products of two involutions in classical groups of characteristic 2 in a corresponding result for fields not of characteristic 2 wonenburger showed in 6 that every orthogonal transformation is the product of two orthogonal involutions whereas every symplectic transformation is the product of two skew symplectic involutions a skew symplectic transformation t satisfies b tu tu u u for u v in v it follows from our theorem that if k is a finite field of even characteristic each element of the symplectic group or of the two nonisomorphic orthogonal groups is conjugate to its inverse and thus the complex characters of these three families of finite groups are all real valued 583 0021 8693 81 080583 09 02 00 0

from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

isotropic isotopy and symplectic null sets capacity is an important numerical invariant of symplectic manifolds this paper studies when a subset of a symplectic manifold is null i e can be removed without affecting the ambient capacity after examples of open null sets and codimension 2 non null sets geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow it follows that sets of dimension 0 and 1 are null for isotropic sets of higher dimensions obstructions to the perturbation are found in homotopy groups of the orthogonal groups

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

a new numerical approach of a lubrication free boundary problem a combination of a semidiscretized scheme and an iterative method is applied to a free boundary problem the considered problem is issued from a cavitation model in lubrication theory and treats on the determination of the cavitation area estimates l w which provide the convergence of the approximated solution is obtained finally some numerical test examples are presented to illustrate the good performance of the method

a new method for cavitations approximation in some general lubrication devices we apply in this paper a new numerical method to approximate cavitation phenomenons in some general devices in lubrication theory the proposed method is based on some conservation laws satisfied by lubricants contained in the devices and it combines a method of lines with an iterative algorithm solving at each step a linear problems with regular solutions some l estimations providing convergence results are given and numerical applications to an elastic journal bearing are presented to show the good performance of the method

solvability of dirac type equations abstract this paper develops a weighted l 2 method for the half dirac equation for dirac bundles over closed riemann surfaces we give a sufficient condition for the solvability of the half dirac equation in terms of a curvature integral applying this to the dolbeault dirac operator we establish an automatic transversality criteria for holomorphic curves in kahler manifolds on compact riemannian manifolds we give a new perspective on some well known results about the first eigenvalue of the dirac operator and improve the estimates when the dirac bundle has a z 2 grading on riemannian manifolds with cylindrical ends we obtain solvability in the l 2 spaces with suitable exponential weights while allowing mild negativity of the curvature

hamiltonian collapsing of irrational lagrangian submanifolds with small first betti number among the main symplectic invariants of a closed lagrange submanifoldl of the cotangent of n is the tubular radiusr l defined as the smallest tube d r n 1 of n t n in whichl can be pushed by an hamiltonian diffeotopy of n we show here using pseudo holomorphic techniques that such a submanifold cannot collapse if the first betti number ofl is smaller than 3 and if the maslov class ofl does not vanish in other words r l is then strictly positive and one can actually give an explicit lower bound in terms of the liouville and maslov classes ofl

an iterative method for solving a free boundary problem for an infinite journal bearing the hydrodynamic lubrication is concerned with a particular form of creeping flow between surfaces in relative motion where cavitation takes place the determination of the cavitation area is then of a fundamental importance in order to compute the caracteristics of the mechanisms a one dimensional nonlinear elliptic problem is considered the approximate solution is obtained through a process of successive approximations where at each step the non homogenous term of the approximated problem search the cavitation region

convergence of yang mills higgs fields in this paper we study the convergence of yang mills higgs ymh fields defined on fiber bundles over riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the underlying surface is allowed to vary we show that away from the nodes the ymh fields converges up to gauge to a smooth ymh field modulo finitely many harmonic spheres while near the nodes where the conformal structure degenerates the ymh fields converges to a pair consisting of a flat connection and a twisted geodesic with potential in particular we generalize the recent compactness results on both harmonic maps from surfaces and twisted holomorphic curves to general ymh fields