Isotope effects in Raman spectra of crystalline alkali-metal chlorates and bromates

Halogen and oxygen atom isotope effects have been observed in Raman spectra of single crystal NaClO₃, KClO₃, NaBrO₃, and KBrO₃. Orientational splitting of ³⁵Cl¹⁶O₂¹⁸O^? and ³⁷Cl¹⁶O₂¹⁸O^? ion vibrational modes was observed in KClO₃. Splitting of the v₁ mode of ⁷⁹Br and ⁸¹Br isotopes of singly substituted ¹⁷O and ¹⁸O bromate ions in NaBrO₃ and KBrO₃ is on the order of 1.5 cm^?1 in agreement with a calculation of isotopic frequencies. However, the predicted splitting between v₁ of the major isotopes, ⁷⁹Br¹⁶O₃^? and ⁸¹Br¹⁶O₃^?, was not observed, and the results of a band contour analysis suggest that a single k = 0 phonon is derived from the totally symmetric stretching mode of both species.     

Vibrational spectrum, ab initio calculation, conformational equilibria and torsional modes of 1,3-dibromopropane

The infrared and Raman spectrum of 1,3-dibromopropane is reported in the crystalline, liquid and gaseous states. These measurements are compared to the results of ab initio calculations carried out using the 6-31+g* Gaussian basis set for a restricted Hartree-Fock computation. The calculation was repeated using second order Moeller-Ploesset perturbation theory to accommodate electron correlation using the 6-31 g* basis set. The three most stable conformers are GG (C2), AG (C1) and AA (C2v), where A and G stand for anti and gauche orientations of the bromomethyl group relative to the plane of the carbon atoms. The point group symmetry of each structure is given in parentheses. The fourth conformer, G'G (Cs) is of such high energy that it is not observed experimentally in isotropic media in either the infrared or Raman spectrum. In the crystalline state, comparison of the infrared and Raman spectrum with that calculated for the C2 conformer shows that only the GG (C2) conformer survives, and the doublet structure of many of the bands in the spectrum indicates at least two molecules per unit cell. The ab initio calculations predict and the temperature dependence of the Raman spectrum of the liquid confirms that the stability order is C2相似文献   

Optimality of monotonic policies for two-action Markovian decision processes,with applications to control of queues with delayed information

We consider a discrete-time Markov decision process with a partially ordered state space and two feasible control actions in each state. Our goal is to find general conditions, which are satisfied in a broad class of applications to control of queues, under which an optimal control policy is monotonic. An advantage of our approach is that it easily extends to problems with both information and action delays, which are common in applications to high-speed communication networks, among others. The transition probabilities are stochastically monotone and the one-stage reward submodular. We further assume that transitions from different states are coupled, in the sense that the state after a transition is distributed as a deterministic function of the current state and two random variables, one of which is controllable and the other uncontrollable. Finally, we make a monotonicity assumption about the sample-path effect of a pairwise switch of the actions in consecutive stages. Using induction on the horizon length, we demonstrate that optimal policies for the finite- and infinite-horizon discounted problems are monotonic. We apply these results to a single queueing facility with control of arrivals and/or services, under very general conditions. In this case, our results imply that an optimal control policy has threshold form. Finally, we show how monotonicity of an optimal policy extends in a natural way to problems with information and/or action delay, including delays of more than one time unit. Specifically, we show that, if a problem without delay satisfies our sufficient conditions for monotonicity of an optimal policy, then the same problem with information and/or action delay also has monotonic (e.g., threshold) optimal policies.     

On the convergence of successive approximations in dynamic programming with non-zero terminal reward

This paper considers the convergence of the finite-horizon optimal value functions of dynamic programming to the infinite-horizon optimal value function, when there is a non-zero terminal-reward function. The model and methods follow closely these used by Schäl in a recent paper, in which a terminal reward of zero was assumed. We first present convergence conditions that are direct extensions of Schäl's, then related conditions in which the terminal-reward function is an upper or lower bound for the infinite-horizon optimal value function. Some applications to problems in queueing control are mentioned briefly. We also comment on the relation between our conditions and the more restrictive conditions of strongly convergent and contractive models, and present a very general result concerning uniqueness of the solution to the infinite-horizon optimality equation.

