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Extensive mathematical English
The length unit L stands for length, and the English full name is "length"; W stands for width, and the full English name is "width".

Length is a measure of one-dimensional space and the distance from point to point.

Usually, when measuring the side length of a straight line in two-dimensional space, the one with a large length value is called long, which is neither greater than its value nor wider than the side length. So width is actually a measure of length, so the height of "vertical length" is measured in three-dimensional space.

The decay width of particles and forward scattering amplitude of unstable particles are not zero. Hamiltonian is not Hermite, its energy is unobservable, and its imaginary part is energy uncertainty. According to the uncertainty relation, the width and life are ≥ 1 (natural unit).

Extended data:

First, the basic theory of width:

As a basic concept of approximation theory, it was first put forward by the Soviet mathematician α η Andrei Andrey Kolmogorov in 1935. Its basic idea can be extracted from the following geometric problems.

On the Euclidean plane R2, the set of given points M is a graph surrounded by ellipses, and the origin (0,0) is the symmetrical center of M. Consider the deviation degree of any one-dimensional linear subspace F 1 of R2 from M. Every F 1 is a straight line passing through the origin o.

If the slope of F 1 changes, the deviation of F 1 from m will also change.

When F 1 coincides with the x axis, this quantity is the smallest and equal to the semi-short axis of the ellipse. This minimum value is called the one-dimensional width of point set m in R2 space (Andre Andrey Kolmogorov width). Generally speaking, if m is a symmetric set Fn about point o in Banach space X.

formula

Is the distance of any point xFn in any n-dimensional linear subspace of x and m.

The (overall) deviation between MFN treatment is.

formula

If Fn changes (n remains unchanged), choose fn to minimize the overall deviation of MFn. This will naturally lead to the following extreme problems: calculation

And find out the reason why Fn makes the lower bound come true.

Number dn (m; X) is called m, Kolmo in x.

formula

N-dimensional width in the sense of Grove.

The study of width in approximation theory mainly includes two aspects, namely, given DN (m; X), and find out all the n-dimensional linear subspaces that can realize the width. The research on these problems is not only of theoretical significance, but also of practical value. Because this will lead to finding a new and better approximation method of m.

In 1935, α η André Andrey Kolmogorov studied the widths of some function classes in X=l2 (squared summable function space). The systematic study of width theory began with Kiha Milov in 1950s, and great progress has been made in this field in recent 20 years.

Second, the length measurement

The measurement of length is the most basic measurement, and the most commonly used tool is the scale.

Length refers to the dimension of space. The international unit of length is meter (m), and commonly used units are kilometer (km), decimeter (dm), centimeter (cm), millimeter (mm), micron (micron) and nanometer (nm).

When converting length units, small units are converted into large units by multiplication and large units are converted into small units by division.

References:

Baidu Encyclopedia-Length

Baidu Encyclopedia-Width