8,547 research outputs found
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
Iterated Differential Forms I: Tensors
We interpret tensors on a smooth manifold M as differential forms over a
graded commutative algebra called the algebra of iterated differential forms
over M. This allows us to put standard tensor calculus in a new differentially
closed context and, in particular, enriches it with new natural operations.
Applications will be considered in subsequent notes.Comment: 9 pages, extended version of the published note Dokl. Math. 73, n. 2
(2006) 16
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
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 will be discussed in subsequent notes.Comment: 7 pages, submitted to Math. Dok
Iterated Differential Forms VI: Differential Equations
We describe the first term of the --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 V: C-Spectral Sequence on Infinite Jet Spaces
In the preceding note math.DG/0610917 the
--spectral sequence, whose first term is composed of
\emph{secondary iterated differential forms}, was constructed for a generic
diffiety. In this note the zero and first terms of this spectral sequence are
explicitly computed for infinite jet spaces. In particular, this gives an
explicit description of secondary covariant tensors on these spaces and some
basic operations with them. On the basis of these results a description of the
--spectral sequence for infinitely prolonged PDE's
will be given in the subsequent note.Comment: 9 pages, to appear in Math. Dok
Major Landmark in the Investigation of Outer Space
Press conference on Lunik X, and geochemical assessment of dat
The effect of temperature and pressure on the distribution of iron group elements between metal and olivine phases in the process of differentiation of protoplanetary material
The distribution patterns of Ni, Co, Mn, and Cr were studied in olivines of various origins: from meteorites (chondrites, achondrites, pallasites), which are likely analogs of the protoplanetary material, to peridotite inclusions in kimberlite pipes, which are analogs of mantle material. According to X-ray microanalysis data, nickel is concentrated in peridotite olivines, while manganese is concentrated in meteoritic olivines. The maximum chromium content was found in ureilites, which were formed under reducing conditions. Experiments at pressures of 20 to 70 kbar and temperatures of 1100 to 2000 C have shown that in a mixture of olivine and Ni metal or NiO, nickel enters the silicate phase, displacing Fe into the metallic phase. Equilibrium temperatures were estimated from the Fe, Ni distribution coefficients between the metal and olivine: 1500 K for pallasites, 1600 K for olivine-bronzite H6 chondrites, 1200 K for olivine-hypersthene L6, 900 K for LL6, and 1900 K for ureilites (at P = 1 atm). The equilibrium conditions of peridotites are close to T = 1800 K and P over 100 kbar. It is concluded that there is a sharp difference between the conditions of differentiation of the protoplanetary material at the time meteorites were formed and the conditions of differentiation of the planets into concentric layers
Low-temperature specific heat of real crystals: Possibility of leading contribution of optical and short-wavelength acoustical vibrations
We point out that the repeatedly reported glass-like properties of
crystalline materials are not necessarily associated with localized (or
quasilocalized) excitations. In real crystals, optical and short-wavelength
acoustical vibrations remain damped due to defects down to zero temperature. If
such a damping is frequency-independent, e.g. due to planar defects or charged
defects, these optical and short-wavelength acoustical vibrations yield a
linear-in- contribution to the low-temperature specific heat of the crystal
lattices. At low enough temperatures such a contribution will prevail over that
of the long-wavelength acoustical vibrations (Debye contribution). The
crossover between the linear and the Debye regime takes place at , where is the concentration of the defects responsible for the
damping. Estimates show that this crossover could be observable.Comment: 5 pages. v4: Error in Appendix corrected, which does not change the
main results of the pape
Algebraic theories of brackets and related (co)homologies
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets
in the category of modules over a commutative algebra is described. Some
related structures and (co)homology invariants are discussed, as well as
applications to geometry.Comment: 14 pages; v2: minor correction
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