Multidimensional Iterative Interpolation

1991 ◽  
Vol 43 (2) ◽  
pp. 297-312 ◽  
Author(s):  
Gilles Deslauriers ◽  
Jacques Dubois ◽  
Serge Dubuc
Keyword(s):  
Euclidean Space ◽  
Discrete Subgroup ◽  
Interpolation Process ◽  
Sufficient Condition ◽  
Interpolation Function ◽  
Necessary And Sufficient Condition ◽  
Schwartz Distributions ◽  
Algebraic Properties ◽  
Iterative Interpolation ◽  
Necessary And Sufficient

AbstractWe define an iterative interpolation process for data spread over a closed discrete subgroup of the Euclidean space. We describe the main algebraic properties of this process. This interpolation process, under very weak assumptions, is always convergent in the sense of Schwartz distributions. We find also a convenient necessary and sufficient condition for continuity of each interpolation function of a given iterative interpolation process.

scholarly journals On the Differential Equation Governing Torqued Vector Fields on a Riemannian Manifold

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1941
Author(s):  
Sharief Deshmukh ◽  
Nasser Bin Turki ◽  
Haila Alodan
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Compact Riemannian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Rigidity Results ◽  
Necessary And Sufficient

In this article, we show that the presence of a torqued vector field on a Riemannian manifold can be used to obtain rigidity results for Riemannian manifolds of constant curvature. More precisely, we show that there is no torqued vector field on n-sphere Sn(c). A nontrivial example of torqued vector field is constructed on an open subset of the Euclidean space En whose torqued function and torqued form are nowhere zero. It is shown that owing to topology of the Euclidean space En, this type of torqued vector fields could not be extended globally to En. Finally, we find a necessary and sufficient condition for a torqued vector field on a compact Riemannian manifold to be a concircular vector field.

A class of sub-almost distributive lattices in an associate almost distributive lattice through a filter

2019 ◽  
Vol 13 (07) ◽  
pp. 2050136
Author(s):  
S. Ramesh ◽  
Jogarao Gunda
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Distributive Lattices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Algebraic Properties ◽  
Necessary And Sufficient

In this paper, we introduce a class of sub-almost distributive lattices in an associate almost distributive lattice through a filter. We obtain several algebraic properties on the class of sub-almost distributive lattices and prove that the above class forms a distributive lattice. We derive a necessary and sufficient condition that the class to become a Boolean algebra.

scholarly journals HILBERT MODULAR PSEUDODIFFERENTIAL OPERATORS OF MIXED WEIGHT

2003 ◽  
Vol 46 (2) ◽  
pp. 269-277 ◽  
Author(s):  
Min Ho Lee ◽  
Hyo Chul Myung
Keyword(s):  
Pseudodifferential Operator ◽  
Modular Forms ◽  
Pseudodifferential Operators ◽  
Discrete Subgroup ◽  
Subject Classification ◽  
Sufficient Condition ◽  
Hilbert Modular Forms ◽  
Necessary And Sufficient Condition ◽  
Hilbert Modular ◽  
Necessary And Sufficient

AbstractWe introduce an action of a discrete subgroup $\varGamma$ of $SL(2,\mathbb{R})^n$ on the space of pseudodifferential operators of $n$ variables, and construct a map from the space of Hilbert modular forms for $\varGamma$ to the space of pseudodifferential operators invariant under such a $\varGamma$-action, which is a lifting of the symbol map of pseudodifferential operators. We also obtain a necessary and sufficient condition for a certain type of pseudodifferential operator to be $\varGamma$-invariant.AMS 2000 Mathematics subject classification: Primary 11F41; 35S05

scholarly journals Canal surfaces in 4-dimensional Euclidean space

2016 ◽  
Vol 7 (1) ◽  
pp. 83-89 ◽  
Author(s):  
Betül Bulca ◽  
Kadri Arslan ◽  
Bengü Bayram ◽  
Günay Öztürk
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Four Dimensions ◽  
Canal Surfaces ◽  
Curvature Ellipse ◽  
Normal Vectors ◽  
Necessary And Sufficient

