Constructing C3 shape preserving interpolating space curves

We present a method for constructing shape-preserving C ³ interpolants in R ³. The resulting curve is obtained by adding a polynomial perturbation of high degree to a curve which is shape-preserving but not sufficiently smooth. The degree of the perturbed curve is selected in order to maintain the shape properties of the basic curve.     

连续波锁模Pr3+:YLF激光器

本文报导了采用氩离子激光器来泵浦Pr³⁺:YLF晶体,应用声光调制器实现了主动锁模;同时应用振动─高反射平面镜也实现了被动锁模,两种锁模均得到了ps光脉冲.据作者了解这是这种晶体材料的第一次锁模运转.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

On the hyperspace of a non-separable metric space

We prove the following two results. 1) There exists a non-separable complete metric space whose Wijsman hypertopology is not Cech-complete. 2) There exist a non-separable metrizable space and two compatible metrics on it, such that the collections of the Borel sets generated by the relative Wijsman hypertopologies do not coincide.

     

Hydrodynamic limits for the Boltzmann process

We study the behavior of the nonlinear Markov process associated to the Boltzmann equation under both hyperbolic and parabolic space-time scalings. In the first case the limit of the process is the solution of an o.d.e. with vector field given by a solution of the Euler equation, while in the second case the limit of the process, in the incompressible case, turns out to be a diffusion process whose drift is a solution of the incompressible Navier-Stokes equation.     

Light Electrospun Polyvinylpyrrolidone Blanket for Low Frequencies Sound Absorption

Light polymeric soundproofing materials(density = 63 kg/m~3) of interest for the transportation industry were fabricated through electrospinning. Blankets of electrospun polyvinylpyrrolidone(average fiber diameter =(1.6 ± 0.5) or(2.8 ± 0.5) μm) were obtained by stacking disks of electrospun mats. The sound absorption coefficients were measured using the impedance tube instrument based on ASTM E1050 and ISO 10534-2. For a given set of disks(from a minimum of 6) the sound absorption coefficient changed with the frequency(in the range 200–1600 Hz) following a bell shape curve with a maximum(where the coefficient is greater than 0.9) that shifts to lower frequencies at higher piled disks number and greater fiber diameter. This work showed that electrospinning produced sound absorbers with reduced thickness(2–3 cm) and excellent sound-absorption properties in the low and medium frequency range.     

Polarization-multiplexed x((2)) solitary-wave interactions

We investigate interactions between vectorial solitary waves through typeII second-harmonic generation. We demonstrate that one can tune the collision distance of two initially codirectional solitary waves changing their polarization state. Moreover, by adiabatic perturbation analysis, it is possible to predict such a collision distance as a function of solitary-wave separation, in good agreement with numerical simulations.