This paper deals with recent progress and connections between several open problems in the theory of syzygies, ideals of height two, factorial rings of small embedding codimension, and vector bundles of small rank. Throughout the paper (unless stated otherwise) R will denote a regular local ring with maximal ideal m. All modules will be finitely generated. The central problem which we will disc...

In this note we consider asymptotically flat manifolds with non-negative scalar curvature and an inner boundary which is an outermost minimal surface. We show that there exists an upper bound on the mean curvature of a constant mean curvature surface homologous to a subset of the interior boundary components. This bound allows us to find a maximizer for the constant mean curvature of a surface ...

We consider the linear thermoelastic plate equations with free boundary conditions in the Lp in time and Lq in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform C-domain, which includes the cases of a bounded domain and of an exterior domain with C-boundary. Moreover, we prove uniform a priori-estimates for the solution. The proof is ...

The purpose of this study was to quantify the inter-session reliability of force-velocity-power profiling and estimated maximal strength in youth. Thirty-six males (11-15 years old) performed a ballistic supine leg press test at five randomized loads (80%, 100%, 120%, 140%, and 160% body mass) on three separate occasions. Peak and mean force, power, velocity, and peak displacement were collecte...

Kinesio taping has also been used for athletes with Medial Elbow Epicondylar Tendinopathy (MET) as an additional treatment method. The purpose of this study was to determine the clinical effectiveness of Kinesio tape on maximal grip strength and absolute and related force sense in athletes with MET when applied to the medial forearm. 27 male athletes who voluntarily participated in this study w...

Ground reaction forces (GRFs) are often used in inverse dynamics analyses to determine joint loading. These GRFs are usually measured using force plates (FPs). As an alternative, instrumented force shoes (FSs) can be used, which have the advantage over FPs that they do not constrain foot placement. This study tested the FS system in one normal weight subject (77kg) performing 19 different lifti...

We show that there is a measure μ, defined on the hyperbolic plane and with polynomial growth, such that the centered maximal operator associated to μ does not satisfy weak type (1, 1) bounds.

As shown in [A1], the lowest constants appearing in the weak type (1, 1) inequalities satisfied by the centered Hardy-Littlewood maximal operator associated to certain finite radial measures, grow exponentially fast with the dimension. Here we extend this result to a wider class of radial measures and to some values of p > 1. Furthermore, we improve the previously known bounds for p = 1. Roughl...

For a family of weight functions, hκ, invariant under a finite reflection group on R, analysis related to the Dunkl transform is carried out for the weighted L spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a m...

We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of f, M f, by an expression involving the nonincreasing rearrangement of f. This estimate is used to obtain necessary and suucient conditions for the boundedness of M between classical Lorentz spaces.