Mathematical modeling and optimization of intratumor drug transport

A pseudohyperbolic problem of optimal control of intratumoral drug distribution is formulated. It takes into account the heterogeneity of tumor tissues and effects of convection diffusion in a fissured porous medium. A mathematical model constructed and the corresponding optimal control problem are shown to be correct. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 147–154, November–December 2007.     

利用数学模型分析复吹转炉吹炼工艺

在冶金热力学和动力学及反应工程学原理的基础上，建立了模拟复吹转炉冶炼过程的数学模型．在用梅钢150t复吹转炉工业试验的结果对模型加以验证之后，利用模型对具有中高磷铁水特点的梅钢转炉吹炼工艺进行了分析讨论．     

Mathematical modelling of the alcoholic fermentation of glucose by Zymomonas mobilis mobilis

The kinetics of alcoholic fermentation of a strain of Zymomonas mobilis, isolated from sugarcane juice, has been studied with the objective of determining the constansts of a non-structured mathematical model that represents the fermentation process. Assays in batch and in continuous culture have been carried out with different initial concentrations of glucose. The final concentrations of glucose, ethanol and biomass were determined. The following kinetic parameters were obtained: μ_max, 0·5 h^?1; K_s, 4·64 g dm^?3; P_max, 106 g dm^?3; Y_x/s, 0·0265 g g^?1; m, 1·4 g g^?1 h^?1; α, 17·38 g g^?1; β, 0·69 g g^?1 h^?1.     

金属快速凝固方法的数学模型

本文综述了与几种典型的快速凝固方法相应的数学模型，并对每种模型作了相应的分析和评价。文中重点介绍了“活塞－砧法”，“双辊法”，“单辊法”和“雾化沉积法”数学模型的理论基础，建模过程，理论优缺点及实用局限性。     

基金最佳使用计划

本文给出了基金存款策略的数学模型.对于基金M使用n年的情况而言,首先把M分成n份,其中第i(1≤i≤n)份存款xi存期为i年,那么只有当第i(i ≤n-1)份资金按最佳存款策略存款到期后的本息和等于当年的奖学金数,并且第n份资金按最佳存款策略存款n年后的本息和等于原基金M与当年的奖学金数之和时,每年发放的奖学金才能达到最多.通过求解此模型,我们得到了基金的最佳存款策略,并求出了在n=10年,M=5000万元的情况下,基金的最佳使用方案.在可存款也可购买国库券时,采取一种转化方法,将国库券购买情况转化为相应年期的定期存款,结合问题(一)即可求得在n=10年,M=5000万元的情况下,基金的最佳使用方案;在第三年校庆时奖学金数额比其它年度多20%的问题的分析方法和模型的解决方法与前相同.     

A method for quantifying cell size from differential interference contrast images: validation and application to osmotically stressed chondrocytes

An automatic image analysis method was developed to determine the shape and size of spheroidal cells from a time series of differential interference contrast (DIC) images. The program incorporates an edge detection algorithm and dynamic programming for edge linking. To assess the accuracy and working range of the method, results from DIC images of different focal planes and resolutions were compared to confocal images in which the cell membrane was fluorescently labelled. The results indicate that a 1‐µm focal drift from the in‐focus plane can lead to an overestimation of cell volume up to 14.1%, mostly due to shadowing effects of DIC microscopy. DIC images allow for accurate measurements when the focal plane lies in a zone slightly above the centre of a spherical cell. In this range the method performs with 1.9% overall volume error without taking into account the error introduced by the representation of the cell as a sphere. As a test case, the method was applied to quantify volume changes due to acute changes of osmotic stress.     

Models and observations of fcc/bcc interfaces

Whereas models of the structure and periodicity of CSL or near CSL high angle grain boundaries are relatively well developed and have been to some extent verified by experiment, the nature of more general (e.g. fcc/bcc) interfaces is very imperfectly understood. One of the major differences between homo- and heterophase boundaries is the occurrence, in the latter case, of reproducible orientation relationships due to the crystallographic requirements of phase transformation (e.g. a glissile interface for martensitic growth, low energy interfaces for classical nucleation). A review is given of the relationships commonly observed to obtain between fcc and bcc crystals (as well as ordered phases based upon these structures). Within a given relationship, it is possible to use models of the available interfaces to predict their dislocation content; the success of the various approaches is considered. It is shown that the dislocation arrays identified on fcc/bcc boundaries are consistent with the occurrence of a primary structural relaxation, but that the latter does not appear to be complete. Possible reasons for this are discussed, together with the extent to which secondary structural models may be applicable. Attempts to rationalize the observed orientation relationships and morphologies are discussed, and it is pointed out that these all rely on searches for situations of minimum primary misfit, but that the way in which the latter is quantified determines the results of the analyses. Nevertheless, the implication is that the primary misfit does appear to determine the actual behaviour, though no structural or mechanistic conclusions can safely be drawn from this observation.     

MCS接枝共聚物的结构和形态

将甲基丙烯酸甲酯（ＭＭＡ）、苯乙烯（Ｓ）在氯化聚乙烯（ＣＰＥ）存在下进行悬浮接枝共聚，获得ＭＣＳ树脂。本文着重考察了ＭＣＳ树脂的化学结构及胶粒形态。结果表明，确实发生了接枝共聚。ＣＰＥ用量、ＲＳＨ含量、引发剂浓度、反应温度、溶胀时间及聚合转化率对ＭＣＳ树脂的接枝率、接枝效率均有影响。ＭＣＳ树脂是接枝共聚物、ＭＭＡ／Ｓ共聚物与ＭＭＡ均聚物的混合物，橡胶相ＣＰＥ在ＭＣＳ树脂中的分散情况为“海岛结构”，     

Image segmentation towards new image representation methods

Very low bit-rate video coding has recently become one of the most important areas of image communication and a large variety of applications have already been identified. Since conventional approaches are reaching a saturation point, in terms of coding efficiency, a new generation of video coding techniques, aiming at a deeper “understanding” of the image, is being studied. In this context, image analysis, particularly the identification of objects or regions in images (segmentation), is a very important step. This paper describes a segmentation algorithm based on split and merge. Images are first simplified using mathematical morphology operators, which eliminate perceptually less relevant details. The simplified image is then split according to a quad tree structure and the resulting regions are finally merged in three steps: merge, elimination of small regions and control of the number of regions.     

共晶强制性熔化的界面形态

对透明共晶系ＣＢｒ４－８．４ｗｔ－％Ｃ２Ｃ１６生长的典型层片共晶组织强制熔化进行实时实地观测．表明相对于强制生长时的“界面滞后”现象，熔化界面温度高于静止时界面温度，熔化界面比静止界面更靠近热端，称为“界面超前”．随熔化速度增大，“界面超前量”增大；共晶组织分层熔化，出现两个熔化界面，α和β相熔化秩序不同，α，β相分别单独熔化，两熔化界面的相对位置由α，β相成分，熔化速度和共晶相间距等因素决定．