Invariance of stationary probabilities of states for network of multiserver queues

A queueing network consisting of multiserver nodes with different sources of customers is considered. We investigate stationary probability distributions of network states. Their invariance with respect to the functional form of distributions of input and service processes is established under fixed expectations of these distributions and service discipline when any entering customer has a preemptive resume discipline.     

｜x｜^α的Lagrange插值多项式在零点的收敛速度

S.M.Lozinskii指出了函数｜x｜基于等距节点的Lagrange插值多项式在零点的收敛速度.2000年,M.Revers把S.M.Lozinskii的结果推广到｜x｜~α(0<α1).本文考虑的是把等距节点改为修改的Chebyshev节点,从而把零点处的收敛速度从M.Revers证明的O(n-α)提高O(n-2α).     

On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes.     

基于切比雪夫节点的一类带显式系数的广义高斯求积公式(英文)

The goal here is to give a simple approach to a quadrature formula based on the divided diffierences of the integrand at the zeros of the nth Chebyshev polynomial of the first kind,and those of the（n-1）st Chebyshev polynomial of the second kind.Explicit expressions for the corresponding coefficients of the quadrature rule are also found after expansions of the divided diffierences,which was proposed in[14].     

Parameterizing the global attractor of the navier-stokes equations by nodal values

In this paper we give an affirmative answer to the conjecture of Foias and Tern am that the elements of the global attractor of the two dimensional Navier Stokes equations are uniquely determined by their nodal values at a finite number of points in the underlying physical domain. This is kind of a sampling theorem for the elements of the the global attractor of the Navier Stokes equations.     

Controllable Synthesis of Porphyrin‐Based 2D Lanthanide Metal–Organic Frameworks with Thickness‐ and Metal‐Node‐Dependent Photocatalytic Performance

Synthesizing 2D metal–organic frameworks (2D MOFs) in high yields and rational tailoring of the properties in a predictable manner for specific applications is extremely challenging. Now, a series of porphyrin‐based 2D lanthanide MOFs (Ln‐TCPP, Ln=Ce, Sm, Eu, Tb, Yb, TCPP=tetrakis(4‐carboxyphenyl) porphyrin) with different thickness were successfully prepared in a household microwave oven. The as‐prepared 2D Ln‐TCPP nanosheets showed thickness‐dependent photocatalytic performances towards photooxidation of 1,5‐dihydroxynaphthalene (1,5‐DHN) to synthesize juglone. Particularly, the Yb‐TCPP displayed outstanding photodynamic activity to generate O₂^? and ¹O₂. This work not only provides fundamental insights into structure designing and property tailoring of 2D MOFs nanosheets, but also pave a new way to improve the photocatalytic performance.     

A New Layer W/Cu/S Polymer with Heterobimetallic Nodes and Tridentate Trithiocyanuric Acid

Solvothermal reaction of [WS4]2-with CuCN and trithiocyanuric acid(L1) in orga-nic solvents gave rise to a new W/Cu/S polymer with a 2D anionic network,namely [Et4N]2[WS4Cu3(C3N3S3H1.5)2](1).The anionic layer of 1 is constructed by the T-shaped {WS4Cu3} subunits as nodes and L1 as linkers and features a(4,4) topology.Both 1 and its isomorphous compound [Et4N]2[MoS4Cu3(C3N3S3H1.5)2](2) have been fully characterized by X-ray crystal analysis,IR and microanalyses.Compounds 1 and 2 show optical transitions with band gaps of 2.17 and 1.84 eV,respectively.     

A Generalization of the Hilbert Basis Theorem

A generalization of the Hilbert basis theorem in the geometric setting is proposed. It asserts that, for any well-describable (in a certain sense) family of polynomials, there exists a number C such that if P is an everywhere dense (in a certain sense) subfamily of this family, a is an arbitrary point, and the first C polynomials in any sequence from P vanish at the point a, then all polynomials from P vanish at a.     

New Semiclassical and Numerical Approaches to Locate Zeros of Wave Functions Asiri Nanayakkara

A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficients of this polynomial are evaluated using WKB and semi quantum action variable methods. For certain potentials WKB expressions for moments are obtained exactly. Almost explicit formulae for moments are obtained for the potential V (x) = xN. Examples are given to illustrate both methods. Using semi quantum action variable method, complex zeros of the wave functions of the PT symmetric complex system V(x) = x4 iAx are obtained. These zeros exhibit complex version of interlacing.     

Inhalation MR lymphography: A new method for selective enhancement of the lung hilar and mediastinal lymph nodes

On MR lymphography, a new approach to the lung hilar and mediastinal nodes was developed in an animal model. Five rabbits were made to inhale iron colloid (cideferron) that was nebulized to aerosol. Two days after inhalation of the agent, the mediastinal lymph nodes decreased in signal on SE 2000/30 and SE 2000/60 images and proved to have iron on histological evaluation, whereas the popliteal nodes did not have any iron. Experimental results indicate that inhalational administration can deliver the agent to the pulmonary lymphatic system and has the potential of lung hilar and mediastinal MR lymphography.