Solvable Baumslag–Solitar Groups are not Almost Convex

The arguments of Cannon, Floyd, Grayson and Thurston (Geom. Dedicata (1989), 291–300) showing that solvegeometry groups are not almost convex apply to solvable Baumslag-Solitar groups.     

Mixed dominating matrices

We characterize the class of matrices for which the set of supports of nonnegative vectors in the null space can be determined by the signs of the entries of the matrix. This characterization is in terms of mixed dominating matrices, which are defined by the nonexistence of square submatrices that have nonzeros of opposite sign in each row. The class of mixed dominating matrices is contained in the class of L-matrices from the theory of sign-solvability, and generalizes the class of S-matrices. We give a polynomial-time algorithm to decide if a matrix is mixed dominating. We derive combinatorial conditions on the face lattice of a Gale transform of a matrix in this class.     

荧光读取多层CD光盘(CDLROM)的研制原理

本文研究了在卤化银光敏层的基础上构建多层CD盘的原理,研制了将影像中的银转化为产生荧光产物的方法,从而在应用荧光读取信息时可极大地提高其信噪比.研究后作者得出结论,传统的卤化银照相术能在制造多层光盘CDLROM中得到应用.     

Problème de Gleason et interpolation pour les fonctions hyper-analytiquesGleason's problem and interpolation for hyperholomorphic functions

We prove a Gleason type theorem in the setting of functions hyperholomorphic in the unit ball of $\text{R}{}^4$. We give an interpretation of the result in terms of pairs of functions defined in the unit ball of $\text{C}{}^2$. Finally we use the theorem to study the homogeneous interpolation problem in the setting of hyperholomorphic functions. To cite this article: D. Alpay, M. Shapiro, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 889–894.     

Inference of statistical bounds for multistage stochastic programming problems

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal (minimum) value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. We also indicate that fixing a feasible first-stage solution and then solving the sampling approximation of the corresponding (T–1)-stage problem, does not give a valid statistical upper bound for the optimal value of the true problem.Supported, in part, by the National Science Foundation under grant DMS-0073770.     

Intercalation compounds of phenols and poly-N-vinylcaprolactam

Intercalation compounds of phenols and poly-N-vinylcaprolactam (PVC) form when their aqueous solutions are mixed. Using¹³C NMR and IR spectroscopy complexation was shown to proceed through the formation of hydrogen bonds between the carbonyl groups of the caprolactam moieties and phenolic hydroxyls as well as through displacement of water from the polymer structure and its compaction. The processes of the formation of intercalation compounds of PVC with phenol andtert-butyl alcohol were compared.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 2251–2255, September, 1996.     

Reaction of polymethine dyes with hydroperoxides and free radicals

The interaction kinetics of the cationic and anionic polymethine dyes with radicals has been studied. Azoinitiator AAPH, as well as tert-butyl hydroperoxide, and hydrogen peroxide were used as radical initiators in water and buffer solutions at 37 °C. It is shown that the dyes are active scavengers of peroxyl radicals. It is found that reactivity and behavior of dyes in relation to the peroxides are strongly dependent on the structure of lateral substituents in polymethine chains.     

Shock wave attenuation by grids and orifice plates

The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.     

Gravitational migration of fuel in porous media

Fuel migration in a water flowing through a porous medium generally occurs parallel to porous strata, which may not be horizontal. In this case, gravity tends to cause vertical segregation of fluids, depending on their densities. This phenomenon can exert a strong effect on fuel migration. The gravitational force creates the buoyancy force which acts upon the fuel, and may be either parallel or anti-parallel to the water flow direction.In this study, the above effects are investigated using the one-dimensional model of Pistineret al. We go beyond the latter investigation in describing the influence of the gravitational forces upon the movement of fuel saturation fronts in a vertical porous layer against and along the water flow direction.It is found that when the directions of the buoyancy force and of the water flow are anti-parallel, fuel migrates in the direction of the buoyancy force, provided the latter is strong enough. However, in the case of a weak buoyancy force, the direction of migration of the fuel depends on its mass. Small fuel masses move mainly in the direction of the water flow. However, big fuel slugs possessing large masses will move mainly in the direction of the buoyancy force. Slugs, characterized by intermediate masses, have no preferable moving direction and are almost stagnant.     

On the nonequilibrium segregation state of a two-phase mixture in a porous column

The problem of segregation of a two-phase multicomponent mixture under the action of thermal gradient, gravity and capillary forces is studied with respect to component distribution in a thick oil-gas-condensate reservoir. Governing equations are derived on the basis of nonequilibrium thermodynamics. A steady state of the two-phase mixture with nonzero diffusion fluxes and exchange between phases is described. In the case of binary mixtures analytical formulae for saturation, component distribution and flow in the two-phase zone are obtained.