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Zusammenfassung In der Arbeit wird die Konvergenz von Wertfunktionen dynamischer Optimierungsprobleme mit endlichem Planungshorizont gegen die Wertfunktionen bei unendlichem Planungshorizont betrachtet, wobei die Endauszahlung verschieden von Null ist. Modell und Vorgehensweise lehnen sich an entsprechende Resultate von Schäl an für den Fall, daß die Endauszahlung Null ist. Zunächst werden Konvergenzbedingungen angegeben, welche unmittelbare Erweiterungen der Schälschen Ergebnisse sind, gefolgt von Bedingungen, bei denen die Endauszahlung eine obere oder untere Schranke für die Endauszahlung bei unendlichem Planungshorizont ist. Einige Anwendungen auf Probleme der Steuerung von Warteschlangen werden erwähnt. Ferner werden der Zusammenhang zwischen unseren Bedingungen und den restriktiveren Bedingungen bei stark konvergenten und Kontraktions-Modellen erläutert und ein sehr allgemeines Modell über die Eindeutigkeit der Lösung der Optimalitätsgleichung bei unendlichem Planungshorizont angegeben.

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An earlier draft of this paper appeared as: On the Convergence of Successive Approximations and Uniqueness of the Solution to the Functional Equation of Dynamic Programming. IMSOR Report 2190, The Institute of Mathematical Statistics and Operations Research, The Technical University of Denmark, May 1977 (revised, July 1977).

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This research was partially supported by NATO Research Grant No. SRG.SS.5, administered by the NATO Special Programme Panel on Systems Science, and was begun while the author was guest professor at The Institute of Mathematical Statistics and Operations Research at The Technical University of Denmark, January to July, 1977. Further support was provided by the National Science Foundation under Grant No. ENG78-24420.     

A filtered ASTA property

Recently, the PASTA (Poisson Arrivals See Time Averages) property has been extended to ASTA (Arrivals See Time Averages) by eliminating the need for Poisson arrivals and weakening the LAA (Lack of Anticipation Assumption). This paper presents a strengthening of ASTA under the original LAA of Wolff. We consider a stochastic processX with an associated point processN that admits a stochastic intensity and satisfies LAA. Various authors have noted in various contexts that ASTA holds if and only if the arrival intensity is state independent. For a class of point processes that includes doubly stochastic as well as ordinary Poisson processes, we prove that the point process obtained by restricting the processX to any given set of states not only has the same intensity but also the same probabilistic structure as the original point process. In particular, if the original point process is Poisson, the new point process is still Poisson with the same parameter as the original point process. For a discrete-time version, of interest in its own right, we provide a simple proof of a strengthened version of ASTA in discrete time. Unlike other discrete-time versions of ASTA, ours is valid for point processes with stationary but not necessarily independent increments. The continuous-time results are obtained using martingale theory. A corollary is a simple proof of PASTA under conditions that require only that the relevant limits exist. Our results may also provide some insight into characterizing Poisson flows in queueing systems.The research of this author was partially supported by the National Science Foundation under Grant No. DDM-8719825. The Government has certain rights in this material. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.     

Concentration-dependent depolarized Raman spectra of HCl and DCl in solution in liquid carbon dioxide

The depolarized component of Paman scattering by pure liquid HCl and DCl and of solutions of these acid halides in liquid CO₂ are reported. At room temperature the band contours show no S branch intensity in pure acid halide liquid, but in solution in liquid CO₂ and S branch is increasingly evident with increasing CO₂ concentration. The frequency shifts are a function of the dielectric constant and refractive index of the solution. Reorientational correlation functions calculated from the anisotropic scattering decay more slowly in the first few tens of femtoseconds than predicted for monomeric acid halides, suggesting contribution to the composite correlation function by species of larger moments of inertia but vibrational frequencies identical with those of the monomers.