Related papers: A minimal integrity basis for the elasticity tenso…
This paper deals with necessary and sufficient conditions for weak and strong minimizers of functionals $\Phi(u)=\int_a^b f(x,u(x),u'(x))\,dx$, where $u\in C^1([a,b],{\mathbb R}^N)$. We first derive conditions which are simpler than the…
The main result of the paper is that a system of invariant subspaces of a (completely non-unitary) Hilbert space contraction $T$ with finite defects (rank$(I-T^*T)<\infty$, rank$(I-TT^*)<\infty$) is an unconditional basis (Riesz basis) if…
We develop a method for finding the independent invariant tensors of a gauge theory. Our method uses a theorem relating invariant tensors and constant configurations in field space. We apply our method to an $SU(3)$ gauge theory with matter…
A nonconforming linear element method is developed for a three-dimensional generalized tensor-valued Stokes equation associated with the Hessian complex in this paper. A discrete Helmholtz decomposition for the piecewise constant space of…
We prove the non integrability of the colinear $3$ and $4$ body problem, for any masses positive masses. To deal with resistant cases, we present strong integrability criterions for $3$ dimensional homogeneous potentials of degree $-1$, and…
We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
Tensegrity structures have been extensively studied over the last years due to their potential applications in modern engineering like metamaterials, deployable structures, planetary lander modules, etc. Many of the form-finding methods…
We construct a new set of combinations from the mass matrices of the charged leptons and neutrinos that are invariant under basis transformation, hereafter {\it the} invariants. We use these invariants to study various symmetries and…
A procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant (RPI) set for a linear discrete-time system subject to unknown, bounded disturbances. The procedure computes, via the…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…
Let $X$ be a nonempty real variety that is invariant under the action of a reflection group $G$. We conjecture that if $X$ is defined in terms of the first $k$ basic invariants of $G$ (ordered by degree), then $X$ meets a $k$-dimensional…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with…
In this article we present two new algorithms to compute the Groebner basis of an ideal that is invariant under certain permutations of the ring variables and which are both implemented in SINGULAR (cf. [DGPS12]). The first and major…
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…
The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For…
The lowest order nonconforming rectangular element in three dimensions involves 54 degrees of freedom for the stress and 12 degrees of freedom for the displacement. With a modest increase in the number of degrees of freedom (24 for the…
We prove a version of Linnik's basic lemma uniformly over the base field using theta-series and geometric invariant theory in the spirit of Khayutin's approach (Duke Math. J., 168(12), 2019). As an application, we establish entropy bounds…
We study extensions of compressive sensing and low rank matrix recovery to the recovery of low rank tensors from incomplete linear information. While the reconstruction of low rank matrices via nuclear norm minimization is rather…