带生长函数的非定常森林发展系统

讨论非定常森林发展系统的动力学模型,证明了方程解的存在唯一性,并用Lyapunov稳定性理论讨论了系统的稳定性.     

高分子物理课程知识体系的构建革新

高分子物理是高分子材料相关专业的专业基础课,内容丰富,章节间关系复杂,课程主线往往不容易把握。本文从运动对高聚物性质(性能)的决定性作用角度,提出了构建高分子物理课程知识体系的观点:在高分子结构部分,充实原子、键等部分作用的论述,完善高分子结构划分的层次;明确高分子不同结构层次都具有运动与变化能力的认知,重点突出不同高分子结构运动、变化的特征和规律;根据根据每一个结构层次运动特征,综合理解结构、结构的变化对高分子性能的影响。     

Approximate and efficient calculation of dominant Lyapunov exponents of high-dimensional nonlinear dynamic systems

This short communication presents an efficient method for calculating dominant Lyapunov exponents (LEs) of high-dimensional nonlinear dynamic systems based on their reduced-order models obtained from the linear model reduction theory. Mathematical derivation shows that the LEs of the reduced-order models correspond to the dominant LEs of the original systems. Two numerical examples are provided to demonstrate the effectiveness of the method.     

CARTscans: A Tool for Visualizing Complex Models

We present CARTscans, a graphical tool that displays predicted values across a fourdimensional subspace. We show how these plots are useful for understanding the structure and relationships between variables in a wide variety of models, including (but not limited to) regression trees, ensembles of trees, and linear regressions with varying degrees of interactions. In addition, the common visualization framework allows diverse complex models to be visually compared in a way that illuminates the similarities and differences in the underlying methods, facilitates the choice of a particular model structure, and provides a useful check for implausible predictions of future observations in regions with little or no data.     

On oscillatory third order difference equations

In this paper, sufficient conditions have been obtained for oscillation/nonoscillation of a class of homogeneous/nonhomogeneous linear difference equations of third order.     

Existence theorems for boundary value problems in difference equations

In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants.     

Convergence of a Difference Equation and Its Applications

In this paper, we establish a sufficient condition for every solution of the forced difference equation $$x_{n+1} - x_n + p_nx_{n-k} = r_n, \ \ n=0, 1, \ldots$$     

Oscillation theorems for symplectic difference systems

We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same problem was treated and an essential ingredient was to establish the concept of the multiplicity of a focal point. But there was still a rather restrictive condition needed, which is eliminated here by using the concept of finite eigenvalues (or zeros) from the theory of matrix pencils.     

Construction of mononuclear transition metal(II) complexes with bi- and tridentate,neutral hydrazone ligands with a quinoxaline hub

A series of Co(II), Ni(II), Cu(II), and Zn(II) complexes of bi- and tridentate hydrazones were prepared. Ligands L¹ and L² were synthesized by the condensation of 2-mercapto-3-hydrazinoquinoxaline with 2-hydroxy-3-formylquinoline and 3-acetylcoumarin, respectively. The compounds were characterized by various spectro-analytical techniques and magnetic moment studies. The complexes are found to be monomeric and non-electrolytes. In these complexes, [CuL¹Cl₂] has square pyramidal geometry and others have octahedral. The copper complexes are electrochemically active in the applied potential range.     

Differential equation dynamical system based assessment model in GNSS interoperability

With the development of Global Navigation Satellite System (GNSS),the idea of GNSS interoperability is born and has become the focus of study in the field of satellite navigation.The popularity for GNSS to augment the interoperability with the existing ones necessitates the study of the assessment algorithm of this idea.In this paper,an assessment algorithm for interoperability comprehensive benefits based on the differential equation dynamical system is discussed.There are two important aspects in GNSS tha...