Implications of non-feasible transformations among icosahedral hh orbitals

The symmetric group $S_6$ that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group $I$. Owing to the correspondence $h\leftrightarrow d$, the calculation of the Coulomb energies for the icosahedral configurations $h^N$ based on the sequence $O(5) \supset S_6 \supset S_5 \supset I$ can be brought to bear on Racah's classic theory for the atomic d shell based on $SO(5) \supset SO_L(3) \supset I$. Among the elements of $S_6$ is the kaleidoscope operator ${\cal K}$ that rotates the weight space of SO(5) by $\pi/2$. Its use explains some puzzling degeneracies in d^3 involving the spectroscopic terms ^2P, ^2F, ^2G and ^2H.Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5, 99. Revtex, 1 ps figur

Penalty discount rate: I

Monetary policy - United States ; Discount

New methodology for assessing the probability of contaminating Mars

Methodology is proposed to assess the probability that the planet Mars will be contaminated by terrestrial microorganisms aboard a spacecraft. The present NASA methods are extended to permit utilization of detailed information on microbial characteristics, the lethality of release and transport mechanisms, and of other information about the Martian environment. Different types of microbial release are distinguished, and for each release mechanism a probability of growth is computed. Using this new methodology, an assessment was carried out for the 1975 Viking landings on Mars. The resulting probability of contamination for each Viking lander is 6 x 10 to the -6 power, and is amenable to revision as additional information becomes available

Penalty discount rate: II

Monetary policy - United States ; Discount ; Bank reserves

Quantifying Finite Temperature Effects in Atom Chip Interferometry of Bose-Einstein Condensates

We quantify the effect of phase fluctuations on atom chip interferometry of Bose-Einstein condensates. At very low temperatures, we observe small phase fluctuations, created by mean-field depletion, and a resonant production of vortices when the two clouds are initially in anti-phase. At higher temperatures, we show that the thermal occupation of Bogoliubov modes makes vortex production vary smoothly with the initial relative phase difference between the two atom clouds. We also propose a technique to observe vortex formation directly by creating a weak link between the two clouds. The position and direction of circulation of the vortices is subsequently revealed by kinks in the interference fringes produced when the two clouds expand into one another. This procedure may be exploited for precise force measurement or motion detection.Comment: 7 pages, 5 figure

Assessment of the probability of contaminating Mars

New methodology is proposed to assess the probability that the planet Mars will by biologically contaminated by terrestrial microorganisms aboard a spacecraft. Present NASA methods are based on the Sagan-Coleman formula, which states that the probability of contamination is the product of the expected microbial release and a probability of growth. The proposed new methodology extends the Sagan-Coleman approach to permit utilization of detailed information on microbial characteristics, the lethality of release and transport mechanisms, and of other information about the Martian environment. Three different types of microbial release are distinguished in the model for assessing the probability of contamination. The number of viable microbes released by each mechanism depends on the bio-burden in various locations on the spacecraft and on whether the spacecraft landing is accomplished according to plan. For each of the three release mechanisms a probability of growth is computed, using a model for transport into an environment suited to microbial growth

Modeling Uncertainty in Large Natural Resource Allocation Problems

The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. This study introduces a novel numerical method to solve large-scale dynamic stochastic natural resource allocation problems that cannot be addressed by conventional methods. The method is illustrated with an application focusing on the allocation of global land resource use under stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters, the range of land conversion is considerably smaller for the dynamic stochastic model as compared to deterministic scenario analysis. The scenario analysis can thus significantly overstate the magnitude of expected land conversion under uncertain crop yields

Rough set theory applied to pattern recognition of partial discharge in noise affected cable data

This paper presents an effective, Rough Set (RS) based, pattern recognition method for rejecting interference signals and recognising Partial Discharge (PD) signals from different sources. Firstly, RS theory is presented in terms of Information System, Lower and Upper Approximation, Signal Discretisation, Attribute Reduction and a flowchart of the RS based pattern recognition method. Secondly, PD testing of five types of artificial defect in ethylene-propylene rubber (EPR) cable is carried out and data pre-processing and feature extraction are employed to separate PD and interference signals. Thirdly, the RS based PD signal recognition method is applied to 4000 samples and is proven to have 99% accuracy. Fourthly, the RS based PD recognition method is applied to signals from five different sources and an accuracy of more than 93% is attained when a combination of signal discretisation and attribute reduction methods are applied. Finally, Back-propagation Neural Network (BPNN) and Support Vector Machine (SVM) methods are studied and compared with the developed method. The proposed RS method is proven to have higher accuracy than SVM and BPNN and can be applied for on-line PD monitoring of cable systems after training with valid sample data

More on coupling coefficients for the most degenerate representations of SO(n)

We present explicit closed-form expressions for the general group-theoretical factor appearing in the alpha-topology of a high-temperature expansion of SO(n)-symmetric lattice models. This object, which is closely related to 6j-symbols for the most degenerate representation of SO(n), is discussed in detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and Discussion, References adde

Transfer function characterization for HFCTs used in partial discharge detection

High frequency current transformers (HFCTs) are widely employed to detect partial discharge (PD) induced currents in high voltage equipment. This paper describes measurements of the wideband transfer functions of HFCTs so that their influence on the detected pulse shape in advanced PD measurement applications can be characterized. The time-domain method based on the pulse response is a useful way to represent HFCT transfer functions as it allows numerical determination of the forward and reverse transfer functions of the sensor. However, while the method is accurate at high frequencies it can have limited resolution at low frequencies. In this paper, a composite time-domain method is presented to allow accurate characterization of the HFCT transfer functions at both low and high frequencies. The composite method was tested on two different HFCTs and the results indicate that the method can characterize their transfer functions ranging from several kHz to tens of MHz. Results are found to be in good agreement with frequency-domain measurements up to 50 MHz. Measurement procedures for using the method are summarized to facilitate further applications