Related papers: Dev-Div- and DevSym-DevCurl-inequalities for incom…

Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the…

The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the…

This article introduces a trace-based metric on the space of positive semi-definite (PSD) tensors, offering a geometric perspective that connects their algebraic structure to their intrinsic geometric properties. It defines the…

It is well known that boundary conditions on quantum fields produce divergences in the renormalized energy-momentum tensor near the boundaries. Although irrelevant for the computation of Casimir forces between different bodies, the…

Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local…

In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in…

We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the length L of the curve and the thickness r (maximal radius of an…

We prove a Korn-type inequality in H(Curl) for tensor fields.

Differential equations need boundary conditions (BC's) for their solution. It is commonly acknowledged that differential equations and BC's are representative of independent physical processes, and no correlations between them is required.…

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple axisymmetric…

This paper investigates the joint source-channel coding problem of sending a memoryless source over a memoryless broadcast channel. An inner bound and several outer bounds on the admissible distortion region are derived, which respectively…

In this work, we apply the concept about operator connection to consider bivariate random tensor means. We first extend classical Markov and Chebyshev inequalities from a random variable to a random tensor by establishing Markov inequality…

Two types of finite element spaces on a tetrahedron are constructed for divdiv conforming symmetric tensors in three dimensions. The key tools of the construction are the decomposition of polynomial tensor spaces and the characterization of…

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely its sectional curvature and scalar curvature on one side;…

We prove global and local versions of the so-called div-curl-lemma, a crucial result in the homogenization theory of partial differential equations, for mixed boundary conditions on bounded weak Lipschitz domains in 3D with weak Lipschitz…

We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for…

Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its…

3D asymmetric tensor fields have found many applications in science and engineering domains, such as fluid dynamics and solid mechanics. 3D asymmetric tensors can have complex eigenvalues, which makes their analysis and visualization more…

Detection and quantification of entanglement in quantum resources are two key steps in the implementation of various quantum-information processing tasks. Here, we show that Bell-type inequalities are not only useful in verifying the…

We are interested in the numerical reconstruction of a vector field with prescribed divergence and curl in a general domain of R 3 or R 2 , not necessarily contractible. To this aim, we introduce some basic concepts of finite element…