The credit risk(+) model with general sector correlations

We consider an enhancement of the credit risk+ model to incorporate correlations between sectors. We model the sector default rates as linear combinations of a common set of independent variables that represent macro-economic variables or risk factors. We also derive the formula for exact VaR contributions at the obligor level.

On Calculation Of Breakdown Voltages Of Mixtures Of Electron Attaching Gases

In this paper we report the analysis of dc breakdown tests on mixtures of CC12F2, SF6, C-C4F8, 2-C4F8, N2, C02, CF4, CHF3, and 1,1,1-CH3CF3 gases on the basis of the NKH formula Vmix=k(pd)aNbUC developed by us earlier for the binary mixtures of SF6 with air, N2, N20, and CO2. It is shown that while a and c have the values 0.915 and 0.850 respectively as earlier, k and b depend on the component gases. There is a good agreement between the calculated values on the basis of the formula and measured values reported in the literature.

A computational algorithm for the verification of tautologies in propositional calculus

A computational algorithm (based on Smullyan's analytic tableau method) that varifies whether a given well-formed formula in propositional calculus is a tautology or not has been implemented on a DEC system 10. The stepwise refinement approch of program development used for this implementation forms the subject matter of this paper. The top-down design has resulted in a modular and reliable program package. This computational algoritlhm compares favourably with the algorithm based on the well-known resolution principle used in theorem provers.

On Calculation Of Breakdown Voltages Of Mixtures Of Electron Attaching Gases

In this paper we report the analysis of dc breakdown tests on mixtures of CC12F2, SF6, C-C4F8, 2-C4F8, N2, C02, CF4, CHF3, and 1,1,1-CH3CF3 gases on the basis of the NKH formula Vmix=k(pd)aNbUC developed by us earlier for the binary mixtures of SF6 with air, N2, N20, and CO2. It is shown that while a and c have the values 0.915 and 0.850 respectively as earlier, k and b depend on the component gases. There is a good agreement between the calculated values on the basis of the formula and measured values reported in the literature.

Superstructures exhibited by oxides of the aurivillius family, (Bi2O2)2+ (Anâ 1BnO3n+1)2â

Bi5Ti3FeO15 and Bi7Ti3Fe3O21 which are n=4 and n=6 members of the family of oxides of the general formula (Bi2O2)2+(An−1BnO3n+1)2− show unusual superstructures, possibly due to cation ordering. Bi5Ti3FeO15; Bi7Ti3Fe3O21; oxides.

Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

Stochastic kinetics of ribosomes: Single motor properties and collective behavior

Syntheses of protein molecules in a cell are carried out by ribosomes.A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an exact analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a Michaelis-Menten-type'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechanochemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in three-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.

Calculation of Sparking Potentials of SF6 and SF6-GAS Mixtures in Uniform and Non-Uniform Electric Fields

A simple formula is developed to predict the sparking potentials of SF6 and SF6-gas mixture in uniform and non-uniform fields. The formula has been shown to be valid over a very wide range from 1 to 1800 kPa·cm of pressure and electrode gap separation for mixtures containing 5 to 100% SF6. The calculated values are found to be in good agreement with the previously reported measurements in the literature. The formula should aid design engineers in estimating electrode-spacings and clearances in power apparatus and systems.

Interaction of Metal Ions with 2'-Deoxyribonucleotides. Crystal and Molecular Structure of a Cobalt(l1) Complex with 2'-Deoxyinosine 5'-Monophosphate

The crystal structure of the cobalt( 11) complex with 2'-deoxyinosine 5'-monophosphate (5'- dlMP), [Co(5'-dlMP) (H,0),]-2H20, has been analysed by X-ray diffraction. The complex crystallizes in the space group P2,2,2, with a = 6.877(3), b = 10.904(2), c = 25.421 (6) A, and Z = 4. The structure was solved by the heavy-atom method and refined to an R value of 0.043 using 1 776 unique reflections. The cobalt ion binds only to the 6-oxopurine base of the nucleotide at the N(7) position, the octahedral co-ordination of the metal being completed by five water oxygens. The phosphate oxygens are involved in hydrogen bonding with the co-ordinated water molecules. The structure is closely similar to that of the corresponding ribonucleotide complex. The nucleotide has the energetically preferred conformation: an anti base, a C(3') -endo sugar pucker, and a gauche-gauche conformation about the C(4')-C( 5') bond. The significance of sugar puckering in the monomeric complexes of general formula [ M (5'-nucleotide) (H20),] is explained in terms of the structural requirements for metal-water-phosphate bridging interactions.

