quintic

简明释义

英[ˈkwɪntɪk]美[ˈkwɪntɪk]

adj. （数学）五次方的；五次的

n. （数学）五次多项式（方程）

英英释义

单词用法

同义词

反义词

例句

1.The applied interpolation method adopts quintic spline and derivatives generation approach for discrete points by using quartic polynomial, which can better meet the needs of high-accuracy machining.

所提出的插补方法采用五次样条和四次曲线多项式微分法近似求取导数，能够更好的满足精确加工的需要。

2.At the same time, the center conditions and bifurcation of limit cycles at the origin of the quintic polynomial system are also investigated.

同时还研究了一类五次系统原点的中心条件及在同步扰动下原点与无穷远点的极限环分支问题。

3.A algorithm to reconstruct the corner with quintic spline curves was proposed for improving cutter's motion stability and transition velocity.

为提高裁刀拐角过渡速度及获得良好的运动平稳性，提出五次样条曲线拐角重构算法。

4.In this paper, we consider some planar quintic Hamiltonian vector field with Z3-equivariant property, get its global phase portraits, and classify its parameter space.

文章考虑了一类具有等变性质的五次哈密顿向量场的全局性质，得到了其全局相图并对参数空间进行了划分。

5.This paper present a sufficient and necessary condition of constructing quintic PH curves and analyze the geometric meaning of the control polygon.

本文给出了构成五次PH曲线的充要条件，分析了其控制多边形的几何意义。

6.Based on the curve of quintic polynomial, the take-up CAM is designed, and the method of optimized design is presented in this paper.

利用五次多项式曲线对挑线凸轮进行了设计；并根据刺绣机的特殊要求，提出了刺绣机最优化设计方法。

7.In this paper, the problem of limit cycles bifurcated from the equator for a quintic polynomial system is investigated.

本文研究一类五次平面多项式系统赤道极限环分支问题。

8.In Chapter 4 and Chapter 5, complete researches have been done respectively on the center conditions and center integral of a quintic system and a septic system.

在第四章和第五章，分别对一类五次系统和七次系统的无穷远点的中心条件和中心积分进行了完整研究。

9.It is the first time that 7 limit cycles can bifurcated from the infinity for a class of quasi quintic system.

首次证明了拟五次多项式系统在无穷远点能分支出7个极限环。

10.The solution to the equation is a complex quintic 五次方程 that requires numerical methods.

这个方程的解是一个复杂的quintic 五次方程，需要数值方法。

11.In algebra, a quintic 五次多项式 can have up to five real roots.

在代数中，一个quintic 五次多项式最多可以有五个实根。

12.Graphing a quintic 五次函数 reveals its intricate behavior near the roots.

绘制一个quintic 五次函数的图形可以揭示其在根附近的复杂行为。

13.The quintic 五次方程 is often studied in advanced calculus courses.

在高级微积分课程中，通常会研究quintic 五次方程。

14.Finding the roots of a quintic 五次多项式 can be a challenging task.

寻找一个quintic 五次多项式的根可能是一项具有挑战性的任务。

作文

In the realm of mathematics, particularly in algebra, the term quintic refers to a polynomial of degree five. This means that the highest exponent of the variable in the polynomial is five. Understanding quintic equations is essential for students who wish to delve deeper into advanced mathematical concepts. A quintic equation can be represented in the general form as: ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, where a, b, c, d, e, and f are constants, and a cannot be zero. The complexity of quintic equations often arises from their non-linear nature, making them significantly more challenging to solve compared to quadratic or cubic equations. Many real-world problems can be modeled using quintic equations. For example, in physics, the motion of certain objects can be described by quintic functions when considering the effects of forces acting on them over time. Additionally, in engineering, quintic polynomials can be used to design curves and surfaces in computer graphics and robotics. The ability to manipulate and solve quintic equations is a valuable skill that can lead to a better understanding of these applications. However, solving quintic equations is not straightforward. Unlike quadratic and cubic equations, which have well-defined formulas for finding their roots, there is no general formula for quintic equations. This was famously proven by the mathematician Niels Henrik Abel in the early 19th century, establishing that general polynomial equations of degree five or higher cannot be solved using radicals. As a result, mathematicians often rely on numerical methods or special techniques to approximate the solutions of quintic equations. One of the most common methods for solving quintic equations is to use numerical algorithms, such as Newton's method or the Durand-Kerner method. These methods provide approximate solutions, which can be refined further depending on the required accuracy. Additionally, graphing calculators and computer software can help visualize the behavior of quintic functions, allowing students and professionals alike to gain insights into the roots and characteristics of these equations. In conclusion, the concept of quintic equations plays a crucial role in various fields of study, including mathematics, physics, and engineering. Although they present unique challenges due to their complexity and the absence of a general solution, understanding quintic equations is vital for anyone looking to explore higher-level mathematics. By mastering the techniques to analyze and solve these equations, one can unlock a deeper appreciation for the beauty and intricacies of mathematical relationships that govern our world.

在数学的领域，特别是代数中，术语quintic指的是五次多项式。这意味着多项式中变量的最高指数为五。理解quintic方程对于希望深入研究高级数学概念的学生来说至关重要。quintic方程可以用一般形式表示为：ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0，其中a、b、c、d、e和f是常数，且a不能为零。quintic方程的复杂性通常源于其非线性特性，使其比二次或三次方程更具挑战性。 许多现实世界的问题可以用quintic方程建模。例如，在物理学中，某些物体的运动可以通过quintic函数来描述，当考虑到作用在它们上的力随时间变化的影响时。此外，在工程学中，quintic多项式可以用于计算机图形学和机器人技术中的曲线和表面的设计。能够操纵和解决quintic方程是一项宝贵的技能，可以使人们更好地理解这些应用。 然而，解决quintic方程并不简单。与有明确公式可用于寻找根的二次和三次方程不同，没有通用公式可以解决quintic方程。这一点在19世纪初由数学家尼尔斯·亨里克·阿贝尔（Niels Henrik Abel）著名证明，确立了五次或更高次数的多项式方程不能用根式求解。因此，数学家们通常依赖数值方法或特殊技术来近似求解quintic方程的解。 解决quintic方程最常用的方法之一是使用数值算法，例如牛顿法或杜兰德-科尔纳法。这些方法提供了近似解，可以根据所需的准确性进一步精炼。此外，图形计算器和计算机软件可以帮助可视化quintic函数的行为，使学生和专业人员能够深入了解这些方程的根和特征。 总之，quintic方程的概念在数学、物理和工程等多个学科中发挥着至关重要的作用。尽管由于其复杂性和缺乏通用解而带来了独特的挑战，但理解quintic方程对于任何希望探索更高水平数学的人来说都是至关重要的。通过掌握分析和解决这些方程的技术，人们可以打开对支配我们世界的数学关系之美和复杂性的更深层次的欣赏。