INERTIAL MANIFOLDS FOR NONAUTONOMOUS SEMILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH TIME DELAYS

The present paper deals with the long-time behavior of a class of nonautonomous retarded semilinear parabolic differential equations. When the time delays are small enough and the spectral gap conditions hold, the inertial manifolds of the nonautonomous retard parabolic equations are constructed by using the Lyapunov-Perron method.     

Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems

The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by ＂smooth＂ operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results.     

Signal generation and spatial resolution in scanning electron acoustic microscopy

The thermal conduction and Navier-Stokes equations are usedto obtain the stress field generated by a chopped electron beam incident ona disk sample.The piezoelectric equation is then used to obtain the out-put signal of the transducer coupled to the sample.The results lead to aconsideration of the signal generation mechanism and spatial resolution inscanning electron acoustic microscopy(SEAM).It is shown that atime-variant heat source generated both a thermal wave and an acousticwave simultaneously,and thermal-to-acoustic wave mode conversion oc-cured on the boundary surfaces depends on the amplitudes and the gra-dients at boundary surfaces of both heat source and thermal waves.It isargued that the spatial resolution of a imaging system operated in thenear field,such as SEAM and thermal wave microscope,is dependent onthe distance between the heat source and scatterer and,at best,the lateralresolution in SEAM is of the order of the diameter of the focal spot ofthe electron beam.     

矩孔金属光栅矢量模式理论的数值计算

根据矩孔金属光栅的矢量模式理论，计算了不同入射方向，波长及偏振态情况下衍射场的分布，研究了不同光栅结构对衍射效率，偏振态变化的影响；同时，根据实际需要，加工制作了一批不同深度的矩孔光栅样品，进行了实验测量，并将计算值与实验值进行了比较，两者基本相符。     

高效液相色谱死体积的热力学定义

本文讨论了高效液相色谱死体积的定义和如何以吉布斯热力学理论为基础对其测定。推荐的热力学理论方法能应用于任何一种液相色谱方法,如正相、反相、离子交换、甚至体积排斥色谱。提出了一种能在整个浓度范围内准确计算流动相组分干扰峰死体积的方法。对某些化合物容量因子出现负值也作了解释。     

Mathematics Reading

A great discovery solves a great problembut there is a grain of discovery in the solu-tion of any problem.Your problem may bemodest;but if it challenges your curiosityand bring into play your inventive faculties,and if you solve it by your own means,youmay experience the tension and enjoy the tri-umph of discovery.Such experience at a sus-ceptible age may create a tasle for mentalwork and leave their imprint on mind andcharacter for a lifetime.     

A FAMILY OF BERNSTEIN QUASI-INTERPOLANTS ON[0,1]

Suppose that we want to approximate fC[0,1]by polynomials in P_n,using only itsvalues on X_n={i/n,0≤i≤n}.This can be done by the Lagrange interpolant L_n f or theclassical Bernstein polynomial B_n f.But,when n tends to infinity,L_n f does not converge to fin general and the convergence of B_n f to fis very slow.We define a family of operators B~(k)_n,n≥k,which are intermediate ones between B(0)_n=B~(1)_n=B_n and B~(n)_n=L_n,and we studysome of their properties.In particular,we prove a Voronovskaja-type theorem which assertsthat B~(k)_n f-f=0(n~(-[(k+2)/2))for f sufficiently regular.Moreover,B(k)_n f uses only values of B_n f and its derivaties and can be computed by DeCasteljau or subdivision algorithms.     

博湖县芦苇板厂苇板生产线的技术改造

博湖县芦苇板厂苇板生产线的技术改造杨发宝，林庶宏，杨隽，钟晓敏（新疆大学计算中心，乌鲁木齐８３００４６）１概述巴州博湖县苇板厂利用协所瞩用丰富的芦苇资源作原料，生产出的芦苇板畅销全国各地，以芦苇为原料问作人拉饭，该厂用国内第一家．在等权的生产过程中，...     

Studies on the properties of flow-induced oscillation and sound radiation in streamlined protuberant special cavities

I.IntroductionAsanuidpassingthroughthecavityatcertainflowrate,themediuminthemouthandthccavityisoscillatingandsoundisradiated.Noton1ystochasticturbu1encenoiscispossi-blyproducedbutsinglefrequencysoundofspecia1lydesignatedpitchisalsoproduced.Andthusthespcctrumofthcradiatedsoundisshownascontinuousspectrumandcharacteristiclinespcctrum.Inthiscascwcmaycallitflow-inducedosci1lation.Flow-inducedoscillationandsoundradiationcanbeproducedasafluid(waterorgas)passingthroughthecavitybysinkingcavityunderint…     

钛-茜素黄R-CTMAB三元体系的研究及其应用

在酸性溶液中,有CTMAB存在下,钛能与茜素黄R反应形成橙色配合物,其最大吸收波长在450nm处,配合物中钛与茜素黄R的摩尔比为1:3。25毫升溶液中含钛量在0—15微克范围内遵守比尔定律,所拟定的方法用于测定硅酸盐矿石中的钛,结果满意。