Iterated Differential Forms IV: C-Spectral Sequence

For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the algebra of secondary iterated differential forms on (O,C). This allows to develop secondary tensor analysis on generic diffieties, some simplest elements of which are sketched here. The presented here general theory will be specified to infinite jet spaces and infinitely prolonged PDEs in subsequent notes.Comment: 8 pages, submitted to Math. Dok

Domains in Infinite Jets: C-Spectral Sequence

Domains in infinite jets present the simplest class of diffieties with boundary. In this note some basic elements of geometry of these domains are introduced and an analogue of the C-spectral sequence in this context is studied. This, in particular, allows cohomological interpretation and analysis of initial data, boundary conditions, etc, for general partial differential equations and of transversality conditions in calculus of variations. This kind applications and extensions to arbitrary diffieties will be considered in subsequent publications.Comment: 7 pages; no proofs give

Iterated Differential Forms VI: Differential Equations

We describe the first term of the $\Lambda_{k-1}\mathcal{C}$--spectral sequence (see math.DG/0610917) of the diffiety (E,C), E being the infinite prolongation of an l-normal system of partial differential equations, and C the Cartan distribution on it.Comment: 8 pages, to appear in Dokl. Mat

Iterated Differential Forms III: Integral Calculus

Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms are computed. Various applications and the integral calculus over the algebra $\Lambda_{\infty}$ will be discussed in subsequent notes.Comment: 7 pages, submitted to Math. Dok

Iterated Differential Forms II: Riemannian Geometry Revisited

A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.Comment: 12 pages, extended version of the published note Dokl. Math. 73, n. 2 (2006) 18

Do CDS spreads reflect default risks? Evidence from UK bank bailouts

CDS spreads are generally considered to reflect the credit risks of their reference entities. However, CDS spreads of the major UK banks remained relatively stable in response to the recent credit crisis. We suggest that this can be explained by changes in loss given default (LGD). To obtain the result we first derive the probabilities of default from stock option prices and then determine the LGD consistent with actual CDS spreads. Our results reveal a significant decrease in the LGD of bailed out banks over the observed period in contrast to banks which were not bailed out and non-financial companies

Analytical Representation of the Longitudinal Hadronic Shower Development

The analytical representation of the longitudinal hadronic shower development from the face of a calorimeter is presented and compared with experimental data. The suggested formula is particularly useful at designing, testing and calibration of huge calorimeter complex like in ATLAS at LHC.Comment: 5 pages, 1 figur

Scalar differential invariants of symplectic Monge–Ampère equations

All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère PDEs with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. A series of invariant differential forms and vector fields are also introduced: they allow one to construct numerous scalar differential invariants of higher order. The introduced invariants give a solution to the symplectic equivalence problem for Monge-Ampère equations

Non-Compensation of the Barrel Tile Hadron Module-0 Calorimeter

The detailed experimental information about the electron and pion responses, the electron energy resolution and the e/h ratio as a function of incident energy E, impact point Z and incidence angle $\Theta$ of the Module-0 of the iron-scintillator barrel hadron calorimeter with the longitudinal tile configuration is presented. The results are based on the electron and pion beams data for E = 10, 20, 60, 80, 100 and 180 GeV at $\eta$ = -0.25 and -0.55, which have been obtained during the test beam period in 1996. The results are compared with the existing experimental data of TILECAL 1m prototype modules, various iron-scintillator calorimeters and with some Monte Carlo calculations.Comment: 33 pages, 20 figure