We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, ...and that are used by designers in order to control curves by manipulating control points. Our curves have cyclic symmetry, i.e. the control points can be cyclically arranged and the curve does not change when the control points are cyclically permuted. We provide an explicit formula for the elevation of the degree from
n to
n
+
r
,
r
⩾
1
and prove that the control polygon of the degree elevated curve converges to the curve itself if
r tends to infinity. Variation diminishing property of the curve is also verified. The proposed basis functions are suitable for the description of closed curves and surfaces with
C
∞
continuity at all of their points.
A link L in S3 possibly admits an involution of the exterior E(L) with fixed point set a closed surface, which is not extendable to an involution of S3. In this paper, we focus on the case of graph ...links and show that the genus of the surface provides a lower estimate of the number of link components.
In this paper, we investigated the focal performance of the dual-closed-surface microlens arrays (DCSMAs) based on rigorous electromagnetic theory and boundary element method (BEM) in the case of TE ...polarization. The DCSMAs are designed with different substrate thickness and different distance between microlenses. DCSMAs designed according to different wavelengths are surveyed. The DCSMAs with different incident angles are also studied. Several focusing performance measures, such as the focal spot size, the focal position on the preset focal plane, the diffraction efficiency and the normalized transmitted power, are presented. Numerical results indicate the DCSMAs with different parameters can implement focusing beams and the focal performance of DCSMAs is easily influenced by the substrate thickness and the incident wavelength. Furthermore, the optimal thickness for the maximal diffraction efficiency of the DCSMAs is given. It is expected that the DCSMAs may be used as a parallel processing device in micro-optics systems.
In this work, we propose an efficient multiresolution method for fitting scattered data functions on a sphere
S
, using a tensor product method of periodic algebraic trigonometric splines of order 3 ...and quadratic polynomial splines defined on a rectangular map of
S
. We describe the decomposition and reconstruction algorithms corresponding to the polynomial and periodic algebraic trigonometric wavelets. As application of this method, we give an algorithm which allows to compress scattered data on spherelike surfaces. In order to illustrate our results, some numerical examples are presented.
Lemniscatas 3D Ortega, Rafael; Paluszny, Marco
Revista de matemática, teoria y aplicaciones,
02/2009, Letnik:
9, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Una lemniscata 3D es una superficie que consiste en los puntos cuyo producto de distancias a un conjunto (finito) de puntos fijos ó focos es constante. En este trabajo se introducen las lemniscatas ...3D en el contexto de la modelación geométrica, se explora en particular, el caso de tres focos, especialmente en lo relativo a la deformación controlada.
It is demonstrated that the dependence of Fermi’s energy on the magnetic field causes a set of the Shubnikov – de Haas (SDH) oscillation frequencies to change, and their relative contribution to the ...total longitudinal conductivity of layered crystals depends on whether the scattering of current carriers is isotropic or anisotropic. Owing to the topological transition in a strong magnetic field, Fermi’s surface (FS) is transformed from open into closed one and is compressed in the magnetic field direction. Therefore, in an ultraquantum limit, disregarding the Dingle factor, the longitudinal electrical conductivity of the layered crystal tends to zero as a reciprocal square of the magnetic field for the isotropic scattering and as a reciprocal cube of the magnetic field for the anisotropic scattering. All calculations are performed in the approximation of relaxation time considered to be constant versus the quantum numbers for the isotropic scattering and proportional to the longitudinal velocity of current carriers for the anisotropic scattering.
On minimally 3-connected graphs on a surface Ota, Katsuhiro; Hagita, Mariko
AKCE international journal of graphs and combinatorics,
20/1/1/, Letnik:
1, Številka:
1
Journal Article
Recenzirano
It is well-known that the maximal size of minimally 3-connected graphs of order n ≥ 7 is 3n - 9. In this paper, we shall prove that if G is a minimally 3-connected graph of order n, and is embedded ...in a closed surface with Euler characteristic χ, then G contains at most 2n - min{2,2
χ
} edges. This bound is best possible for every closed surface.
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