinsky that states a necessary and sufficient condition for Segre varieties to have codimension one duals. On the other hand, a negative answer is given to a problem raised by S. Kleiman and R. Piene as follows: For a projective variety of dimension at least two, do the Gauss map and the natural projection from the conormal variety to the dual variety have the same inseparable degree?