focal involution

简明释义

焦点对合

英英释义

例句

1.The study of focal involution is crucial in understanding the development of certain tumors.

研究局部内卷对于理解某些肿瘤的发展至关重要。

2.The pathologist noted that focal involution can indicate a response to therapy in cancer patients.

病理学家指出，局部内卷可能表明癌症患者对治疗的反应。

3.Research has shown that focal involution can affect the prognosis of breast cancer.

研究表明，局部内卷可能会影响乳腺癌的预后。

4.In our recent project, we observed focal involution in the tissue samples taken from patients.

在我们最近的项目中，我们观察到从患者取出的组织样本中有局部内卷现象。

5.During the seminar, the speaker highlighted the significance of focal involution in histopathology.

在研讨会上，演讲者强调了局部内卷在组织病理学中的重要性。

作文

In the realm of mathematics and physics, concepts often take on intricate meanings that can be challenging to grasp. One such term is focal involution, which refers to a specific geometric transformation involving points and lines in a plane. Understanding this concept requires a deep dive into the principles of projective geometry, where the relationships between various geometric entities become paramount. Focal involution can be visualized through the interaction of conic sections, particularly ellipses and hyperbolas. To illustrate, consider an ellipse with two foci. The focal involution involves a transformation that maps points on the ellipse to points on another curve while maintaining certain invariant properties. This transformation is not merely a change of position; it preserves the harmonic properties of the points involved. For instance, if we take two points on the ellipse and apply the focal involution, the resulting points will maintain a specific ratio that reflects their original positions relative to the foci.The significance of understanding focal involution extends beyond theoretical mathematics; it has practical applications in fields such as optics and engineering. In optics, the principles of focal involution can help in designing lenses that manipulate light paths effectively. Engineers utilize these geometric transformations to optimize structures and materials, ensuring that they perform efficiently under various conditions.Moreover, the study of focal involution also opens doors to advanced topics in mathematics, such as the exploration of dualities and symmetries within geometric frameworks. It encourages students and researchers alike to think critically about how different mathematical concepts interconnect. By mastering focal involution, individuals gain a deeper appreciation for the elegance of mathematics and its ability to describe the world around us.In conclusion, focal involution is a fascinating concept that encapsulates the beauty of geometric transformations. Its applications in various scientific fields underscore the importance of understanding such terms in depth. As we continue to explore the intricate relationships within mathematics, the role of focal involution serves as a reminder of the underlying connections that bind different areas of study together. Ultimately, grasping this concept not only enriches our mathematical knowledge but also enhances our ability to engage with the complexities of the universe.

在数学和物理的领域中，概念往往具有复杂的含义，这些含义可能难以理解。一个这样的术语是焦点反演，它指的是涉及平面中点和线的特定几何变换。理解这个概念需要深入研究射影几何的原理，在这一领域，各种几何实体之间的关系变得至关重要。焦点反演可以通过圆锥曲线之间的相互作用来可视化，特别是椭圆和双曲线。为了说明这一点，考虑一个具有两个焦点的椭圆。焦点反演涉及一种变换，它将椭圆上的点映射到另一条曲线上的点，同时保持某些不变性质。这种变换不仅仅是位置的变化；它保留了相关点的谐和性质。例如，如果我们取椭圆上的两个点并应用焦点反演，结果点将保持特定的比率，反映出它们相对于焦点的原始位置。理解焦点反演的重要性超越了理论数学；它在光学和工程等领域具有实际应用。在光学中，焦点反演的原理可以帮助设计有效操控光线路径的透镜。工程师利用这些几何变换来优化结构和材料，确保它们在各种条件下高效运行。此外，研究焦点反演还为高级数学主题打开了大门，例如探索几何框架中的对偶性和对称性。它鼓励学生和研究人员批判性地思考不同数学概念之间的相互联系。通过掌握焦点反演，个人能够更深刻地欣赏数学的优雅及其描述我们周围世界的能力。总之，焦点反演是一个迷人的概念，它概括了几何变换的美。它在各个科学领域的应用突显了深入理解此类术语的重要性。当我们继续探索数学中的复杂关系时，焦点反演的角色提醒我们不同研究领域之间的基本联系。最终，掌握这个概念不仅丰富了我们的数学知识，还增强了我们与宇宙复杂性互动的能力。