Theoretical study on K, L, and M X-ray transition energies and rates of neptunium and its ions

The transition energies and electric dipole （El） transition rates of the K, L, and M lines in neutral Np have been theoretically determined from the MultiConfiguration Dirac-Fock （MCDF） method. In the calculations, the contributions from Breit interaction and quantum electrodynamics （QED） effects （vacuum polarization and self-energy）, as well as nu- clear finite mass and volume effects, are taken into account. The calculated transition energies and rates are found to be in good agreement with other experimental and theoretical results. The accuracy of the results is estimated and discussed. Furthermore, we calculated the transition energies of the same lines radiating from the decaying transitions of the K-, L-, and M-shell hole states of Np ions with the charge states Np1＋ to Np6＋ for the first time. We found that for a specific line, the corresponding transition energies relating to all the Np ions are almost the same; it means the outermost electrons have a very small influence on the inner-shell transition processes.     

Convergence rates in ℓ1-regularization when the basis is not smooth enough

Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation with respect to a fixed basis. We drop this sparsity assumption and provide error estimates for nonsparse solutions. After discussing a result in this direction published earlier by one of the authors and co-authors, we prove a similar error estimate under weaker assumptions. Two examples illustrate that this set of weaker assumptions indeed covers additional situations which appear in applications.     

Memory feedback controller design for stochastic Markov jump distributed delay systems with input saturation and partially known transition rates

This paper considers the problem of stabilization for a class of stochastic Markov jump distributed delay systems with partially known transition rates subject to saturating actuators. By employing local sector conditions and an appropriate Lyapunov function, a state memory feedback controller is designed to guarantee that the resulted closed-loop constrained systems are mean-square stochastic asymptotically stable. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

A cyclical square-root model for the term structure of interest rates

This paper presents a cyclical square-root model for the term structure of interest rates assuming that the spot rate converges to a certain time-dependent long-term level. This model incorporates the fact that the interest rate volatility depends on the interest rate level and specifies the mean reversion level and the interest rate volatility using harmonic oscillators. In this way, we incorporate a good deal of flexibility and provide a high analytical tractability. Under these assumptions, we compute closed-form expressions for the values of different fixed income and interest rate derivatives. Finally, we analyze the empirical performance of the cyclical model versus that proposed in Cox et al. (1985) and show that it outperforms this benchmark, providing a better fitting to market data.     

Convergence rates of trinomial tree methods for option pricing under regime-switching models

Recently trinomial tree methods have been developed to option pricing under regime-switching models. Although these novel trinomial tree methods are shown to be accurate via numerical examples, it needs to give a rigorous proof of the accuracy which can theoretically guarantee the reliability of the computations. The aim of this paper is to prove the convergence rates (measure of the accuracy) of the trinomial tree methods for the option pricing under regime-switching models.     

General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity

This work deals with the study of a new class of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity. A decay result of the energy of solutions for the problem without imposing the usual relation between a certain relaxation function and its derivative is established. This result generalizes earlier ones to an arbitrary rate of decay, which is not necessarily of exponential or polynomial decay.     

A numerical method for a nonlinear structured population model with an indefinite growth rate coupled with the environment

A numerical method is developed for a general structured population model coupled with the environment dynamics over a bounded domain where the individual growth rate changes sign. Sign changes notably exhibit nonlocal dependence on the population density and environmental factors (e.g., resource availability and other habitat variables). This leads to a highly nonlinear PDE describing the time‐evolution of the population density coupled with a nonlinear‐nonlocal system of ODEs describing the environmental time‐dynamics. Stability of the finite‐difference numerical scheme and its convergence to the unique weak solution are proved. Numerical experiments are provided to demonstrate the performance of the finite difference scheme and to illustrate a range of biologically relevant potential applications.     

高真空多层绝热结构中一氧化钯吸氢特性研究

对高真空下的一氧化钯吸附氢气的特性进行了分析和研究,实验测定了一氧化钯吸附氢气的机理,不同条件下一氧化钯对氢气的吸附特性,以及设置一氧化钯对夹层漏放气的影响。实验证明,在夹层中使用恰当的混合吸附剂,可以有效减小夹层的漏放气量,提高低温储罐的寿命。