Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

Anharmonic force fields of cis- and trans-S1 C2H2

We calculate second-order vibrational perturbation theory (VPT2) anharmonic force fields for the cis and trans conformers of S₁ C₂H₂, and compare the results to experiment. The vibrational assignments of recently observed levels belonging to the cis well are of particular interest. A refined estimate of the cis origin position (44,870?±?10?cm^?1) is proposed, and preliminary low-energy fits to the global J?=?K?=?0 trans level structure are also described. The performance of perturbation theory in this isomerizing system is examined, and both surprising successes and failures are encountered. We examine these and their causes, and offer practical suggestions for avoiding the pitfalls of applying perturbation theory to systems with large amplitude motions.     

On one-point functions for sinh-Gordon model at finite temperature

Using fermionic basis we conjecture the exact formulae for the expectation values of local fields in sinh-Gordon model. The conjecture is checked against previously known results.     

THE GENERALIZED RIEMANN PROBLEM FOR A SCALAR NONCONVEX COMBUSTION MODEL-THE PERTURBATION ON INITIAL BINDING ENERGY

In this article,we study the generalized Riemann problem for a scalar nonconvex Chapman-Jouguet combustion model in a neighborhood of the origin (t ＞ 0) on the (x,t) plane.We focus our attention to the...     

SOLUTION WITH SHOCK-BOUNDARY LAYER AND SHOCK-INTERIOR LAYER TO A CLASS OF NONLINEAR PROBLEMS

In this paper,the shock behaviors of solution to a class of nonlinear singularly perturbed problems are considered.Under some appropriate conditions,the outer and interior solutions to the original problem are constructed.Using the special limit and matching theory,the expressions of solutions with the shock behavior near the boundary and some interior points are given and the domain for boundary values is obtained.     

Rovibrational and energetic analysis of the hydroxyethynyl anion (CCOH−)

For the first time, high-level structural and rovibrational data are provided for the hyroxyethynyl anion, CCOH^?. CCOH^? is a promising molecule for interstellar detection even though no new anions have been observed in the interstellar medium for the past half-decade. The large dipole moment of the corresponding neutral radical may be key for its creation as has been hypothesised and supported for other anions known to exist in various astronomical environments. Highly accurate quartic force fields are employed where previous benchmarks have produced spectroscopic constants and anharmonic vibrational frequencies within 20 MHz and 1 cm^?1, respectively, of experiment. This same approach is applied here for CCOH^? and its deuterated isotopologue with the goal of assisting laboratory experiments and/or astronomical observers in the potential detection of this anion.     

一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

D-admissible hybrid control of a class of singular systems

This paper mainly studies the problem of designing a hybrid state feedback D-admissible controller for a class of linear and nonlinear singular systems. Based on the relationship between singular discrete systems and singular delta operator systems, several necessary and sufficient conditions for a linear singular delta operator system to be D-admissible (i.e. regular, causal and all finite poles lie in a prescribed circular region) with different representations are derived. Then, the existence conditions and explicit expressions of a desirable D-admissible controller are given by means of matrix inequalities and strict linear matrix inequalities, respectively. We further extend the obtained results to singular delta operator systems with Lipschitz nonlinear perturbations, and the design methods of hybrid controller are presented for the nonlinear case as well. Finally, numerical examples as well as simulations are provided to illustrate the effectiveness of the theoretical outcomes obtained in the paper.