The lion and man problem revisited

A pursuerP, whose speed is bounded by 1, wants to get closer to an evaderE, whose speed is bounded by >1.P wants to reduce his distancePE fromE below the capture radius . Both players are confined to a circular arena. This problem is equivalent to a problem discussed by Flynn, who characterized and gave numerical bounds to the least upper boundd* on the values ofPE thatE can maintain. He used direct methods and did not use Isaacs' theory.We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds ond* by analytical (exact) values for various speeds .The support of the TW Department of THT, Enschede, Holland, is gratefully acknowledged.     

Behaviour of organic pollutants in paper and board samples intended to be in contact with food

This paper deals with the study of volatile compounds present in a set of three paper and board (P&B) samples of different composition, surface treatment, grammage and thickness. The volatile compounds released by the packaging material (P&B) can be trapped on the food and may then affect the safety and health of consumers. To evaluate if the recycled P&B could be used as food packaging material, adsorption studies have been performed with a selection of chemical substances. The adsorption isotherms are provided. Partition coefficients between paper and air have been calculated for a series of volatile compounds used as model compounds to represent different families of contaminants commonly present in P&B. Values from 4 to 3243 were obtained at different temperatures. The analysis of volatile compounds have been carried out by automatic headspace coupled on-line with GC/MS in SIM mode. The results obtained are shown and discussed.     

应用反向传播神经网络预测化合物脑血分配系数

选用27种三维结构性质描述符对脑血分配系数预测建立神经网络模型.网络模型选用典型的适合函数逼近的两层结构神经网络对脑血分配系数(lgBB,BB为脑血浓度比)进行预测,计算中采用的模型具有一个双曲正切型激活函数的隐含层和一个线性激活函数的输出层.计算表明,使用小心选择的反向传播神经网络模型对化合物脑血分配系数具有较好的预测能力.     

Determination of partition behavior of organic surrogates between paperboard packaging materials and air

The suitability of recycled paperboard packaging materials for direct food contact applications is a major area of investigation. Chemical contaminants (surrogates) partitioning between recycled paper packaging and foods may affect the safety and health of the consumer. The partition behavior of all possible organic compounds between cardboards and individual foodstuffs is difficult and too time consuming for being fully investigated. Therefore it may be more efficient to determine these partition coefficients indirectly through experimental determination of the partitioning behavior between cardboard samples and air. In this work, the behavior of organic pollutants present in a set of two paper and board samples intended to be in contact with foods was studied. Adsorption isotherms have been plotted and partition coefficients between paper and air have been calculated as a basis for the estimation of their migration potential into food. Values of partition coefficients (Kpaper/air) from 47 to 1207 were obtained at different temperatures. For the less volatile surrogates such as dibutyl phthalate and methyl stearate higher Kpaper/air values were obtained. The adsorption curves showed that the more volatile substances are partitioning mainly in air phase and increasing the temperature from 70 to 100 degrees C their concentrations in air (Cair) have almost doubled. The analysis of surrogates was performed with a method based on solvent extraction and gas chromatographic-flame ionization detection (GC-FID) quantification.     

Statistical mechanics of a dynamical system based on Conway's game of Life

We study a discrete dynamical system whose evolution is governed by rules similar to those of Conway's game of Life but also include a stochastic element (parametrized by a temperature). Statistical properties that are examined are density as a function of temperature and entropy (suitably defined). A phase transition and a certain thermodynamic constant of the motion are observed.Lady Davis Visiting Scientist at the Technion 1974–75.     

Prediction of soil organic carbon partition coefficients by soil column liquid chromatography

To avoid the limitation of the widely used prediction methods of soil organic carbon partition coefficients (KOC) from hydrophobic parameters, e.g., the n-octanol/water partition coefficients (KOW) and the reversed phase high performance liquid chromatographic (RP-HPLC) retention factors, the soil column liquid chromatographic (SCLC) method was developed for KOC prediction. The real soils were used as the packing materials of RP-HPLC columns, and the correlations between the retention factors of organic compounds on soil columns (ksoil) and KOC measured by batch equilibrium method were studied. Good correlations were achieved between ksoil and KOC for three types of soils with different properties. All the square of the correlation coefficients (R2) of the linear regression between log ksoil and log KOC were higher than 0.89 with standard deviations of less than 0.21. In addition, the prediction of KOC from KOW and the RP-HPLC retention factors on cyanopropyl (CN) stationary phase (kCN) was comparatively evaluated for the three types of soils. The results show that the prediction of KOC from kCN and KOW is only applicable to some specific types of soils. The results obtained in the present study proved that the SCLC method is appropriate for the KOC prediction for different types of soils, however the applicability of using hydrophobic parameters to predict KOC largely depends on the properties of soil concerned.     

Mixed strategy solutions forN-person quadratic games

Mixed strategy -equilibrium points are given forN-person games with cost functions consisting of quadratic, bilinear, and linear terms and strategy spaces consisting of closed balls in Hilbert spaces. The results are applied to linear-quadratic differential games with no information and quadratic integral constraints on the control functions.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.     

Interactions of dicarboxylic porphyrins with membranes in relation to their ionization state

The interactions of dicarboxylic porphyrins with membrane systems are discussed with particular emphasis on the effect of the charge of the porphyrin and the nature of the side-chains. The incorporation of hematoporphyrin or related dicarboxylic porphyrins within small unilamellar vesicles as membrane models is favored by a decrease of the pH in the range of physiological pH values. This effect might play an important role in the retention of porphyrins by tumors, which are more acidic than normal tissues. Kinetics studies also show that the partition of the porphyrin between the lipidic bilayer and the aqueous phase is governed by its release rate rather than by its incorporation rate.     

Perfect equilibria in stochastic games

We examine stochastic games with finite state and action spaces. For the -discounted case, as well as for the irreducible limiting average case, we show the existence of trembling-hand perfect equilibria and give characterizations of those equilibria. In the final section, we give an example which illustrates that the existence of stationary limiting average equilibria in a nonirreducible stochastic game does not imply the existence of a perfect limiting average equilibrium.Support was provided by the Netherlands Organization for Scientific Research NWO via the Netherlands Foundation for Mathematics SMC, Project 10-64-10.     

Partition function zeros for the one-dimensional ordered plasma in Dirichlet boundary conditions

We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacity in an applied electric fieldE with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in the plane occupy the imaginary axis from –i to –i_c and i_c to i for some _c. They also occupy the diamond shape of four straight lines from ±i_c to _c and from ±i_c to –_c. The fugacity acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric fieldE. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented.