Optimal selectors for stochastic linear programs

The “distribution problem” of stochastic linear programming consists in answering the following two questions: Is the optimal value of a given stochastic linear program—regarded as a function—measurable, and if so, what is its distribution? In the present note we make use of a general selection theorem to answer the first question positively. By this approach, an answer to the second question is obtained—at least theoretically—at the same time.     

The rigidity of the surface of phase separation in the ising ferromagnet

A model due to Onsager and Temperley for the interface between thermodynamic phases in classical lattice gases is examined. It is found that a field is needed for stabilisation in two dimensions; in three dimensions, on the other hand, the interface is localised, unlike the drumhead model without cutoff.     

Mehrphononen Ramanprozesse in ultramikroskopischen Streuzentren von LiF-Einkristallen

Stokes-Ramanspectra of ultramicroscopic scattering centres in LiF single crystals excited by a focussed 2 mW He-Ne-gaslaser radiating at 632.8 nm reveal a striking difference in their structure to those formerly obtained with a 20 mW laser. Ten more lines appear and the spectrum changes its shape. One set of lines very closely corresponds to the theoretically predictable positions of those of the two-phonon processes of the second order Ramaneffect in the ideal crystal lattice. Other lines are due to three-phonon processes with zero momentum transfer. This is corroborated by ultrasonic measurements ofde Klerk andKlemens and structural disparities in the spectra found at different power levels.     

Solving stochastic dynamic programming problems by linear programming — An annotated bibliography

Summary As has been known for a long time, stochastic dynamic decision processes with finite state and action spaces can be handled by policy and value iteration, both typical dynamic programming techniques, as well as by linear programming. In the present paper, the most important results concerning the latter are reported and an outlook on more general settings is given.

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Zusammenfassung Seit langem ist bekannt, daß zur Optimierung stochastischer dynamischer Entscheidungsprozesse im Falle endlicher Zustands- und Aktionenräume neben den für die dynamische Optimierung typischen Verfahren der Politik- und Wertiteration auch die lineare Programmierung herangezogen werden kann. In der vorliegenden Arbeit werden die wichtigsten diesbezüglichen Resultate referiert und ein Ausblick auf allgemeinere Ansätze gegeben.

     

Decay rates of solutions to thermoviscoelastic plates with memory

We consider the thermoelastic plate under the presence of along range memory. We find uniform rates of decay (in time)of the energy, provided that suitable assumptions on the relaxationfunctions are given. Namely, if the relaxation decays exponentiallythen the first order energy also decays exponentially. Whenthe relaxation g satisfies -c₁g(t)^1+1/_p g'(t) -c_og(t)^1+1/_p; and g,g^1-1/_p L¹ (R) withp > 2 then the energy decays as 1/(1+t)^p. A new Liapunov functionalis built for this problem.     

Lattice models of hydrogen-bonded solvents. II

We consider a lattice model of a binary mixture in which each molecule of one component can form zero, one, or two bonds to molecules of the same species on neighboring vertices of the square lattice. We allow the energy of molecules with two bonds to depend on the valence angle, thus generalizing the first paper in this series. If straight polymeric configurations are favored over all others, then a phase transition occurs for low enough temperature. On the other hand, if bent configurations are favored, there is no phase transition. Analogous results are obtained for the hexagonal lattice, where we distinguish energetically betweencis andtrans isomerism of four bonded molecules.Supported by the Danish Science Foundation under grant 511-3635.     

Calculations of Isoelectronic Series of He Using Noninteger n‐Slater Type Orbitals in Single and Double Zeta Approximations

Using integer and noninteger n-Slater type orbitals in single- and double-zeta approximations, the Hartree-Fock-Roothaan calculations were performed for the ground states of first ten cationic members of the isoelectronic series of He atom. All the noninteger parameters and orbital exponents were fully optimized. In the case of noninteger n-Slater type orbitals in double zeta basis sets, the results of calculations obtained are more close to the numerical Hatree-Fock values and the average deviations of our ground state energies do not exceed 2×10^－6 hartrees of their numerical results.