A stochastic model of nanowire growth by molecular beam epitaxy

In this paper, a stochastic model of nanowire growth by molecular beam epitaxy based on probability mechanisms of surface diffusion, mutual shading, rescattering of adatoms, and survival probability is proposed. A direct simulation algorithm based on this model is constructed. A comprehensive study of kinetics of the growth of a family of nanowires initially distributed at a height from about tens of nanometers to about several thousand nanometers is carried out. The time range corresponds to an experimental growth of nanowires of up to 3–4 hours. The following statement is formulated and confirmed numerically: under certain conditions, which can be implemented in real experiments, the height distribution of nanowires narrows with time, that is, in the ensemble of nanowires their heights become aligned with time. For this, the initial radii distribution of the nanowires must be narrow and the density of the nanowires on the substrate must not be very high.     

Synthesis and characterization of C3N4 crystal (I)

A successful experimental synthesis of pure crystalline β- and α-C₃N₄ films on Si(100) substrate was carried out by bias-assisted hot filament chemical vapor deposition (bias-HFCVD). It is found that a mixed-phase C₃-_I-Si_xN_y buffer layer was formed between the Si substrate and the C-N film. A “lattice match selection” was proposed to study the growth mechanism of C₃N₄ clusters composed of many crystal columns with hexagonal facets. Project supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences.     

On the Predator-Prey System with Holling-（n ＋ 1） Functional Response

The qualitative properties of a predatorprey system with Holling-（n ＋ 1） functional response and a fairly general growth rate are completely investigated. The necessary and sufficient condition to guarantee the uniqueness of limit cycles is given. Our work extends the previous relevant results in the reference.     

Growth theorem of convex mappings on bounded convex circular domains

The growth theorem and the 1/2-covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex. Project supported by the National Natural Science Foundation of China and the State Education Commission Doctoral Foundation.     

一个耦合系统自由边界问题的整体古典解

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｄｉｓｃｕｓｓｔｈｅｇｌｏｂａｌｃｌａｓｓｉｃａｌｓｏｌｕｔｉｏｎｏｆａｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｑｕａｓｉｓｔａｔｉｏｎａｒｙｐｒｏｂｌｅｍ .Ｔｈｅｐｒｏｂｌｅｍｃｏｍｅｓｆｒｏｍｔｈｅｄｉｓｃｕｓｓｉｏｎｏｆａｇｒｏｗｔｈｍｏｄｅｌｏｆｓｅｌｆｍａｉｎｔａｉｎｉｎｇｐｒｏｔｏｃｅｌｌ(ｓｅｅ [1— 3])ｉｎｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｃａｓｅ .Ｔｈｅｐｒｏｔｏｃｅｌｌｃａｎｂｅｖｉｓｕａｌｉｚｅｄａｓｈａｖｉｎｇａｐｏｒｏｕｓｓｔ…     

Bubble growth in superheated liquid based on nonequilibrium thermodynamic theory

A mathematical model describing the bubble growth in nucleate boiling is proposed based on non-equilibrium thermodynamics. Numerical simulation of the bubble growth process is performed. Some new arguments are suggested to explain the phenomenon which are distinct from the existing articles. Project supported by the National Natural Science Foundation of China.     

On solutions of algebraic differential equations whose coefficients are entire functions of finite order

Summary We determine bounds for the growth of entire solutions of first order equations whose coefficients are entire functions of finite order. Entrata in Redazione il giorno 8 gennaio 1969. This research was supported in part by the National Science Foundation (GP 7374).     

On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations

This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda＇s results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations.     

Systematic study for grey particles in relativistic nucleus + emulsion (Ag) interactions

The hadronic and string cascade model and the corresponding event generator LUCIAE are used to study systematically the production of the grey particles in (14.6, 60 and 200A GeV)0 + Em, (2004 GeV)Si + Em, (200A GeV)S + Em and (11.6A GeV)Au + Em reactions. The dependences of the mean multiplicity, the multiplicity distributions and the polar angular distributions of the grey particles on the incident energy, the projectile mass and the collision centrality observed in emulsion experiments, respectively, are all reproduced by LUCIAE calculations. In addition the effects of the rescattering on the grey particle production are also investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 19575071 and 19875019) and DFG of Germany.     

Groups with super-exponential subgroup growth

We show that, if the subgroup growth of a finitely generated (abstract or profinite) groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.The first author was partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T7441. The second author was partially supported by the Israeli National Science Foundation.     

