A Law of Large Numbers for the Power Variation of Fractional Lévy Processes

We prove a law of large numbers for the power variation of an integrated fractional process in a pure jump model. This yields consistency of an estimator for the integrated volatility where we are no longer restricted to a Gaussian model.     

Global Nonparametric Sufficient Optimality Conditions for Semi-Infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η, ρ)-Invex Functions

In this paper, we establish a set of necessary optimality conditions and discuss a fairly large number of sets of global nonparametric sufficient optimality criteria under various generalized (η, ρ)-invexity assumptions for a minmax fractional programming problem with infinitely many nonlinear inequality and equality constraints.     

Solvability and iterative algorithms for a higher order nonlinear neutral delay differential equation

The paper is concerned with the higher order nonlinear neutral delay differential equation

     

Birkhoff‐Frink representations as functors

In an earlier article we characterized, from the viewpoint of set theory, those closure operators for which the classical result of Birkhoff and Frink, stating the equivalence between algebraic closure spaces, subalgebra lattices and algebraic lattices, holds in a many‐sorted setting. In the present article we investigate, from the standpoint of category theory, the form these equivalences take when the adequate morphisms of the several different species of structures implicated in them are also taken into account. Specifically, our main aim is to provide a functorial rendering of the Birkhoff‐Frink representation theorems for both single‐sorted algebras and many‐sorted algebras, by defining the appropriate categories and functors, covariant and contravariant, involved in the process (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Infinitely many solutions for fractional Schrodinger-Maxwell equations

In this paper using fountain theorems we study the existence of infinitely many solutions for fractional Schr\"{o}dinger-Maxwell equations \[\begin{cases} (-\Delta)^\alpha u+\lambda V(x)u+\phi u=f(x,u)-\mu g(x)|u|^{q-2}u, \text{ in } \mathbb R^3,\(-\Delta)^\alpha \phi=K_\alpha u^2, \text{ in } \mathbb R^3, \end{cases}\] where $\lambda,\mu >0$ are two parameters, $\alpha\in (0,1]$, $K_\alpha=\frac{\pi^{-\alpha}\Gamma(\alpha)}{\pi^{-(3-2\alpha)/2}\Gamma((3-2\alpha)/2)}$ and $(-\Delta)^\alpha$ is the fractional Laplacian. Under appropriate assumptions on $f$ and $g$ we obtain an existence theorem for this system.     

A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth

We study radial solutions of the semilinear elliptic equation

$\mathrm{\Delta }u+f(u)=0$

under rather general growth conditions on f. We construct a radial singular solution and study the intersection number between the singular solution and a regular solution. An application to bifurcation problems of elliptic Dirichlet problems is given. To this end, we derive a certain limit equation from the original equation at infinity, using a generalized similarity transformation. Through a generalized Cole–Hopf transformation, all the limit equations can be reduced into two typical cases, i.e., $\mathrm{\Delta }u+u^p=0$ and $\mathrm{\Delta }u+e^u=0$.     

Dynamics and effective actions of BCS superconductors

We derive the effective dynamical theory for BCS superconductors, based on the effective action formalism. Both the metallic regime and the superconducting regime are studied in the clean and dirty limit. The full electrodynamics of the problem is formulated in a manifestly gauge-invariant and transparent way. Furthermore, we consider the effect of particle-hole asymmetry in the band structure, and discuss its consequences for vortex dynamics and the topological term in the effective action. The effective action is the starting point for treating (quantum-) dynamical problems involving BCS superconductors. Received 23 November 1998     

LFC bumps on separable Banach spaces

In this note we construct a C^∞-smooth, LFC (Locally depending on Finitely many Coordinates) bump function, in every separable Banach space admitting a continuous, LFC bump function.