Magnetic interactions in the oxide systems LaNi1-xMxO3 (M = Cr, Fe, or Co)

Magnetic susceptibilities of several members of the series of oxides of the general formula LaNi1-xMxO3 (M = Cr, Fe, or Co) are reported. The oxides show evidence for interesting ferrimagnetic (Cr and Co) and antiferromagnetic (Fe) interactions.

Intensity of a Raman Overtone Band

Placzek [1] was the first to derive general expressions for the intensities of overtones in case of Raman scattering. He assumed electrical anharmonicity. However, he left the expressions for the derivations of the polarizability tensor undetermined. In 1941, a classical and semiempirical theory was developed by Wolkenstein [2]. He assumed the validity of the additivity of bond polarizabilities. However, the expressions derived by him for the intensities of overtones remain yet to be verified. It is the purpose of this paper to derive a formula for Raman polarizability tensor for overtones of (intramolecular) vibrational spectra along the lines of Kondilenko et al. [3,4].

Geometrical interpretation of Inönü-Wigner contractions

The Inönü-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincaré, and Galilean groups.

X-ray studies on crystalline complexes involving amino acids. IV. The structure of L-arginine L-ascorbate

L-Arginine ascorbate, C6HIsN40+.C6H706, a 1"1 crystalline complex between the amino acid arginineand the vitamin ascorbic acid, crystallizes in the monoclinic space group P21 with two formula units in a cell of dimensions a = 5.060 (8), b = 9.977 (9), c = 15.330 (13) A, fl = 97.5 (2) °. The structure was solved by the symbolic addition procedure and refined to an R of 0.067 for 1501 photographically observed reflec- tions. The conformation of the arginine molecule in the structure is different from any observed so far. The present structure provides the first description of the ascorbate anion unaffected by the geometrical constraints and disturbances imposed by the requirements of metal coordination. The lactone group and the deprotonated enediol group in the anion are planar and the side chain assumes a conformation which appears to be sterically the most favourable. In the crystals, the arginine molecules and the ascorbate anions aggregate separately into alternating layers. The molecules in the arginine layer are held together by interactions involving a-amino and ~t-carboxylate groups, a situation analogous to that found in proteins. The two layers of unlike molecules are interconnected primarily through the interactions of the side-chain guanidyl group of arginine with the ascorbate ion. These involve a specific ion-pair interaction accompanied by two convergent hydrogen bonds and another pair of nearly parallel hydrogen bonds.

Studies on crystalline complexes involving amino acids. V. The structure of L-serine-L-ascorbic acid

L-Serine-L-ascorbic acid, C3HTNOa. C6HsO6, a 1:1 complex between the amino acid serine and the vitamin ascorbic acid, crystallizes in the orthorhombic space group P2~2~2~ with four formula units in a cell of dimensions a = 5.335(3), b = 8.769(2), c = 25.782 (5) A. The structure was solved by direct methods and refined by full-matrix least squares to an R of 0.036 for 951 observed reflections. Both molecules are neutral in the structure. The conformation of the serine molecule is different from that observed in the crystal structures of L-serine, DL-serine and L-serine monohydrate. The enediol group in the ascorbic acid molecule is planar, whereas significant departures from planarity are observed in the lactone group. The conformation of this molecule is similar to that observed in arginine ascorbate. The unlike molecules aggregate into separate columns in the crystal structure. The columns are held together by hydrogen bonds. Among these, a pair of hydrogen bonds between the enediol group of ascorbic acid and the carboxylate group of serine provides a possible model for a specific interaction between ascorbic acid and a carboxylate ion.

Crystal Physics, Diffraction, Theoretical and General Crystallography

A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method. The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them. The theoretical values are in good agreement with those obtained by earlier workers from computer simulations. The present method makes it easier to optimize the number and the actual wavelengths to be employed in the multiwavelength method. The maximum benefits of this method are expected in experiments employing synchrotron radiation or neutrons.