We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D b...

Archimedean tilings are periodic polygonal tessellations that are created by placing regular polygons edge-to-edge around a vertex to fill the plane. Here we show that three- and four-arm DNA junction tiles with specifically designed arm lengths and intertile sticky-end interactions can be used to form sophisticated two-dimensional (2D) and three-dimensional (3D) tessellation patterns. We demon...

In an Open-Pit Production Scheduling (OPPS) problem, the goal is to determine the mining sequence of an orebody as a block model. In this article, linear programing formulation is used to aim this goal. OPPS problem is known as an NP-hard problem, so an exact mathematical model cannot be applied to solve in the real state. Genetic Algorithm (GA) is a well-known member of evolutionary algorithms...

OBJECTIVES The purpose of this study was to test the hypothesis that a formula incorporating 3-dimensional (3D) fractional thigh volume would be superior to the conventional 2-dimensional (2D) formula of Hadlock et al (Am J Obstet Gynecol 1985; 151:333-337) for predicting birth weight and macrosomia. METHODS We conducted a prospective cohort study of pregnancies complicated by pregestational ...

The well-documented sex difference in mental rotation favoring males has been shown to emerge only for 2-dimensional presentations of 3-dimensional objects, but not with actual 3-dimensional objects or with virtual reality presentations of 3-dimensional objects. Training studies using computer games with mental rotation-related content have demonstrated training effects on mental rotation perfo...

introduction: breast conserving radiotherapy is one of the most common procedures performed in any radiation oncology department. a tangential parallel-opposed pair is usually used for this purpose. this technique is performed using 2d or 3d treatment planning systems. the aim of this study was to compare 2d treatment planning with 3d treatment planning in tangential irradiation in breast conse...

A mixed semi-analytical cum numerical approach is presented in this paper which accounts for the coupled mechanical and electrical response of piezoelectric, functionally graded (FG) and layered composite hollow circular cylinders of finite length. Under axisymmetric mechanical and electrical loadings, the three-dimensional problem (3D) gets reduced to a two-dimensional (2D) plane strain proble...

In the title coordination compound, catena-poly[[[bis[diaquacadmium(II)]-mu(2)-trans-1,2-bis(4-pyridyl)ethene]bis{mu(2)-2,2'-[(5-carboxymethoxy-m-phenylene)dioxy]diacetato}] trans-1,2-bis(4-pyridyl)ethene solvate dihydrate], {[Cd(2)(C(12)H(10)O(9))(2)(C(12)H(10)N(2))(H(2)O)(4)].C(12)H(10)N(2).2H(2)O}(n), (I), each Cd(II) centre adopts a pentagonal-bipyramidal coordination geometry. The incomple...