Related papers: Orthogonal basis with a conicoid first mode for sh…
This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
The static behavior of orientational glasses is discussed in terms of a replica theory based on the infinite range random bond--random field model. A general version of the model applicable to dipolar and quadrupolar glasses is presented…
In this paper, helicoidal flat surfaces in the $3$-dimensional sphere $\mathbb{S}^3$ are considered. A complete classification of such surfaces is given in terms of their first and second fundamental forms and by linear solutions of the…
A method is suggested for construction of quadrangulations of the closed orientable surface with given genus g and either (1) with given chromatic number or (2) with given order allowed by the genus g. In particular, N. Hartsfield and G.…
Zernike polynomials are widely used to describe the wavefront phase as they are well suited to the circular geometry of various optical apertures. Non-conventional optical systems, such as future large optical telescopes with highly…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed…
Orthogonal rational functions (ORF) on the unit circle generalize orthogonal polynomials (poles at infinity) and Laurent polynomials (poles at zero and infinity). In this paper we investigate the properties of and the relation between these…
We study the multiplicity sets of first order symbols associated with differential operators on two dimensional surfaces. This work is inspired by the phenomenon of conical refraction explained by the existence of singularities in the…
In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometrics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid…
In this paper, orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal…
We make a computational study to know what kind of isospectralities among lens spaces and lens orbifolds exist considering the Hodge--Laplace operators acting on smooth $p$-forms. Several evidenced facts are proved and some others are…
Mode sorting is an essential function for optical systems exploiting the orthogonality of photonic orbital angular momentum mode space. The familiar log-polar optical transformation provides an efficient yet simple approach, however with…
Spatial mode sorting has come to prominence as an optical processing modality capable of saturating fundamental limits to numerous sensing tasks including wavefront sensing, coronagraphy, and superresolution imaging. But despite their…
In this work, we present a cogredient standard form of an orthogonal space over a finite local ring of odd characteristic.
We give a simple construction of an orthogonal basis for the space of m by n matrices with row and column sums equal to zero. This vector space corresponds to the affine space naturally associated with the Birkhoff polytope, contingency…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
We demonstrate experimentally a simple and easy-to-use technique aimed at measuring the complex orbital angular momentum spectrum of an arbitrary optical field making use of just polarization measurements. The technique can be applied to…
In the present paper, a new type of ruled surfaces called osculating-type (OT)-ruled surface is introduced and studied. First, a new orthonormal frame is defined for OT-ruled surfaces. The Gaussian and the mean curvatures of these surfaces…