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相关概念视频

Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

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In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
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Rigid Body Equilibrium Problems - I00:49

Rigid Body Equilibrium Problems - I

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A rigid body is said to be in static equilibrium when the net force and the net torque acting on the system is equal to zero. To solve for rigid body equilibrium problems, do the following steps.
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Categories of Equilibrium01:30

Categories of Equilibrium

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Equilibrium is a crucial concept in physics, enabling us to understand how forces interact with bodies to produce no or constant motion. In two-dimensional equilibrium, force systems can be classified into different categories based on their characteristics.
One of the categories of equilibrium is collinear equilibrium, which involves forces acting along a straight line. This type of equilibrium requires only one force equation in the direction of the forces, as the other equations are...
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Alternative Sets of Equilibrium Equations01:31

Alternative Sets of Equilibrium Equations

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When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments acting on a system balance each other, resulting in no net movement or rotation. In many cases, equilibrium can be described by a set of standard equations. However, in some situations, alternative sets of equilibrium equations must be used to describe the system's behavior accurately.
One example of such a situation can be observed in a...
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Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

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The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
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Dynamic Equilibrium02:20

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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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用混合类型固定点约束来解决平衡问题的算法.

Lifang Guo1, Imo Kalu Agwu2, Umar Ishtiaq3

  • 1School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, China.

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概括
此摘要是机器生成的。

这项研究引入了新的非线性映射 (θ-严格不对称的伪合约型多值映射) 和一种新的代方法. 该方法汇聚到平衡问题的解决方案和共同的固定点,增强现有文献.

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科学领域:

  • 非线性分析是一种非线性分析.
  • 功能分析是一种功能分析.
  • 优化理论 优化理论

背景情况:

  • 均衡问题 (EP) 是应用数学和经济学的基本问题.
  • 对于多值映射的固定点理论对于解决各种数学模型至关重要.
  • 现有的方法往往缺乏对复杂的映射类型的融合保证.

研究的目的:

  • 引入一个新的映射类别: θ-严格不对称的伪合约型多值映射 (θ-SAPM).
  • 开发和分析一种新的代方法来解决平衡问题并找到共同的固定点.
  • 在非线性分析和固定点理论中扩展和概括现有结果.

主要方法:

  • 在希尔伯特空间中定义和分析 θ-SAPM.
  • 启动一个新的代算法.
  • 在非线性函数分析中使用标准技术进行收分析.
  • 展示映射类独立性的演示.
  • 拟议方法的数值说明.

主要成果:

  • 代方法与EP的解决方案集的强烈融合.
  • 两个映射家族 (θ-SAPM和 θ-严格伪合约型多值映射 - θ-SPM) 的共同固定点集的强烈趋同.
  • 证明所考虑的映射类的独立性.
  • 通过数值示例验证方法的可执行性.

结论:

  • 拟议的方法为解决平衡问题和找到共同的固定点提供了一个强大的工具.
  • 新引入的 θ-SAPM 类扩大了研究的非线性映射的范围.
  • 这些发现概括并改进了文献中的几个现有结果.