Related papers: Linear expand-contract plasticity of ellipsoids in…
This work is aimed to describe linear expand-contract plastic ellipsoids given via quadratic form of a bounded positively defined self-adjoint operator in terms of its spectrum.
The article deals with plastic and non-plastic sub-spaces $A$ of the real line ${\mathbb{R}}$ with the usual Euclidean metric $d$. It investigates non-expansive bijections, proves properties of such maps and demonstrates their relevance by…
This paper demonstrates the expand-contract plasticity of the unit spheres of $\ell_1$, $\ell_{\infty}$, and $c$. Furthermore, it establishes the strong plasticity of the unit spheres of Hilbert spaces.
The aim of this paper is to explain a link between symplectic isotopies of open objects such as balls and flexibility properties of symplectic hypersurfaces. We get connectedness results for spaces of symplectic ellipsoids or maximal…
It is known that if any function acting from precompact metric space to itself increases the distance between some pair of points then it must decrease distance between some other pair of points. We show that this is not the case for…
In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and…
Petrovskii elliptic systems of linear differential equations given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the…
Semi-cosimplicial objects in the category of Hilbert spaces with isometries which are motivated by non-commutative probability theory, in particular by the distributional symmetry of spreadability, are introduced and systematically…
We show that the elasticity Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…
An inverse problem of elasticity of $n$ elastic inclusions embedded into an elastic half-plane is analyzed. The boundary of the half-plane is free of traction. The half-plane and the inclusions are subjected to antiplane shear, and the…
We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…
The aim of this paper is state of conditions that ensure the convexity of a Chebyshev sets in Hilbert spaces .
We revisit the issue of the geometrical separability of the Hilbert space of physical states on lattice Abelian theories in the context of entanglement entropy. We discuss the conditions under which vectors in the Hilbert space, as well as…
The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and nature of asphericity as well as their respective averages we find two distinct shape regimes…
We establish some characterizations of elliptic hyperboloids (resp., ellipsoids) in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$, using the $n$-dimensional area of the sections cut off by hyperplanes and the $(n+1)$-dimensional…
The new integrable systems associated to the space of elliptic branched coverings are constructed. The relationship of these systems with elliptic Schlesinger's system is described. For the standard two-fold elliptic coverings the…
The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…
The manuscript establishes a series expansion of the core integral that relates changes in longitude and latitude along the geodetic line in oblate elliptical coordinates, and of a companion integral which is the path length along this line…
We give a new variant of $L^2$-extension theorem for the jets of holomorphic sections and discuss the relation between the extension problem of singular Hermitian metrics with semipositive curvature.