Intrinsic square functions and commutators on Morrey-Herz spaces with variable exponents

In this article, we will study the boundedness of intrinsic square functions on the Morrey‐Herz spaces . The boundedness of commutators generated by functions and intrinsic square functions is also discussed on the aforementioned Morrey‐Herz spaces

Law of large numbers and central limit theorem for Donsker's delta function of diffusions I

Limit theorems in the space of Hida distributions, similar to the law of large numbers and the central limit theorem, are shown for composites of the Dirac distribution with solutions of one-dimensional, non-degenerate Itô equations

Relating phase field and sharp interface approaches to structural topology optimization

A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement

Studentization in Edgworth Expansions for Estimates of Semiparametric Index Models - (Now published in C Hsiao, K Morimune and J Powell (eds): Nonlinear Statistical Modeling (Festschrift for Takeshi Amemiya), (Cambridge University Press, 2001), pp.197-240.)

We establish valid theoretical and empirical Edgeworth expansions for density-weighted averaged derivative estimates of semiparametric index models.Edgeworth expansions, semiparametric estimates, averaged derivatives

Rate of growth of a transient cookie random walk

We consider a one-dimensional transient cookie random walk. It is known from a previous paper that a cookie random walk $(X_n)$ has positive or zero speed according to some positive parameter $\alpha >1$ or $\le 1$. In this article, we give the exact rate of growth of $(X_n)$ in the zero speed regime, namely: for $0<\alpha <1$, $X_n/n^{\frac{\alpha+1}{2}}$ converges in law to a Mittag-Leffler distribution whereas for $\alpha=1$, $X_n(\log n)/n$ converges in probability to some positive constant

Existence and approximation of solutions to an anisotropic phase field system of Penrose-Fife type

This paper is concerned with a phase field system of Penrose-Fife type for a non-conserved order parameter χ with a kinetic relaxation coefficient depending on the gradient of χ. This system can be used to model the dendritic solidification of liquids. A time discrete scheme for an initial-boundary value problem tothis system is presented. By proving the convergence of this scheme, the existence of a solution to the problem is shown

On Bloom type estimates for iterated commutators of fractional integrals

In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse domination that we provide as well in this paper and also in techniques de- veloped in the recent paper [22]. We extend as well the necessity established in [15] to iterated commutators providing a new proof. As a consequence of the preceding results we recover the one weight estimates in [7, 1] and es- tablish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space

Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity

The asymptotic behaviour for t → ∞ of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress law and also in the phase evolution equation are described by using the mathematical theory of hysteresis operators