Related papers: Variational properties of the discrete Hilbert-Ein…
Aiming at simulating elastic rods, we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods. After reviewing this model and discussing topological effects of periodic rods, we prove…
This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions and piecewise cubic functions are investigated and their…
This is a survey article on Hilbert-Kunz multiplicity and the F-signature.
The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of…
A short survey of the role of unitarity for hard diffractive cross-sections is given
We analyze the Wigner function constructed on the basis of the discrete rotation and displacement operators labeled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyze the…
Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.
We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction is the definition of discrete deformation gradients and discrete Cauchy-Green deformation…
This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of…
In this note we first review the concept of D-function, closely connected with Cauchy-Schwarz inequality, and then introduce the notion of P-covariance on a Hilbert space, where $P$ is an orthogonal projection. We show that when P is…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
Discrete strip-concave functions considered in this paper are, in fact, equivalent to an extension of Gelfand-Tsetlin patterns to the case when the pattern has a not necessarily triangular but convex configuration. They arise by releasing…
We discuss some differential geometry pertaining to continuum mechanics and the route recently taken by D.N. Arnold, R.S. Falk, and R. Winther in deriving new improved finite element schemes in linear elasticity from constructions in…
We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…
We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-K\"{a}hler equation in the Hestenes and Joyce forms. It is shown that left and right chiral states for these discrete equations can be…
This note studies Arveson's curvature invariant for d-contractions specialized to the case d=1 of a single contraction operator on a Hilbert space. It establishes a formula which gives an easy-to-understand meaning for the curvature of a…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
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…