On the integration of data and mathematical modeling languages

This paper examines ways in which the addition of data modeling features can enhance the capabilities of mathematical modeling languages. It demonstrates how such integration is achieved as an application of the embedded languages technique proposed by Bhargava and Kimbrough [4]. Decision-making, and decision support systems, require the representation and manipulation of both data and mathematical models. Several data modeling languages as well as several mathematical modeling languages exist, but they have different sets of these capabilities. We motivate with a detailed example the need for the integration of these capabilities. We describe the benefits that might result, and claim that this could lead to a significant improvement in the functionality of model management systems. Then we present our approach for the integration of these languages, and specify how the claimed benefits can be realized.The author's work on this paper was performed in conjunction with research funded by the Naval Postgraduate School.     

Pricing under quality of service uncertainty: Market segmentation via statistical QoS guarantees

This article examines how performance-contingent pricing schemes with long-term statistical performance guarantees can be applied to many IT services. We study two forms of performance-contingent pricing, with rebate proportional to failure rate and fixed rebate for below-threshold performance. We show that threshold-performance contingency pricing can increase both profits and fairness (customers who receive higher benefits pay higher effective price) relative to standard pricing. But an even better solution is to offer a menu of performance guarantees: this can increase the firm’s profit and segment the market. Only service providers whose performance level is sufficiently better than the industry standard can benefit from this pricing mechanism.     

The shapes of the LIII X-ray absorption discontinuity of rhenium in compounds

The X-ray L_III absorption edge of rhenium in the pure metal and in two compounds, namely, K₂ReCl₆ and KReO₄ has been studied using a Cauchois type bent crystal spectrograph of 40 cm diameter. The splitting of the main absorption discontinuity has been observed for the first time in the compounds. This splitting and the edge structure of the Re L_III discontinuity in the compounds have been interpreted on the basis of molecular orbital diagrams. The crystal field splitting, Δ, has been determined experimentally in both the compounds in the solid state.     

X-ray spectroscopic study of chemical bonding in MnSe2 and CoSe2

X-ray absorption study of two intermetallic compounds MnSe₂ and CoSe₂ has been carried out using a Cauchois type bent crystal spectrograph. The metal K absorption edges in both the compounds are found to shift toward the high energy side with respect to the discontinuities in the pure metals. On the other hand, the Se K absorption edge in both these compounds is found to shift toward the lower energies. Emission study of the compound MnSe₂ has shown that the Mn Kβ ₅ band in this compound is shifted toward the high energy side with respect to that in the pure metal. From the magnetic data and the results obtained in this work it is possible to obtain the chemical bonding pictures in these compounds. For MnSe₂ the bondings sp ³ d ² for the metal atom andsp ³ for the metalloid atom have been suggested. For CoSe₂ the bondings appear to bed ² sp ³ for the metal atom andsp ³ for the metalloid atom. These bondings are compatible with the pyrite type structure of these compounds. It is possible to explain the electrical behaviour of the compounds on the basis of these bonding pictures.     

Plasmon excitation in the x ray absorption process

A simple approach is developed to study the excitation of a plasmon due to valence electronic correlations in the x ray absorption process. Assuming a complete separation between the core and the valence electrons, we introduce the plasmons in the system Hamiltonian externally according to the Bohm-Pines collective formalism and carry out the corresponding canonical transformations to separate the x ray photonplasmon-electron term. According to our calculations, the relative intensity of the plasmon process with respect to the main absorption, which represents single particle excitations is 0·12 times the interelectronic separation measured in Bohr radii. The theoretical estimates of the plasmon intensity agree satisfactorily with the experimental values for the Mn K and the Re L_III absorption discontinuities. The shape of the plasmon absorption band resembles the main absorption edge, if the wave vector dependence of the plasmon frequency is neglected. The intensity of the second plasmon harmonic is about 3 per cent of the first plasmon satellite spectrum. The electron plasmon interaction modifies the shape of the plasmon spectrum.     

Practical synthesis of chiral 9,9'-spirobixanthene-1,1'-diol

A concise four-step synthesis of 9,9'-spirobixanthene-1,1'-diol is reported, featuring a practical preparation at large scale without the use of column chromatography purification. Co-crystallization with N-benzylcinchonidinium chloride and N-benzylquininium chloride rendered the optically pure product in both enantiomers.     

Aryl trihydroxyborates: easily isolated discrete species convenient for direct application in coupling reactions

A conceptually and practically simple alternative approach to the use of arylboron species as the organometallic component in cross-coupling processes is described whereby trihydroxyborate salts are isolated and directly employed. The protocol derives practical benefit from the ease and convenience of the isolation and subsequent use of the discrete borate salts, eliminates the need for additional base, and aids the use of correct reaction stoichiometry.     

The Conjugacy Class Number k(G): A Different Perspective

For a finite group G, let m(G) denote the least positive integer such that the union of any m(G) distinct nontrivial conjugacy classes of G together with the identity of G is a subgroup of G. We prove that m(G) = k(G) ?1 for all m(G) ≥2.