Uniqueness of the stationary point for the one-dimensional inverse problem in two-dimensional space

1998 ◽  
Vol 6 (2) ◽  
Author(s):  
A.M. ALEKSEENKO ◽  
S.I. KABANIKHIN
Keyword(s):  
Inverse Problem ◽  
Stationary Point ◽  
Dimensional Space ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One

Nonmonocentric Urban Configurations in a Two-Dimensional Space

1989 ◽  
Vol 21 (3) ◽  
pp. 363-374 ◽  
Author(s):  
H Ogawa ◽  
M Fujita
Keyword(s):  
Land Use ◽  
Dimensional Space ◽  
Urban Land ◽  
Urban Land Use ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Circular Symmetry ◽  
One Dimensional ◽  
Urban Configurations ◽  
The One

A one-dimensional model of nonmonocentric urban land use is extended into a two-dimensional space. Under the assumption of circular symmetry, it is shown that the equilibrium urban configurations in the two-dimensional space are essentially the same as those in the one-dimensional space except for the conditions on the parameters.

On a theorem of van der Corput on uniform distribution

1957 ◽  
Vol 53 (4) ◽  
pp. 781-789 ◽  
Author(s):  
W. J. Coles
Keyword(s):  
Dimensional Space ◽  
Sufficient Condition ◽  
General Criterion ◽  
Two Dimensional ◽  
Necessary And Sufficient Condition ◽  
One Dimensional ◽  
Quantitative Form ◽  
The One ◽  
Sufficiency Part ◽  
Necessary And Sufficient

Van der Corput has shown (2), using a general criterion of Weyl (1), that a necessary and sufficient condition, that a sequence of points Pn = (αn, βn) (n = 1, 2,…) in two-dimensional space be uniformly distributed modulo 1, is that for all pairs of integers (u, v) other than u = v = 0 the one-dimensional sequence (uαn + vβn) (n = 1, 2,…) is uniformly distributed modulo 1. The object of this paper is to give a quantitative form to the sufficiency part of this qualitative criterion.

scholarly journals Topological properties of non-Hermitian Creutz Ladders

2021 ◽  
Author(s):  
Hui-Qiang Liang ◽  
Linhu Li
Keyword(s):  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Skin Effect ◽  
Energy Gap ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Topological Properties ◽  
One Dimensional ◽  
Boundary Correspondence ◽  
The One

Abstract In this work we study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials, and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes. The non-Hermitian skin effect (NHSE), which is known to break the bulk-boundary correspondence (BBC), emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder. The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart, whether with or without the NHSE. In one scenario without the NHSE, the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector. The NHSE itself also possesses some unusual behaviors in this system, including a high spectral winding without the presence of long-range hoppings, and a competition between two types of the NHSE, with the same and opposite inverse localization lengths for the two bands, respectively. Furthermore, it is found that the NHSE in this model does not always break the conventional BBC, which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

MUTUAL EXCLUSION ON OPTICAL BUSES

2002 ◽  
Vol 12 (03n04) ◽  
pp. 341-358
Author(s):  
KRISHNA M. KAVI ◽  
DINESH P. MEHTA
Keyword(s):  
Mutual Exclusion ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Array ◽  
Propagation Delays ◽  
Optical Buses ◽  
The One

This paper presents two algorithms for mutual exclusion on optical bus architectures including the folded one-dimensional bus, the one-dimensional array with pipelined buses (1D APPB), and the two-dimensional array with pipelined buses (2D APPB). The first algorithm guarantees mutual exclusion, while the second guarantees both mutual exclusion and fairness. Both algorithms exploit the predictability of propagation delays in optical buses.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

2022 ◽  
Author(s):  
Bharti bharti ◽  
Debabrata Deb
Keyword(s):  
Molecular Dynamics ◽  
Liquid Crystals ◽  
Molecular Dynamics Simulations ◽  
Liquid Crystalline ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One ◽  
Dynamics Simulations

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the...

Sign in / Sign up

Export Citation Format

Share Document