Effects of Nb and Si on densities of valence electrons in bulk and defects of Fe3Al alloys

Positron lifetime measurements have been performed in binary Fe₃Al and Fe₃Al doping with Nb or Si alloys. The densities of valence electrons of the bulk and microdefects in all tested samples have been calculated by using the positron lifetime parameters. Density of valence electron is low in the bulk of Fe₃Al alloy. It indicates that, the 3d electrons in a Fe atom have strong-localized properties and tend to form covalent bonds with Al atoms, and the bonding nature in Fe₃Al is a mixture of metallic and covalent bonds. The density of valence electron is very low in the defects of Fe₃Al grain boundary, which makes the bonding cohesion in grain boundary quite weak. The addition of Si to Fe₃Al gives rise to the decrease of the densities of valence electrons in the bulk and the grain boundary thus the metallic bonding cohesion. This makes the alloy more brittle. The addition of Nb to Fe₃Al results in the decrease of the ordering energy of the alloy and increases the density of valence electron and the bonding cohesion of the grain boundary. However, since the radius of Nb atom is larger than that of Fe atom, when Nb atoms substitute for Fe atoms, they will distort the lattice and enlarge the volume of the lattice, which decreases the density of valence electron and the cohesion of metallic bond in the bulk of the alloy. Project supported by the National Natural Science Foundation of China (Grant No. 59561001) and the Foundation of Guangxi Education Committee.     

Large-scale preparation of dispersive carbon nanotubes by arc-discharge method

Sintering-free, dispersive, large area and high density carbon nanotubes(CNTs) were obtained in arc-discharge. Both the quality and the production of the CNTs were improved. SEM study showed that the dispersive CNTs intertwined and aligned randomly in the sample. The growth mechanism of the CNTs and the formation of the morphologies in the arc-discharge were discussed. Project supported by the National Natural Science Foundation of China (Grant No. 19774070) and the Innovation Foundation for Young Researcher from the President of the Chinese Academy of Sciences.     

Precise asymptotics for random matrices and random growth models

The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.     

ON THE GROWTH ORDER OF Co-SEMIGROUPS, I

In this paper, by using the theory of semigroup and spectrum, a computation formula on the growth order of one class of Co-semigroups in Banach space is proved.     

Superlinear convergence of a trust region-type successive linear programming method

The convergence rate of the SLP method suggested in Ref. 1 is discussed for composite nondifferentiable optimization problems. A superlinear rate is assured under a growth condition, and it is further strengthened to a quadratic rate if the inside function is twice differentiable. Several sufficient conditions are given which make the growth condition true. These conditions can be relaxed considerably in practical use.This research was supported in part by the National Natural Science Foundation of China.The author is grateful to Professor E. Sachs, Universität Trier, Trier, West Germany, for his helpful suggestions.     

On stability and L p solutions of ordinary differential equations

Summary The usual definition of the stability of a solution of a system of ordinary differential equations is extended by introducing two positive control functions. These functions are used to control the rate of growth of the in?tial position of the solution and the rate of growth of the solution. Definitions and results are also given for the corresponding analogues of boundedness, weak boundedness, and uniform properties of the sotions of differential equations. The problem of determining when solutions of certain linear and weakly nonlinear differential equations lie in a modified Lp-space is also considered. This research was supported by the National Science Foundation under grant GP-8921. Entrata in Redazione il 13 maggio 1969.     

∑-flat manifolds and Riemannian submersions

In this paper, we show that a certain rigidity condition (-flatness) for open nonnegatively curved manifoldsM is preserved by Riemannian submersions. The result can be applied to quotients ofM by groups of isometries. -flat metrics are also used to derive a splitting theorem for distance tubes of maximal volume growth.Research supported by the Heinrich Hertz Foundation (first author), and by grant DMS88-01999 from the National Science Foundation (second author).     

Investigation of a macroeconomic model by the method of region analysis

A macroeconomic model on the relation between economic growth and the environment is investigated with the aim of illustrating how the method of region analysis can be used in solving practical problems formulated as regular optimal control problems with state constraints.This paper was written when the author was invited by Professor R. Bulirsch to work at the Munich University of Technology with the assistance of the Alexander Von Humboldt Foundation. The author would like to express his sincere gratitude to the Alexander Von Humboldt Foundation and to Professor Bulirsch.     

DISTRIBUTION FREE LAWS OF THE ITERATED LOGARITHM FOR KERNEL ESTIMATOR OF REGRESSION FUNCTION BASED ON DIRECTIONAL DATA

The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of design variable. Project supported by the National Natural Science Foundation of China (Nos. 19631040; 19971085), the Doctoral Program Foundation of the Ministry of Education of China and the Special Foundation of Academia Sinica.     

Optimal impulse control problems for degenerate diffusions with jumps

Optimal stopping and impulse control problems for degenerate diffusion with jumps are studied in this paper. Lipschitzian coefficients for the diffusion process, data with polynomial growth, and evolution in the whole space are the main assumptions on the models. Several characterizations of the optimal cost functions are given. Existence of optimal policies is obtained.This research has been supported in part by Army Research Office Contract DAAG29-83-K-0014 and by National Science Foundation Grant DMS-8601998.