相关论文: Localisation of Geometric Anisotropy

We consider an infinitesimal volume where there are many rigid molecules of the same kind, and discuss the description and classification of the local anisotropy in this volume by tensors. First, we examine the symmetry of a rigid molecule,…

We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of…

A complete characterisation is given of all the linear isometries of the Fr\'echet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of…

Bifurcation with symmetry is considered in the case of an isotropy subgroup with a two-dimensional fixed point subspace and non-zero quadratic terms. In general, there are one or three branches of solutions, and five qualitatively different…

We give a microlocal version of the theorem of iterates in multi-anisotropic Gevrey classes for multi-anisotropic hypoelliptic differential operators

We construct examples of 2-step Carnot groups related to quaternions and study their fine structure and geometric properties. This involves the Hamiltonian formalism, which is used to obtain explicit equations for geodesics and the…

Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…

Higher order anisotropic superspaces are constructed as generalized vector superbundles provided with compatible nonlinear connection, distinguished connection and metric structures.

Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…

First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…

A $p$-local compact group is an algebraic object modelled on the homotopy theory associated with $p$-completed classifying spaces of compact Lie groups and p-compact groups. In particular $p$-local compact groups give a unified framework in…

We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…

To a significant extent, the rich physical properties of photonic crystals are determined by the underlying geometry, in which the composed symmetry operators and their combinations contribute to the unique topological invariant to…

Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…

We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice systems. The method yields a systematic generation of all independent, conserved quasilocal operators…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

The angular orientation of an anisotropic scatterer with cylindrical symmetry in a linearly polarized light field represents an optomechanical librator. Here, we propose and theoretically analyze an optimal measurement scheme for the two…

Standard Vision Transformers flatten 2D images into 1D sequences, disrupting the natural spatial topology. While Rotary Positional Embedding (RoPE) excels in 1D, it inherits this limitation, often treating spatially distant patches (e.g.,…

This paper considers the family of Schr\"odinger operators on $\ell^2(\mathbb{Z})$ given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a finite exponential moment and allow the…

Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a…