Overpartitions and real quadratic fields

It is shown that counting certain differences of overpartition functions is equivalent to counting elements of a given norm in appropriate real quadratic fields.     

Yield of 16OS18O from the 18OH initiated oxidation of CS2 in 16O2

The yield of ¹⁶OS¹⁸O from the ¹⁸OH initiated oxidation of CS₂ in ¹⁶O₂ was measured by using a discharge flow reactor coupled to a chemical ionization mass spectrometer. ¹⁶OS¹⁸O is the dominant SO₂ isotopomer produced with a yield of 0.90 ± 0.20 relative to ¹⁸OH loss. The errors are estimates for the uncertainty at the 95% confidence level. The implications of these results to the understanding of the CS₂ oxidation mechanism are discussed. © 1994 John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

A survey of algorithmic methods for partially observed Markov decision processes

A partially observed Markov decision process (POMDP) is a generalization of a Markov decision process that allows for incomplete information regarding the state of the system. The significant applied potential for such processes remains largely unrealized, due to an historical lack of tractable solution methodologies. This paper reviews some of the current algorithmic alternatives for solving discrete-time, finite POMDPs over both finite and infinite horizons. The major impediment to exact solution is that, even with a finite set of internal system states, the set of possible information states is uncountably infinite. Finite algorithms are theoretically available for exact solution of the finite horizon problem, but these are computationally intractable for even modest-sized problems. Several approximation methodologies are reviewed that have the potential to generate computationally feasible, high precision solutions.     

A Bailey lattice

We exhibit a technique for generating new Bailey pairs which leads to deformations of classical -series identities, multiple series identities of the Rogers-Ramanujan type, identities involving partial theta functions, and a variety of representations for -series by number-theoretic objects such as weight 3/2 modular forms, ternary quadratic forms, and weighted binary quadratic forms.

     

Overpartitions

We discuss a generalization of partitions, called overpartitions, which have proven useful in several combinatorial studies of basic hypergeometric series. After showing how a number of finite products occurring in -series have natural interpretations in terms of overpartitions, we present an introduction to their rich structure as revealed by -series identities.

     

Direct evidence of multifractal atmospheric cascades from planetary scales down to 1 km

We use 909 satellite images spanning the scale range 1-5000 km at both visible and infrared wavelengths to show that the variability at all observed scales and at all levels of intensity is very close to that predicted for a direct multiplicative scale invariant cascade starting at planetary scales. To within 1.6%/octave in scale, the observed type of (multi)scaling is very close to that theoretically predicted for universal multifractals, including multifractal phase transitions. Because of the strong vertical stratification, the scaling cannot be isotropic; these findings thus give strong support to the anisotropic "unified scaling" model of atmospheric dynamics.     

Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

Absolute line strengths of 74GeH4 near 5 μm

Line positions and absolute line strengths were measured for 23 Q-branch lines of the ν₃ fundamental of ⁷⁴GeH₄ at 295 K, using an infrared tunable diode laser spectrometer. The spectral range covered was from 2109.9658 to 2110.6218 cm^?1. The average standard deviation of the measured line positions was 0.0006 cm^?1 and that of the line strengths was 3.4%. Vibrational transition dipoles were computed from the measured line strengths, which gave 1226 ± 172 cm^?2 amagat^?1 for the ν₃ integrated band intensity.