1,599 research outputs found
New reductions of integrable matrix PDEs: -invariant systems
We propose a new type of reduction for integrable systems of coupled matrix
PDEs; this reduction equates one matrix variable with the transposition of
another multiplied by an antisymmetric constant matrix. Via this reduction, we
obtain a new integrable system of coupled derivative mKdV equations and a new
integrable variant of the massive Thirring model, in addition to the already
known systems. We also discuss integrable semi-discretizations of the obtained
systems and present new soliton solutions to both continuous and semi-discrete
systems. As a by-product, a new integrable semi-discretization of the Manakov
model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the
elementary function solutions of (a vector/matrix generalization of) the
derivative NLS equation can be expressed as the partial -derivatives of
elementary functions. Explicit soliton solutions are given in the author's
talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida
Serre's "formule de masse" in prime degree
For a local field F with finite residue field of characteristic p, we
describe completely the structure of the filtered F_p[G]-module K^*/K^*p in
characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of
F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's
mass formula in degree p. We also determine the compositum C of all degree p
separable extensions with solvable galoisian closure over an arbitrary base
field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in
the case of the local field F. Our method allows us to compute the contribution
of each character G\to\F_p^* to the degree p mass formula, and, for any given
group \Gamma, the contribution of those degree p separable extensions of F
whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section
Modelling an abrasive wear experiment by the boundary element method
This Note presents a computational technique for simulating friction-induced wear in a tribology experiment on a plan/plan, ring-on-disc contact configuration. The boundary element method results in modest computing times and facilitates the mesh modifications used for tracking the wear profile evolution. A typical wear simulation result is presented and discussed
Tribological and corrosion wear of graphite ring against Ti6Al4V disk in artificial sea water
Severe degradations result from the friction of two antagonists in sea water environment. It is proposed to evaluate materials resistance to wear with a tribocorrosion experimental set-up which is mechanically and electrochemically instrumented. The method is illustrated with graphite and Ti6Al4V.The deposition of graphite on Ti6Al4V samples is observed and modifies the contact characteristics. Processes of graphite wear due to mechanical effect are characterised. Observations clearly indicate that Ti6Al4V degradations depend on the electrochemical potential imposed and more precisely on the electrochemical conditions in the contact zone
N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces
We establish a correspondence between generalized quiver gauge theories in
four dimensions and congruence subgroups of the modular group, hinging upon the
trivalent graphs which arise in both. The gauge theories and the graphs are
enumerated and their numbers are compared. The correspondence is particularly
striking for genus zero torsion-free congruence subgroups as exemplified by
those which arise in Moonshine. We analyze in detail the case of index 24,
where modular elliptic K3 surfaces emerge: here, the elliptic j-invariants can
be recast as dessins d'enfant which dictate the Seiberg-Witten curves.Comment: 42+1 pages, 5 figures; various helpful comments incorporate
Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields
Let be a finite Galois extension of fields with abelian Galois group
. A self-dual normal basis for is a normal basis with the
additional property that for .
Bayer-Fluckiger and Lenstra have shown that when , then
admits a self-dual normal basis if and only if is odd. If is an
extension of finite fields and , then admits a self-dual normal
basis if and only if the exponent of is not divisible by . In this
paper we construct self-dual normal basis generators for finite extensions of
finite fields whenever they exist.
Now let be a finite extension of \Q_p, let be a finite abelian
Galois extension of odd degree and let \bo_L be the valuation ring of . We
define to be the unique fractional \bo_L-ideal with square equal to
the inverse different of . It is known that a self-dual integral normal
basis exists for if and only if is weakly ramified. Assuming
, we construct such bases whenever they exist
Homotopy Lie algebras, lower central series and the Koszul property
Let X and Y be finite-type CW-complexes (X connected, Y simply connected),
such that the rational cohomology ring of Y is a k-rescaling of the rational
cohomology ring of X. Assume H^*(X,Q) is a Koszul algebra. Then, the homotopy
Lie algebra pi_*(Omega Y) tensor Q equals, up to k-rescaling, the graded
rational Lie algebra associated to the lower central series of pi_1(X). If Y is
a formal space, this equality is actually equivalent to the Koszulness of
H^*(X,Q). If X is formal (and only then), the equality lifts to a filtered
isomorphism between the Malcev completion of pi_1(X) and the completion of
[Omega S^{2k+1}, Omega Y]. Among spaces that admit naturally defined
homological rescalings are complements of complex hyperplane arrangements, and
complements of classical links. The Rescaling Formula holds for supersolvable
arrangements, as well as for links with connected linking graph.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol8/paper30.abs.htm
Three embeddings of the Klein simple group into the Cremona group of rank three
We study the action of the Klein simple group G consisting of 168 elements on
two rational threefolds: the three-dimensional projective space and a smooth
Fano threefold X of anticanonical degree 22 and index 1. We show that the
Cremona group of rank three has at least three non-conjugate subgroups
isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein
metric, and we construct a smooth polarized K3 surface of degree 22 with an
action of the group G.Comment: 43 page
Ramification theory for varieties over a local field
We define generalizations of classical invariants of wild ramification for
coverings on a variety of arbitrary dimension over a local field. For an l-adic
sheaf, we define its Swan class as a 0-cycle class supported on the wild
ramification locus. We prove a formula of Riemann-Roch type for the Swan
conductor of cohomology together with its relative version, assuming that the
local field is of mixed characteristic.
We also prove the integrality of the Swan class for curves over a local field
as a generalization of the Hasse-Arf theorem. We derive a proof of a conjecture
of Serre on the Artin character for a group action with an isolated fixed point
on a regular local ring, assuming the dimension is 2.Comment: 159 pages, some corrections are mad
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