Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors

In this paper we study a free boundary problem modelling the growth of nonnecrotic tumors. The main trait of this free boundary problem is that it is essentially multidimensional, so that its well-posedness is hard to establish by using the usual methods in the classical theory of free boundary problems. In this paper we use the functional analysis method based on the theory of analytic semigroups to prove that this problem has a unique local solution in suitable function spaces. Continuous dependence of the solution on the initial data and regularities of the solution can also be easily obtained by using the argument of this paper.     

生长曲线模型中回归系数阵的极大似然估计的精确分布

对于生长曲线模型,基于理论发展和应用效果的考虑,本文引入了Gauss型误差．在此误差下,本文研究了模型中回归系数阵的极大似然估计的精确分布,求出了此分布的密度和特征函数．     

经济增长与宏观经济运行模型

对国民经济进行宏观调控，如同经济增长问题一样是一个永恒问题，对宏观调控的基本内容，手段，方法，国内外学者已进行了较多的规范性讨论，尤其是在数理分析方面，也已有许多具有普遍意义的成果，但是，要把那些成果转化为“生产力”从而变成清晰的，简明的，可操作的手段和方法，尚需人们不断的探索，本文通过对国民经济运行过程中若干宏观经济变量之间的数量关系分析，并以此建立了的国民经济宏观数量模型，就是尝试性的探索。     

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

Slow quenching for a one-dimensional kinetic Ising model: Residual energy and domain growth

A one-dimensional kinetic Ising model with Glauber dynamics subjected to a slow continuous quench to zero temperature is studied. For a rather general class of cooling schemes, described by a time-dependent temperatureT(t), the mean domain sizeL(t) is calculated along with the residual energye _res (r) as a function of the cooling rater. If the attempt frequency =₀ exp(–/kT), entering into the transition rates, is temperature dependent (i.e., the barrier is non-zero), the asymptotic growth ofL(t) is given byL()–L(t)~exp[–/kT(t)]. For this case the residual energy exhibits a power-law behaviore _res(r) ~r ^{/2(1 + )} forr small, where =4J/ andJ is the nearest neighbor coupling constant. For =0 and for certain cooling schemes the residual energy is zero andL(t)~t1/2, independent ofr.     

1-氨基环丙烷-1-羧酸的合成: 新型植物生长调节剂

本文报道了合成1-氨基环丙烷-1-羧酸的简便而价廉的方法,即乙酰乙酸乙酯法和α-氰乙酸乙酯法;并测定了产品的结构。     

取代硫脲化合物对作物的生长调节作用

取代脲类化合物已广泛用作除草剂、杀虫剂、杀鼠剂。根据结构活性关系,亦对烯丙基、甲基、二芳基取代硫脲衍生物的植物生长调节活性进行了研究。本文合成了3类取代硫脲化合物:R_1NHCSNHR_2,其中:R_1=苯基,α-萘基,叔丁基,R_2=α-苯基乙     

三硼酸锂晶体的生长形态

用自由生长系统研究了三硼酸锂ＬｉＢ_３Ｏ_５（ＬＢＯ）晶体的实际生长形态。实验表明，它的各晶面簇的重要性的顺序为：｛１１０｝＞｛０１１｝＞｛２０１｝＞｛１１１｝。讨论了ＬＢＯ晶体的生长习性与内部结构之间的关系并应用负离子配位多面体理论模型解释了ＬＢＯ晶体的生长形态。     

非线性光学材料──水草酸铵

一水草酸铵（简称ＡＯＭ）是一种优良的电光晶体￣［１］。文献￣［１，２］报道了该晶体的晶体结构，化学式为（ＮＨ＿４）＿２Ｃ＿２Ｏ＿２·Ｈ＿２Ｏ，属正交晶系，Ｐ２２２空间群，晶胞参数ａ＝０．８０３５ｎｍ，ｂ＝１。０３１ｎｍ，ｃ＝０．３８０１ｎｍ，ｚ＝２。本文拟报道ＡＯＭ单晶生长，热化学分析，透过波段以及非线性光学性质的初步研究。