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相关概念视频

Design Example: Dimensioning of Concrete Masonry Construction01:13

Design Example: Dimensioning of Concrete Masonry Construction

92
For the construction of a storeroom using concrete masonry units, it's essential to align the dimensions of the structure with the actual sizes of the blocks and the intended mortar joints. On the site in question, there's a stockpile of concrete masonry blocks with a nominal size of eight by eight by sixteen inches, which are to be used in the construction of the storeroom.
The site engineer has laid out a plan for the storeroom with external dimensions of twelve feet in length and...
92
Load along a Single Axis01:29

Load along a Single Axis

283
In structural engineering, the analysis of beams subjected to varying loads is a critical aspect of understanding the behavior and performance of these structural elements. A common scenario involves a beam subjected to a combination of different load distributions.
Consider a beam of length L subjected to a varying load, which is a combination of parabolic and trapezoidal load distribution along the x-axis. In this case, it is essential to determine the resultant loads, their locations, and...
283
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

251
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
251
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

707
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
707
Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

265
One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
265
Design Example: Calculating Safe Diameter for Wind-Exposed Disc01:17

Design Example: Calculating Safe Diameter for Wind-Exposed Disc

43
Assessing safety in wind-exposed installations is crucial to preventing potential failures. This example explores the calculation and design adjustments needed to mount a circular disc on a building facade, where wind forces are a primary concern. A 4-meter diameter disc was initially designed as an aesthetic feature facing winds at a velocity of 25 meters per second, with an air density of 1.25 kilograms per cubic meter. Given these conditions, the drag force on the disc was determined using...
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Quasi-light Storage for Optical Data Packets
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(重新包装) 同等的磁盘成矩形.

Fedor V Fomin1, Petr A Golovach1, Tanmay Inamdar2

  • 1University of Bergen, Bergen, Norway.

Discrete & computational geometry
|November 19, 2024
PubMed
概括
此摘要是机器生成的。

这项研究引入了磁盘重装问题,证明了这一点.

关键词:
循环包装是一个循环包装.计算几何学计算几何学参数化的算法参数化算法.单元磁盘是一个单元磁盘.

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相关实验视频

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科学领域:

  • 计算几何学的计算几何学
  • 离散的数学 离散的数学

背景情况:

  • 同等磁盘包装问题,即在矩形中排列非重叠的磁盘,是一个具有开放计算复杂性的基本几何挑战.
  • 算法概括对于理解包装复杂性和开发高效解决方案至关重要.

研究的目的:

  • 介绍和分析磁盘重装问题:确定少量磁盘重定位是否可以容纳更多的磁盘.
  • 为了确定这个通用包装问题的计算复杂性.

主要方法:

  • 用参数n (磁盘),k (额外的磁盘) 和h (重新定位的磁盘) 来重新包装问题的正式定义.
  • 对重新包装问题的NP硬度的证明,即使对于k.的小值也是如此.
  • 开发一个固定的参数可处理的算法,运行时间取决于输入大小和参数k和h.

主要成果:

  • 磁盘重新打包问题被证明是NP-hard的k=2.
  • 介绍了一种算法,该算法在时间O{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}{\displaystyle O}}}

结论:

  • 重装问题提供了一个可处理的算法方法来解决磁盘包装的挑战.
  • 固定参数可处理算法为解决重新包装问题的实例提供了一种有效的方法.