The Center Problem for a Linear Center Perturbed by Homogeneous Polynomials

The centers of the polynomial differential systems with homogeneous polynomials have been studied for the degrees s = 2, 3, 4, 5. for s = 2, 3, and partially classified for s = 4, 5. In this paper we recall and we give new centers for s = 6, 7 a linear center perturbed by They are completely classified these results for s = 2, 3, 4, 5,     

The numerical approximation of center manifolds in Hamiltonian systems

In this paper we develop a numerical method for computing higher order local approximations of center manifolds near steady states in Hamiltonian systems. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear solver and a low-dimensional invariant subspace is available. Our method combines this restriction from linear algebra with the requirement that the center manifold is parametrized by a symplectic mapping and that the reduced equation preserves the Hamiltonian form. Our approach can be considered as a special adaptation of a general method from Numer. Math. 80 (1998) 1-38 to the Hamiltonian case such that approximations of the reduced Hamiltonian are obtained simultaneously. As an application we treat a finite difference system for an elliptic problem on an infinite strip.     

Parametric Centers for Trigonometric Abel Equations

This article is devoted to one-dimensional perturbative theory on R × S ¹. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques. This extends to the trigonometric case what was done previously for the polynomial case (Israel J. Math. 142, 273–283, 2004). This article is dedicated to Professor Zhang Zhi-Fen on the occasion of her 80th Birthday     

GaAsP混晶中Fe杂质能级的无序分裂

GaAsP混晶中Fe杂质基态与激发态的光离化截面的幅度比S(x)随组分x有规律地变化,本文提出一种理论估算,认为它是Fe能级无序分裂的结果.     

“能源化学”本科专业建设建议

"Energy chemistry" was approved as one of the chemistry majors for undergraduate by the Ministry of Education in 2015. Based on the ideas and ways of emerging engineering education, this paper hereby proposed some of constructive suggestions on the training objectives, graduation requirements, curriculum system, teaching contents, teaching staff and conditions for development of "energy chemistry" major.     

Thermal analysis graphite intercalation compounds with dichlorides of some d-elements: A.S. Skoropanov,G.S. Petrov,A.A. Vecher,Yu.N. Novikov and M.E. Vol'pin,Thermochim. Acta, 90 (1985) 339-342

Kinetic and thermodynamic aspects of the axial base dissociation of solid Co(salen) (X-py) complexes, X = H (1), 3-Me (2), 4-Me (3), 3,4-Me₂ (4), 3,5-Me₂ (5), 3-NH₂ (6), 3-Cl (7), 3-CN (8), 4-CN (9), have been investigated by means of TG-DSC and isothermal weight-loss measurements. These adducts endothermically dissociate the axial base giving rise to the oxygen-active Co(salen) complex. The axial base dissociation reactions fit the contracting disc equation and the kinetic compensation effect is observed for all the adducts excepting Adducts 4–6. For the remaining adducts the kinetic and thermodynamic stabilities of the Co-(X-py) bond are found to increase linearly with increasing Hammett's substitution constants of X except for Adducts 3 and 9. These results are discussed in terms of the σ and π interactions between cobalt(II) and substituted pyridine. Factors dominating the kinetic bond stability are briefly discussed.     

The least element property of center location on tree networks with applications to distance and precedence constrained problems

In the classicalp-center location model on a network there is a set of customers, and the primary objective is to selectp service centers that will minimize the maximum distance of a customer to a closest center. Suppose that thep centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective as close as possible to the central depot. We consider tree networks and twop-center models. We show that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property we prove that there is ap-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of thep centers from the existing central depot.Restricting the location models to a rooted path network (real line) we prove that the above results hold for the respective classicalp-median problems as well.     

Synthesis and electrochemical properties of Zn3V3O8 as novel anode material

Zn₃V₃O₈ two-dimensional micro sheets are successfully synthesized by combination of solvothermal method and heat treatment. The Zn₃V₃O₈ has better electrochemical performances after calcinations.     

Unraveling the mystery of efficacy in Chinese medicine formula: New approaches and technologies for research on pharmacodynamic substances

Traditional Chinese medicine (TCM) is the key to unlock treasures of Chinese civilization. TCM and its compound play a beneficial role in medical activities to cure diseases, especially in major public health events such as novel coronavirus epidemics across the globe. The chemical composition in Chinese medicine formula is complex and diverse, but their effective substances resemble “mystery boxes”. Revealing their active ingredients and their mechanisms of action has become focal point and difficulty of research for herbalists. Although the existing research methods are numerous and constantly updated iteratively, there is remain a lack of prospective reviews. Hence, this paper provides a comprehensive account of existing new approaches and technologies based on previous studies with an in vitro to in vivo perspective. In addition, the bottlenecks of studies on Chinese medicine formula effective substances are also revealed. Especially, we look ahead to new perspectives, technologies and applications for its future development. This work reviews based on new perspectives to open horizons for the future research. Consequently, herbal compounding pharmaceutical substances study should carry on the essence of TCM while pursuing innovations in the field.     

A comparison of phototautomerism in different sites of free-base porphin (H2P) in n-alkane crystals

Selective laser-induced phototautomerism of free-base porphin in different n-alkanes (n-hexane, n-heptane, n-octane, nnonane, n-decane, n-undecane and n-dodecane) has been used to identify tautomer splittings in a number of sites in polycrystalline samples at 2 K. Pairs or lines arising from the two molecular orientations in each site can be reversibly transformed into each other. In the odd n-alkanes the occupation of different sites was not dependent on the rate at which the samples were frozen, but in the even n-alkanes metastable sites were only occupied following rapid quenching.