3,077 research outputs found
Korteweg-de Vries adiabatic index solitons in barotropic open FRW cosmologies
Applying standard mathematical methods, it is explicitly shown how the
Riccati equation for the Hubble parameter H(\eta) of barotropic open FRW
cosmologies is connected with a Korteweg-de Vries equation for adiabatic index
solitons. It is also shown how one can embed a discrete sequence of adiabatic
indices of the type n^2({3/2}\gamma -1)^2 (\gamma \neq 2/3) in the sech FRW
adiabatic index solitonComment: 5 pages, without figure
Darboux class of cosmological fluids with time-dependent adiabatic indices
A one-parameter family of time dependent adiabatic indices is introduced for
any given type of cosmological fluid of constant adiabatic index by a
mathematical method belonging to the class of Darboux transformations. The
procedure works for zero cosmological constant at the price of introducing a
new constant parameter related to the time dependence of the adiabatic index.
These fluids can be the real cosmological fluids that are encountered at
cosmological scales and they could be used as a simple and efficient
explanation for the recent experimental findings regarding the present day
accelerating universe. In addition, new types of cosmological scale factors,
corresponding to these fluids, are presentedComment: document with the following three latex files: 1) quhm.tex: 17 pages,
10 figs, 16 numbered refs, Honorable Mention GRF 2000, 2) errad.tex: Errata
and Addenda (EaA) of 5 pages with 2 figs enclosed, 3) analogy.tex: Negative
friction of Darboux cosmological fluids of 4 page
Matching Logic
This paper presents matching logic, a first-order logic (FOL) variant for
specifying and reasoning about structure by means of patterns and pattern
matching. Its sentences, the patterns, are constructed using variables,
symbols, connectives and quantifiers, but no difference is made between
function and predicate symbols. In models, a pattern evaluates into a power-set
domain (the set of values that match it), in contrast to FOL where functions
and predicates map into a regular domain. Matching logic uniformly generalizes
several logical frameworks important for program analysis, such as:
propositional logic, algebraic specification, FOL with equality, modal logic,
and separation logic. Patterns can specify separation requirements at any level
in any program configuration, not only in the heaps or stores, without any
special logical constructs for that: the very nature of pattern matching is
that if two structures are matched as part of a pattern, then they can only be
spatially separated. Like FOL, matching logic can also be translated into pure
predicate logic with equality, at the same time admitting its own sound and
complete proof system. A practical aspect of matching logic is that FOL
reasoning with equality remains sound, so off-the-shelf provers and SMT solvers
can be used for matching logic reasoning. Matching logic is particularly
well-suited for reasoning about programs in programming languages that have an
operational semantics, but it is not limited to this
Central values of -functions of cubic twists
We are interested in finding for which positive integers we have rational
solutions for the equation The aim of this paper is to compute the
value of the -function for the elliptic curves .
For the case of prime , two formulas have been computed by
Rodriguez-Villegas and Zagier. We have computed formulas that relate to the square of a trace of a modular function at a CM point. This offers a
criterion for when the integer is the sum of two rational cubes.
Furthermore, when is nonzero we get a formula for the number of
elements in the Tate-Shafarevich group and we show that this number is a square
when is a norm in .Comment: Major rewrite, major improvement in result: showing that the order of
Sha is a squar
Equivariant Elliptic Cohomology and Rigidity
Equivariant elliptic cohomology with complex coefficients was defined
axiomatically by Ginzburg, Kapranov and Vasserot and constructed by Grojnowski.
We give an invariant definition of S^1-equivariant elliptic cohomology, and use
it to give an entirely cohomological proof of the rigidity theorem of Witten
for the elliptic genus. We also state and prove a rigidity theorem for families
of elliptic genera.Comment: 23 page
Supersymmetry of FRW barotropic cosmologies
Barotropic FRW cosmologies are presented from the standpoint of
nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of
differential equations to simple harmonic oscillator differential equations.
Employing the factorization procedure, the solutions of the latter equations
are divided into the two classes of bosonic (nonsingular) and fermionic
(singular) cosmological solutions. We next introduce a coupling parameter
denoted by K between the two classes of solutions and obtain barotropic
cosmologies with dissipative features acting on the scale factors and spatial
curvature of the universe. The K-extended FRW equations in comoving time are
presented in explicit form in the low coupling regime. The standard barotropic
FRW cosmologies correspond to the dissipationless limit K =0Comment: 6 page
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