具时滞带非单调反应函数的半比例依赖捕食被捕食系统的持久性

研究了具时滞半比例依赖的捕食被捕食非单调函数反应系统的持久性,得到了比较弱的由积分形式表述的充分条件.     

Stochastic L2-Integration with a Locally Compact Time-Region

This paper contains some results about the theory of stochastic L²-Integration with a general time-region. The starting point of our theory is not a family of σ-algebras but, more generally, a family of projection operators in the Hilbert space of all square integrable random functions. To do this we use some Hilbert space analysis as well as the methods of Metivier and Pellaumail.     

Nucleation kinetics of paracetamol–ethanol solutions from metastable zone widths

A study of the nucleation kinetics for a cooling crystallisation of paracetamol–ethanol solutions in a batch reactor is described in this paper. Metastable zone width (MSZW) experiments were conducted in order to estimate the nucleation kinetics of the system. Measured MSZWs can be affected by numerous process parameters, such as cooling rate, concentration, agitation rate, and working volume. Two theoretical approaches were employed to estimate the nucleation kinetics, the classical mass based approach of Nývlt, and a more recent approach by Kubota, which also considers number density. Both approaches were found to produce similar estimates for the nucleation rates of the paracetamol–ethanol solutions as a function of supersaturation for an assumed nucleus size of 10 μm. The theory of Kubota was found to predict satisfactory estimates for the induction time of the nucleation process from MSZW data. The induction time was observed to be independent of the solution temperature as suggested by Kubota’s theory. This is a novel finding and serves to validate the induction time theory of Kubota. In this investigation, MSZWs were observed to decrease with increased levels of agitation and found to be independent of working volume.     

Deriving Energy-Gap of Some Hamiltonians with Kinetic Coupling by the Invariant Eigen-Operator Method

We begin with proposing a unitary operator responsible for diagonalizing the Hamiltonian with kinetic couplings in particle physics to get a new form of Hamiltonian which has no coupling terms. By virtue of the invariant eigen-operator (IEO) method we search for the invariant eigen-operators for the new Hamiltonian. In this way the energy-gap of the Hamiltonians can be naturally obtained. This method may be generalized to N-mode Hamiltonian with kinetic couplings case. Work supported by the National Natural Science Foundation of China under grant 10475056 and Foundation of President of Chinese Academy of Science.     

Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems

We derive and investigate point implicit Runge–Kutta methods to significantly improve the convergence rate to approximate steady‐state solutions of inviscid flows. It turns out that the point implicit Runge–Kutta can be interpreted as a preconditioned explicit Runge–Kutta method, where the preconditioner arises naturally as local derivative of the residual function. Moreover, many preconditioners suggested in the literature so far are identified as special case of our general ansatz. Conditions will be formulated such that explicit Runge–Kutta methods with local time stepping are equivalent to point implicit methods. In numerical examples, we will demonstrate the improved convergence rates. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of time on the magnetic properties of terbium-doped LaMnO3

The magnetic properties of the perovskite form of LaMnO₃ have been shown strong interest in recent years due to its high potential for use in magnetic devices. In this paper, the magnetic properties of a 30% terbium-doped LaMnO₃ (LMTO) perovskite manganite synthesized by a conventional solid-state reaction were investigated. Data on these properties was recorded periodically via SQUID and VSM to reveal it to be best described magnetically as a spin glass system. Thus, the time effect must be taken into consideration in instantaneously determining this material’s spin glass state as well as the overall magnetic properties in the absence of a magnetic field. The results of this paper point to a more in-depth understanding of the change in magnetic properties associated with doped LaMnO₃.     

Proper-Time Relativistic Dynamics on Hyperboloid

The dynamics of a point-like relativistic particle with respect of the proper time is formulated on the hyperboloid p ² ₀–p ²=M ² c ². The Hamilton-Jacobi equations on the hyperboloid are derived for the particles with mass (M ²=m ², m>0), for the particles with zero-mass (M=0, m>0), and for the neutrino. It is shown, in a certain factorization of the momentum, the model can be identified with Nambu's three-dimensional phase space formalism. A first quantized version of the model is formulated according to a canonical scheme of quantization (Schrödinger quantization scheme).