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The regularity conclusion in Lemma 1.4 is incorrect (G. Pappas gave a counterexample). Regularity of
X must be assumed as a hypothesis, and then the other conclusions follow (see below; also cf. [CEP...
One interesting application of Theorem 0.1 is given in [DG, x3], where it is used to analyze the niteness
of the number of solutions to certain generalized Fermat equations. Another application of T...
We study resolution of tame cyclic quotient singularities
on arithmetic surfaces, and use it to prove that for any subgroup
H μ (Z=pZ)
￡=f§1g the map XH(p) = X1(p)=H ! X0(p) induces
an injection &...
Designing Optical Fibers: Fitting the Derivatives of a Nonlinear Pde-Eigenvalue Problem
Symmetric Indefinite Eigenvalue Gradient Optical Fiber Design
2013/1/30
When trying to fit data to functions of the eigensystem of a pde-eigenvalue problem, such as Maxwell’s equation, numerical differentiation is ineffective and analytic gradients must be supplied. In ou...
Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors
partial hyperbolicity singular-hyperbolicity recurrence decay of correlations local dimension hitting times
2012/4/23
We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue...
Soliton self-frequency blue-shift in gas-filled hollow-core photonic crystal fibers
Soliton self-frequency blue-shift hollow-core photonic crystal fibers
2011/7/7
We show theoretically that the photoionization process in a hollow-core photonic crystal fiber filled with a Raman-inactive noble gas leads to a constant acceleration of solitons in the time domain wi...
Singularity invariants related to Milnor fibers: survey
Singularity invariants Milnor fibers survey
2011/1/21
This brief survey of some singularity invariants related to Milnor fibers should serve as a quick guide to references. We attempt to place things into a wide geometric context while leaving technicali...
Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibers
cylindrical elastic structure identical fibers
2010/11/23
We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical $\epsilon$-periodically distributed fibers of size $r_{\epsilon}$, with $0 < r_{\epsilon} < \epsilon$, fi...
Linearons: highly non-instantaneous solitons in liquid-core photonic crystal fibers
Optics (physics.optics) Mathematical Physics (math-ph) Pattern Formation and Solitons (nlin.PS)
2010/11/10
The nonlinear propagation of light pulses in liquid-filled photonic crystal fibers is considered. Due to the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagatin...
Motivic Milnor fibers over complete intersection varieties and their virtual Betti numbers
Motivic Milnor fibers complete intersection varieties their virtual Betti numbers
2010/11/26
We study the Jordan normal forms of the local and global monodromies over complete intersection subvarieties of Cn by using the theory of motivic Milnor fibers.The results will be explicitly described...
Derivations, generic formal fibers and bad Noetherian rings
Derivations generic formal fibers bad Noetherian rings
2010/12/9
We consider a circle of ideas involving differential algebra, local Noetherian rings, and their generic formal fibers. Connecting these ideas gives rise to what we term a “twisted” subring R of a ring...
Powers of ideals and the cohomology of stalks and fibers of morphisms
Castelnuovo-Mumford regularity powers of ideals Rees algebras
2010/12/1
We first provide here a very short proof of a refinement of a the-orem of Kodiyalam and Cutkosky, Herzog and Trung on the regularity of powers of ideals.