Beyond Beatty sequences: Complementary lattices

2020 ◽  
pp. 1-13
Author(s):  
Sam Vandervelde
Keyword(s):  
Fundamental Property ◽  
Parameter Family ◽  
Two Dimensional ◽  
Geometric Proof ◽  
Complementary Sequences ◽  
Beatty Sequences

Abstract By taking square lattices as a two-dimensional analogue to Beatty sequences, we are motivated to define and explore the notion of complementary lattices. In particular, we present a continuous one-parameter family of complementary lattices. This main result then yields several novel examples of complementary sequences, along with a geometric proof of the fundamental property of Beatty sequences.

Thickness of elemental and binary single atomic monolayers

2020 ◽  
Vol 5 (3) ◽  
pp. 385-399 ◽  
Author(s):  
Peter Hess
Keyword(s):  
2D Materials ◽  
Fundamental Property ◽  
Two Dimensional

The thickness of monolayers is a fundamental property of two-dimensional (2D) materials that has not found the necessary attention. Since the boundary is not well-defined and it changes its value with the surrounding, the thickness is difficult to grasp.

scholarly journals A two-parameter family of an extension of Beatty sequences

2008 ◽  
Vol 308 (20) ◽  
pp. 4578-4588 ◽  
Author(s):  
Shiri Artstein-Avidan ◽  
Aviezri S. Fraenkel ◽  
Vera T. Sós
Keyword(s):  
Parameter Family ◽  
Beatty Sequences ◽  
Two Parameter

scholarly journals Two-dimensional fluid motion referred to a network of orthogonal curves

1949 ◽  
Vol 196 (1045) ◽  
pp. 301-310 ◽  
Keyword(s):  
Coordinate System ◽  
Gaussian Curvature ◽  
Large Scale ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Parameter Family ◽  
Two Dimensional ◽  
Gradient Wind

A theory already developed is applied to the case of two-dimensional motion parallel at each point of space to some member, Ʃ, of a one-parameter family of surfaces, the coordinate-system being a network of orthogonal curves drawn on Ʃ. The geodesic curvatures of the orthogonal curves and their relationship to the Gaussian curvature of Ʃ are worked out.The equations of motion and of continuity are expressed in terms of the geodesic curvatures. Meyer’s aerodynamical equations are derived as particular cases when the network is fixed in space and the surfaces are all planes. A formula for a large-scale gradient wind is also obtained as an example of the use of a moving network drawn on a sphere.

scholarly journals JORDANIAN QUANTUM SPHERES

2001 ◽  
Vol 16 (27) ◽  
pp. 1731-1740 ◽  
Author(s):  
R. CHAKRABARTI ◽  
J. SEGAR
Keyword(s):  
Function Algebra ◽  
Parameter Family ◽  
Two Dimensional ◽  
Quantum Spheres

We introduce and investigate a one-parameter family of quantum spaces invariant under the left (right) co-action of the group-like element [Formula: see text] of the Jordanian function algebra Fun h( SL (2)). These spaces may be regarded as Jordanian quantization of the two-dimensional spheres.

Two-Dimensional Contact Pressure Distribution of a Radial Tire in Motion

1996 ◽  
Vol 24 (4) ◽  
pp. 294-320 ◽  
Author(s):  
H. Shiobara ◽  
T. Akasaka ◽  
S. Kagami
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Fundamental Property ◽  
Leading Edge ◽  
Static Case ◽  
Two Dimensional ◽  
Contact Pressure Distribution ◽  
Radial Tire ◽  
Spring System ◽  
Tread Rubber

Abstract The two-dimensional contact pressure distribution of a running radial tire under load is a fundamental property of the tire structure. The two-dimensional contact pressure distribution in the static case and the one-dimensional contact pressure distribution in the dynamic case were previously analyzed for a spring bedded ring model consisting of a composite belt ring and a spring system for the sidewall and the tread rubber. In this paper, a Voigt-type viscoelastic spring system is assumed for the sidewall and the tread rubber. We analyzed the dynamic deformation of the belt ring in a steady state, and obtained the two-dimensional dynamic contact pressure distribution at speeds up to approximately 60 km/h. The predicted contact pressure distribution for a model with appropriate values for the damping coefficient of each constituent rubber is shown to be in good agreement with experimental results. It is a characteristic feature that increasing velocity yields an increase in the pressure at the leading edge of the crown centerline in the contact area and at the trailing edge of the shoulder line.

Some Properties of Beatty Sequences II

1960 ◽  
Vol 3 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Ian G. Connell
Keyword(s):  
Complementary Sequences ◽  
Beatty Sequences ◽  
Greatest Integer Function ◽  
Image Position

In a previous paper [l] we discussed a property of the complementary sequences1where square brackets denote the greatest integer function and α is any positive irrational. We called {un} and {vn} Beatty sequences of argument α.

Added Mass of a Three-Parameter Family of Two-Dimensional Forces Oscillating in a Free Surface

1959 ◽  
Vol 3 (01) ◽  
pp. 36-48
Author(s):  
L. Landweber ◽  
Matilde Macagno
Keyword(s):  
Free Surface ◽  
Added Mass ◽  
Small Error ◽  
Parameter Family ◽  
Radius Of Gyration ◽  
Two Dimensional ◽  
Transverse Axis ◽  
Section Area ◽  
Added Masses ◽  
The Given

The added-mass characteristics of shiplike forms, oscillating vertically or horizontally in a free surface, are derived for a three-parameter family of forms. The parameters varied are the draft-beam ratio, the section-area coefficient, and the ratio to the draft of the radius of gyration about the transverse axis in the free surface. The added-mass coefficients are presented as a series of curves for about 70 members of this family. It is suggested that the added masses of arbitrary shiplike sections may be obtained, with only small error, from these curves by interpolation at the parametric values of the given section.

ON EXACT SOLUTION OF OPTIMIZATION TASK GENERATED BY THE LAPLACE EQUATION

2018 ◽  
pp. 466-472
Author(s):  
Asaad Naser Mzedawee
Keyword(s):  
Exact Solution ◽  
Laplace Equation ◽  
Existence And Uniqueness ◽  
Parameter Family ◽  
Two Dimensional ◽  
Special Sequence ◽  
Optimization Task ◽  
Finite Dimensional ◽  
Residual Functional

A one-parameter family of finite-dimensional spaces consisting of special two-dimensional splines of Lagrangian type is defined (the parameter N is related to the dimension of the space). The Laplace equation generates in each such space the problem of minimizing the residual functional. The existence and uniqueness of optimal splines are proved. For their coefficients and residuals, exact formulas are obtained. It is shown that with increasing N; the minimum of the residual functional is O(N^(-5) ); and the special sequence consisting of optimal splines is fundamental.

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