In the present study, we consider canal surfaces imbedded in an Euclidean space of four dimensions. The curvature properties of these surface are investigated with respect to the variation of the normal vectors and curvature ellipse. We also give some special examples of canal surfaces in E^4. Further, we give necessary and sufficient condition for canal surfaces in E^4 to become superconformal. Finally, the visualization of the projections of canal surfaces in E^3 are presented.

scholarly journals Framed slant helices in Euclidean 3-space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osman Zeki Okuyucu ◽  
Mevlüt Canbirdi
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Slant Helix ◽  
Spherical Images ◽  
Necessary And Sufficient

AbstractIn this paper, we define framed slant helices and give a necessary and sufficient condition for them in three-dimensional Euclidean space. Then, we introduce the spherical images of a framed curve. Also, we examine the relations between a framed slant helix and its spherical images. Moreover, we give an example of a framed slant helix and its spherical images with figures.

scholarly journals A class of Lie racks associated to symmetric Leibniz algebras

2021 ◽  
pp. 2250230 ◽  
Author(s):  
Hamid Abchir ◽  
Fatima-ezzahrae Abid ◽  
Mohamed Boucetta
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Leibniz Algebras ◽  
Algebraic Properties ◽  
Necessary And Sufficient

We classify symmetric Leibniz algebras in dimensions 3 and 4 and we determine all associated Lie racks. Some of such Lie racks give rise to nontrivial topological quandles. We study some algebraic properties of these quandles and we give a necessary and sufficient condition for them to be quasi-trivial.

scholarly journals Local homeo- and diffeomorphisms: invertibility and convex image

1994 ◽  
Vol 49 (3) ◽  
pp. 377-398 ◽  
Author(s):  
Gaetano Zampieri ◽  
Gianluca Gorni
Keyword(s):  
Euclidean Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Connected Subset ◽  
Local Homeomorphism ◽  
Local Diffeomorphisms ◽  
Open Connected Subset ◽  
One To One ◽  
Necessary And Sufficient

We prove a necessary and sufficient condition for a local homeomorphism defined on an open, connected subset of a Euclidean space to be globally one-to-one and, at the same time, for the image to be convex. Among the applications we give a practical sufficiency test for invertibility for twice differentiable local diffeomorphisms defined on a ball.

scholarly journals On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohammad Abobala
Keyword(s):  
Linear Equations ◽  
Direct Application ◽  
Sufficient Condition ◽  
Algebraic Equations ◽  
Necessary And Sufficient Condition ◽  
Algebraic Properties ◽  
Invertible Elements ◽  
Necessary And Sufficient

This paper studies the problem of determining invertible elements (units) in any n-refined neutrosophic ring. It presents the necessary and sufficient condition for any n-refined neutrosophic element to be invertible, idempotent, and nilpotent. Also, this work introduces some of the elementary algebraic properties of n-refined neutrosophic matrices with a direct application in solving n-refined neutrosophic algebraic equations.

scholarly journals On generating points of a lattice in the region

1964 ◽  
Vol 6 (3) ◽  
pp. 141-155 ◽  
Author(s):  
D. M. E. Foster
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Image Position ◽  
Necessary And Sufficient

A lattice An in n-dimensional Euclidean space En consists of the aggregate of all points with coordinates (xx,…, xn), wherefor some real ars (r, s = 1,…, n), subject to the condition ∥ αrs ∥nn ╪ 0. The determinant Δn of Λn, is denned by the relation , the sign being chosen to ensure that Δn > 0.If A1…, An are the n points of Λn having coordinates (a11, a21…, anl),…, (a1n, a2n,…, ann), respectively, then every point of Λn may be expressed in the formand Ai,…, An, together with the origin O, are said to generate Λn. This particular set of generating points is not unique; it may be proved that a necessary and sufficient condition that n points of Λn should generate the lattice is that the n × n determinant formed by their x coordinates should be ±Δn, or, equivalently, that the n×n determinant formed by their corresponding u-coordinates should be ±1.

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