Bounding multi-stage stochastic programs from above

The purpose of this paper is to present general approaches for bounding some multi-stage stochastic programs from above. The results are based on restricting the solution set, such that the remaining multi-stage stochastic program is easy to solve. An example where the methods can be applied is presented.Supported in part by NATO Collaborative Research Grant No. 0785/87.     

Ions and atoms in superfluid helium (4He)

We review the previous conclusion [J.Y. Ryu, Y.C. Chung and S.D. Choi, Phys. Rev. B 32, 7769 (1984)] that the trace property Tr(ABC) = Tr(CAB) leads to two different cyclotron transition absorption formulae in the electron-phonon systems in the lowest order approximation. The pictorial expression and the calculated linewidths in Ge and Si show that the socalled EWC scheme is more seeming than the socalled MWC scheme. The difference is expected to disappear if we take into account all the higher order perturbation terms or start with the many body formalism in the complete scheme.     

FTIR-spectroscopy as a highly sensitive technique to study adsorption and desorption on ionic film and single crystal surfaces

Sample/spectrum relationships are investigated using both a low resolution rapid-scanning NIR monochromator and a Fourier transform instrument capable of high resolution and are evaluated in terms of whether or not the resolution of the instrument is sufficient for measuring the natural bandwidths corresponding to the sample. Based on the sample/spectrum relationship a criterion is developed which must be followed in order to apply either derivative spectroscopy or deconvolution to enhance the resolution of overlapped bands without generating spectral artifacts.     

Complex of cesium and rubidium fluorides with bromine trifluoride

Vibrational spectra are reported for the new complexes CsF·3BrF₃, RbF·3BrF₃, and RbF·2BrF₃ and the previously known complex CsF·2BrF₃. The spectra suggest that these compounds are salts having general formulas M⁺Br₃F^?₁₀ and M⁺Br₂F^?₇.     

Computer-Assisted Solution of Chemical Problems—The Historical Development and the Present State of the Art of a New Discipline of Chemistry

The topic of this article is the development and the present state of the art of computer chemistry, the computer-assisted solution of chemical problems. Initially the problems in computer chemistry were confined to structure elucidation on the basis of spectroscopic data, then programs for synthesis design based on libraries of reaction data for relatively narrow classes of target compounds were developed, and now computer programs for the solution of a great variety of chemical problems are available or are under development. Previously it was an achievement when any solution of a chemical problem could be generated by computer assistance. Today, the main task is the efficient, transparent, and non-arbitrary selection of meaningful results from the immense set of potential solutions—that also may contain innovative proposals. Chemistry has two aspects, constitutional chemistry and stereochemistry, which are interrelated, but still require different approaches. As a result, about twenty years ago, an algebraic model of the logical structure of chemistry was presented that consisted of two parts: the constitution-oriented algebra of be- and r-matrices, and the theory of the stereochemistry of the chemical identity group. New chemical definitions, concepts, and perspectives are characteristic of this logic-oriented model, as well as the direct mathematical representation of chemical processes. This model enables the implementation of formal reaction generators that can produce conceivable solutions to chemical problems—including unprecedented solutions—without detailed empirical chemical information. New formal selection procedures for computer-generated chemical information are also possible through the above model. It is expedient to combine these with interactive methods of selection. In this review, the Munich project is presented and discussed in detail. It encompasses the further development and implementation of the mathematical model of the logical structure of chemistry as well as the experimental verification of the computer-generated results. The article concludes with a review of new reactions, reagents, and reaction mechanisms that have been found with the PC-programs IGOR and RAIN.     

Separation of closely related structural isomers by inclusion complexation with tailor-made host compounds. Crystal structures of 2,2-di (p-hydroxyphenyl) propane and Its 1:1 complex withp-cresol

The crystal structures of the 2,2-di(p-hydroxyphenyl)propane host and its 1:1 adducts withm-andp-cresol guests have been studied. The preferential complexation of this host withp-cresol overm-cresol is related to the opposite trend exhibited by 1,1-di(p-hydroxyphenyl)cyclohexane; both hosts can separate effectively the two cresols from their liquid mixture by crystalline inclusion. A plausible explanation of the different inclusion features is provided by examining the intermolecular association in the corresponding solids. The analysed structures are stabilized by strong and continuous H-bonding between the constituent entities along two dimensions, and by weak van der Waals forces along the third axis. The p-cresol complex of the title host reveals a unique arrangement within and a more efficient packing of the layered structure, and thus represents a more stable and less soluble crystal lattice than itsm-cresol analog. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82099 (8 pages).     

The Jacobian problem as a system of ordinary differential equations

LetP=x ⁿ +P _n?1(y)x ^n?1+…+P ₀(y),Q=x ^m +Q _m?2(y)x ^m?2+…+Q ₀(y) belong toK[x, y], whereK is a field of characteristic zero. The main result of this paper is the following: Assume thatP _x Q _y ?P _y Q _x =1. Then:*

1. K[Q _m?2(y), …,Q ₀(y)]=K[y],
2. K[P, Q]=K[x, y] ifQ=x ^m +Q _k (y)x ^k +Q _r (y)x ^r