Cauchy problem in the class of monotone increasing functions

The paper establishes some solvability conditions of the Cauchy problem for linear differential equation in the class of monotone increasing functions. The results are applied for clarifying the possibility of flight along a given trajectory under existence of braking forces.     

一类椭圆型方程的多重解

利用极小极大方法获得了一类Dirichlet问题多重解的存在性结果.     

关于半线性热方程整体解的注记

利用Besov空间的热核刻画及压缩映射原理,研究半线性热方程ut-△u＝u|u|a的初值问题,得到了当初值u0∈Lp0(Rn)且||u0||(B·)p-n (1/p0-1/p),∞(Rn)(p0＝na/2,p＞p0)充分小时,整体解的存在性及在一定条件下解的惟一性.     

Complex projections of completely positive quaternionic maps

We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007.     

关于《一类奇异边值问题的正解》的注记

文[4]通过构造反例断言文[1]中定理的必要性证明有误,本文首先指出文[4] 的这个断言不正确,然后对文[4]中定理2.1作了本质性的改进.     

环上半线性椭圆型方程正解的存在性和唯一性

本文讨论了半线性椭圆方程△u+f(u)=0在三种边界条件下正解的存在性和唯一性,给出了正解存在和唯一的一些条件.     

Existence and Life Span of Periodic Solutions for the First Order Quasilinear Hyperbolic Equations

g1.IntroductionWeconsiderthefollowingfirstorderquasilinearhyperbolicequationswithinternaIdissipa-tlveterm:U, A(U)U. F(U)=o(1.1)whereUeR2isunknownvectorfunction,A(U)is2X2knownsmoothmatrix,F(U)is2X2knownsmoothvectorfunction.Itiswell-knownthatCauchyproblemoftheequations(l.1)hasbeenwidelystudied(Ll-6J),however,theequations(l.1)withperiedicinitialdatahasbeenhardlystudiedandonesfindthatitiscomplicatedforproblemwithperiodicinitialdata.Becausetheperiodicdis-turbanceLlirectlyinfluencesthebounde…     

Size exclusion chromatographic determination of hydroxypropyl methyl cellulose and polyethylene glycol 400 in an ophthalmic solution

Summary Hydroxypropyl methyl cellulose (HPMC) and polyethylene glycol 400 (PEG 400) content in HypoTears™ Daily Dose ophthalmic solution are determined simultaneously by size exclusion chromatography. The retention times of HPMC and PEG 400 are 10.6 and 15.4 minutes, respectively. The method requires minimal sample pretreatment and is accurate and reproducible. The peak area response from a refractive index detector versus HPMC and PEG 400 concentration is linear over the range of 50–150 % of their label claims of 2.5 mg/mL and 10 mg/mL, respectively. The mean absolute recoveries of HPMC and PEG 400 at their label claim using the described method are 98.9±1.3 % and 100.4±1.2 % (mean±SD, n=12), respectively.     

A Class of Cauchy Problem for Quasilinear Hyperbolic Systems with the Weakly Dissipative Terms

ＡＣｌａｓｓｏｆＣａｕｃｈｙＰｒｏｂｌｅｍｆｏｒＱｕａｓｉｌｉｎｅａｒＨｙｐｅｒｂｏｌｉｃＳｙｓｔｅｍｓｗｉｔｈｔｈｅＷｅａｋｌｙＤｉｓｓｉｐａｔｉｖｅＴｅｒｍｓ￥ＬｉｕＦａｇｕｉ；ＹａｎｇＱｉａｏ（ＮｏｒｔｈＣｈｉｎａＩｎｓｔｉｔｕｔｅｏｆＷａｔｅ...     

Viscosity solution theory of a class of nonlinear degenerate parabolic equations II. Lipschitz continuity of free boundary

In [1] we construct a unique bounded Hölder continuous viscosity solution for the nonlinear PDEs with the evolutionp-Laplacian equation and its anisotropic version as typical examples. In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however, this result does not include the anisotropic case.This research is supported by the National Natural Sciences Foundation of China.