The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on Hn−1(M,R) is a homogenized version of the Riemannian (n−1)-volume. We study the differentiability properties of the stable norm at points α ∈ Hn−1(M,R). Th...

The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on Hn−1(M,R) is a homogenized version of the Riemannian (n−1)-volume. We study the differentiability properties of the stable norm at points α ∈ Hn−1(M,R). Th...

We consider the notion of a uniformly concave function, using it to characterize those Lorentz spaces Lw,1 that have the weak-star uniform Kadec-Klee property as precisely those for which the antiderivative φ of w is uniformly concave; building on recent work of Dilworth and Hsu. We also derive a quite general sufficient condition for a twice-differentiable φ to be uniformly concave; and explor...

The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on Hn−1(M,R) is a homogenized version of the Riemannian (n−1)-volume. We study the differentiability properties of the stable norm at points α ∈ Hn−1(M,R). Th...

The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on Hn−1(M,R) is a homogenized version of the Riemannian (n−1)-volume. We study the differentiability properties of the stable norm at points α ∈ Hn−1(M,R). Th...

We study the differentiability of the stable norm ‖·‖ associated with a Zn periodic metric on Rn. Extending one of the main results of [Ba2], we prove that if p ∈ Rn and the coordinates of p are linearly independent over Q, then there is a linear 2-plane V containing p such that the restriction of ‖·‖ to V is differentiable at p. We construct examples where ‖·‖ it is not differentiable at a poi...

We investigate the concept of cylindrical Wiener process subordinated to a strictly α–stable Lévy process, with α∈(0,1), in an infinite–dimensional, separable Hilbert space, and consider related stochastic convolution. then introduce corresponding Ornstein–Uhlenbeck focusing on regularizing properties Markov transition semigroup defined by it. In particular, we provide explicit, original formul...

and Applied Analysis 3 In this paper, we firstly present the definition of duality fixed point for a mapping T from E into its dual E∗ as follows. Let E be a Banach space with a single-valued generalized duality mapping Jp : E → E∗. Let T : E → E∗. An element x∗ ∈ E is said to be a generalized duality fixed point of T if Tx∗ Jpx∗. An element x∗ ∈ E is said to be a duality fixed point of T if Tx...

BACKGROUND In diffuse optical tomography (DOT), the image reconstruction is often an ill-posed inverse problem, which is even more severe for breast DOT since there are considerably increasing unknowns to reconstruct with regard to the achievable number of measurements. One common way to address this ill-posedness is to introduce various regularization methods. There has been extensive research...

and Applied Analysis 3 Our results improve and extend the corresponding conclusions announced by many others. 2. Preliminaries Let S X = {x ∈ X :‖ x ‖= 1}. Then the norm of X is said to be Gâteaux differentiable if