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Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…

Mathematical Physics · Physics 2015-05-30 Stephen C. Anco , Steven A. MacNaughton , Thomas Wolf

We survey developments, over the last thirty years, in the theory of Shape Preserving Approximation (SPA) by algebraic polynomials on a finite interval. In this article, "shape" refers to (finitely many changes of) monotonicity, convexity,…

Classical Analysis and ODEs · Mathematics 2011-09-06 K. A. Kopotun , D. Leviatan , A. Prymak , I. A. Shevchuk

In this paper I uncover and explain---using contour integrals and residues---a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\'e scheme for…

Numerical Analysis · Mathematics 2019-11-25 Robert M. Corless

In this paper,we obtain two results on closed Reimainnian manifold $M\times [0,T]$.When $T$ is small enough,to any prescribed scalar curvature, the existence and uniqueness of metrics are obtained on the volume element preserving…

Differential Geometry · Mathematics 2007-05-23 Zhi-Zhang Wang

Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…

Mathematical Physics · Physics 2007-05-23 Stephen C. Anco , Nataliya M. Ivanova

For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…

Mathematical Physics · Physics 2020-08-18 Stephen C. Anco , Alexei F. Cheviakov

We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…

Image and Video Processing · Electrical Eng. & Systems 2022-06-28 Icíar Lloréns Jover , Thomas Debarre , Shayan Aziznejad , Michael Unser

We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…

Numerical Analysis · Mathematics 2020-01-14 Vladimir S. Chelyshkov

This article studies families of curves with monotonic curvature function (MC-curves) and their applications in geometric modelling and aesthetic design. Aesthetic analysis and assessment of the structure and plastic qualities of…

Graphics · Computer Science 2013-05-09 Rushan Ziatdinov , Rifkat I. Nabiyev , Kenjiro T. Miura

Chiral spin textures are researched widely in condensed matter systems and show potential for spintronics and storage applications. Along with extensive condensed-matter studies of chiral spin textures, photonic counterparts of these…

Optics · Physics 2021-12-14 Peng Shi , Luping Du , Mingjie Li , Xiaocong Yuan

This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…

Numerical Analysis · Mathematics 2025-12-02 Xunnian Yang

The conformal nature of smooth curves in $\mathbb{R}^3$ is characterised by conformal length, curvature and torsion. We present a derivation of these conformal parameters via a limiting process using inscribed polygons with circular edges .…

Differential Geometry · Mathematics 2024-02-01 Harald Dorn

This note is the updated outline of the article "Interpolational properties of planar spiral curves", Fund. and Applied Math., 2001, Vol.7, N.2, 441-463, published in Russian. The main result establishes boundary regions for spiral and…

Differential Geometry · Mathematics 2017-08-29 A. Kurnosenko

A conservation-consistent boundary condition is proposed for nonlinear models of soluble-surfactant-laden falling films, ensuring exact conservation of total surfactant mass. The formulation resolves an inconsistency in widely used reduced…

Analysis of PDEs · Mathematics 2026-05-20 Sanghasri Mukhopadhyay , Séverine Millet , Bastien Di Pierro , Asim Mukhopadhyay

We consider the initial value problem for a scalar conservation law in one space dimension with a single spatial flux discontinuity, the so-called two-flux problem. We prove that a well-known front tracking algorithm has a convergence rate…

Analysis of PDEs · Mathematics 2025-09-30 Shyam Sundar Ghoshal , John D Towers

A diffeomorphism of pseudo-Riemannian manifolds is called sectional curvature preserving if it preserves the sectional curvature of all the nondegenerate 2-planes. We consider a similar condition for degenerate 2-planes and we prove that…

Differential Geometry · Mathematics 2010-08-31 Ognian Kassabov

We present infinitely many nonlocal conservation laws, a pair of compatible local Hamiltonian structures and a recursion operator for the equations describing surfaces in three-dimensional space that admit nontrivial deformations which…

Exactly Solvable and Integrable Systems · Physics 2017-10-03 I. S. Krasil'shchik , A. Sergyeyev

We consider the Blum medial axis of a region in $\mathbb R^n$ with piecewise smooth boundary and examine its "rigidity properties", by which we mean properties preserved under diffeomorphisms of the regions preserving the medial axis. There…

Differential Geometry · Mathematics 2020-02-11 James Damon

We classify all possible local linear procedures over triangular meshes resulting in polynomial $C^1$-spline functions with affinely uniform shape for the basic functions at the edges, and fitting the 9 value- and gradient data at the…

Numerical Analysis · Mathematics 2019-03-28 Laszlo Stachó

Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression…

Applications · Statistics 2008-11-12 Mary C. Meyer