Laser gain by electron collisional pumping of Ar VII–V XII

Gain coefficients have been calculated for transitions of singlet levels ns–np of orbital n=4 and n=5 in magnesium-like ions with atomic numbers Z=18, 19, 20, 21, 22 and 23. Population inversions for 4p and 5p levels in these ions were also calculated, via electron collisional excitation, for electron temperature range of 93–231 eV and electron density range of 10¹⁶–10¹⁷ cm⁻³. Under these plasma conditions, the maximum gain that occurred for 4s–4p transition was at electron temperature of 231 eV and electron density of 4×10¹⁷ cm⁻³. Scaling of the maximum gain coefficients with atomic number Z and the plasma parameters is also presented.     

A general analytical method for evaluation of the thermodynamic properties of matters using virial coefficients with Morse potential at high temperature

In this paper, we established an analytical formula for the second virial coefficient (SVC) with Morse potential without using any numerical methods, and the obtained formula is applied to the calculation of the speed of sound of some matter at high temperature. This approach is based on the series expansion formula and special functions, which allows the exact evaluations of any thermodynamic properties of matter using the SVC. As an application, the obtained analytical formula is used for evaluation of the SVC with Morse potential for high‐temperature gas and the plasma region of the intermolecular interactions of neutral atom gases of B, Si, Zn, H₂, N₂, O₂, NO, CO, He, Ne, Ar, Kr , and Xe . Based on the obtained formula of SVC, the speed of sound for gases of N₂, Ar , and Zn are also determined analytically. A specific maximum temperature is chosen for every gas to ensure that there are still neutral atoms in the gas, and low temperatures are avoided due to quantum effects. The results are compared with numerical data and another analytical data from the literature. The new analytical solution is shown to be in good agreement with the compared data and is verified to supply proper thermodynamic data.     

The stabilizability of heat equations with time-dependent coefficients

In this paper, we study the stabilizability of heat equations with time-dependent coefficients. The instability of the systems is illustrated by special solutions. The boundary feedback stabilization results are established by the backstepping method where the growth order of the kernel function depends on time.     

Kinetics studies of 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol,and 2,4,4-trimethyl-1-pentanol with chlorine atoms: Photooxidation mechanism of 2,4,4-trimethyl-1-pentanol

The rate constants for the reaction between chlorine atoms and either 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol, or 2,4,4-trimethyl-1-pentanol at 298 K were determined using the relative method with 2-butanol and 1-pentanol as reference compounds. The values obtained for 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol, and 2,4,4-trimethyl-1-pentanol (k × 10¹⁰ cm³ molec⁻¹ s⁻¹) were, respectively, (2.64 ± 0.5), (2.72 ± 0.5), and (2.50 ± 0.4), in agreement with the values of the rate constants reported in bibliography for similar alcohols and the values estimated by structure activity relationship methods. The photooxidation products of 2,4,4-trimethyl-1-pentanol initiated by chlorine atoms were identified (formaldehyde, 2-propanone, 2,2-dimethyl propanal, 4,4,-dimethyl-2-pentanone, and 3,3-dimethylbutanal), and the reaction mechanism was determined.     

Hall coefficient in solution for a simple dynamical model

A model Liouville equation is proposed for a system composed of an ion moving in a solvent fluid. Using this model, explicit results are obtained for the Ohmic conductivityL and the Hall conductivityh. These results are then used to calculate the Hall coefficientR = ehL^–2, which is a measure of the effect of non-Brownian motion, for several charge carriers of interest. Our results are in agreement with earlier findings based on a stochastic model which predictR > 1 for H⁺(aq). Our results also indicate thatR 1 for charge carriers such as Na⁺, Cl^–, and K⁺ which have a mass greater than that of a solvent molecule (here taken as 18 amu).This research was supported in part by grants from the National Science Foundation and by the Research Foundation of the State University of New York.     

具有正负系数的二阶脉冲中立型方程的振动性

考虑一类具有正负系数的多时滞二阶线性脉冲中立型微分方程,证明了该方程解的振动性等价于一类非脉冲中立型方程解的振动性,得到了方程所有解存在的充分条件.     

Algorithms for Computing U(N) Clebsch Gordan Coefficients

If V ^(m) is an irreducible representation space for the unitary group U(N), then the r-fold tensor product space, is in general reducible. Such a reducible representation can be reduced to a direct sum of irreducible representation spaces, albeit with multiplicity. Clebsch–Gordan coefficients are the overlap coefficients between an orthonormal basis in the tensor product space and an orthonormal basis in the direct sum space. Since such coefficients are basis dependent, bases in the U(N) irrep spaces must be chosen. In this paper we use the Gelfand–Zetlin basis, built out of the chain of subgroups U(N)⊃...⊃U(1). Our first result is to derive algorithms for generating Gelfand–Zetlin bases from Gelfand–Zetlin tableaux. Given these concrete basis realizations we develop algorithms for computing the Clebsch–Gordan coefficients themselves.      

Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

^** Email: todor{at}math.ethz.ch^*** Corresponding author. Email: schwab{at}math.ethz.ch A scalar, elliptic boundary-value problem in divergence formwith stochastic diffusion coefficient a(x, ) in a bounded domainD ^d is reformulated as a deterministic, infinite-dimensional,parametric problem by separation of deterministic (x D) andstochastic ( ) variables in a(x, ) via Karhúnen–Loèveor Legendre expansions of the diffusion coefficient. Deterministic,approximate solvers are obtained by projection of this probleminto a product probability space of finite dimension M and sparsediscretizations of the resulting M-dimensional parametric problem.Both Galerkin and collocation approximations are considered.Under regularity assumptions on the fluctuation of a(x, ) inthe deterministic variable x, the convergence rate of the deterministicsolution algorithm is analysed in terms of the number N of deterministicproblems to be solved as both the chaos dimension M and themultiresolution level of the sparse discretization resp. thepolynomial degree of the chaos expansion increase simultaneously.     

Clebsch-Gordan系数的对称性

利用Schur引理确定了角动量耦合的Clebsch-Gordan系数按照其定义所允许的任意程度,然后利用正交归一关系和相位知识,导出了Clebsch-Gordan系数的对称性.