Chapter 56: Mathematical Rhapsody III

After using Fermi's mimetic potential to replace the interaction between hard spheres--- beyond the scope of the lowest-order perturbation theory, the ground state energy divergence--the divergence difficulty is overcome by the derogation procedure

The spatiotemporal expression of production and inhibitors keeps the production of blood vessels under control

Theory lies in entanglement, both the coupling of various concepts and the continuous negation of development

The wave-particle duality --- in the non-abelian gauge field (non-reciprocal, sequential operation, no time inversion) ---in the non-abelian gauge field (non-reciprocal, sequential operation, no time inversion), and the probability performance may be expressed in a larger whole: abc=acb≠cab

The cosmic symmetry is not conserved, which is the tendency of space that makes contradictions occur

PCR is used inside cells to amplify genes that affect various expressions: transcripts and cell cycle regulators, DNA repair, replication, backbone proteins (substances, information transfer), cell adhesion molecules (information exchange), GTPases, phosphatases (energy)

Dirac's equation

The electron spin turns out to be a relativistic effect under the conservation of total angular momentum, which is necessary for coupling

To assemble a differential into an equation, there must first be an equation, and with an equation, the quantities on both sides of the equation are replaced by partial differentiation of the wave function, and the required differential equation comes out

In general, it is impossible to write a power higher than 2 as the sum of two powers of the same power. Pen Fun Pavilion wWw. biquge。 info is the following:

x^n+y^n=z^n, when n is greater than 2 there is no integer solution.

The first order is a one-dimensional line that allows addition

The second order is a two-dimensional area with a square sum relation on the three sides of a triangle

The third order is a three-dimensional volume, infinitely diverging

There is no unique factorization property of imaginary numbers, which may be the source of quantum

The undecidability theorem

The first undecidability theorem: If axiomatic set theory is compatible, then there are theorems that can neither be proved nor disproved.

= Completeness is impossible to achieve

The second indecidability theorem: There is no constructive process that proves that axiom systems are compatible.

= Compatibility can never be proven

sin and cos are similar to 1 and 0, and their coupling provides some relations: sin^2+cos^2=1^2+0^2=1; 1 and 0 are only different in phase, but their whole is similar (waveform), so probability is used as an important concept

Any periodic function can be seen as a superposition of sine waves of different amplitudes and phases, i.e., an infinite series of trigonometric functions

A thought of infinite approximation

The amplitude can be converted to and from the phase

Each harmonic is called a frequency component of the signal

Superposition, symmetry, time-shift, frequency-shift, time-scale variation, differential, convolutional

The product of the Fourier transform of the two functions is equal to the Fourier transform after their convolution

The Fourier transform of a function convolution is the product of the Fourier transform of the function. That is, a convolution in one domain is equivalent to a product in another, e.g. a convolution in the time domain corresponds to a product in the frequency domain.

f(g(x)*f(x))=f(g(x))f(f(x))

Polynomials are multiplied together, which is equivalent to the convolution of the coefficient vector. Convolution operations can be thought of as a string of inner product operations

The inertial mass is the resistance to the change in the state of motion, while the gravitational mass controls the strength of the force

The concentric circle structure of the solar system (which allows individual energy levels to change with constant orbits) (which should be integrated spin coupling) --- probability space of the electron cloud

The energy gained and lost in the transition is equal (think of the transition as a matrix operation, a kind of information, and not easy to reconcile)

Probability is also reflected in the change of orbit, and the spectral line is a kind of observer effect, which is the result of statistics

Level transitions --- vibrations of fluctuating strings

The wave function is related to the charge distribution of electrons around the nucleus, and does this account for the effect of charge density on the endpoint of the string

Motion is related to forces--- and is related to symmetry (the existence of forces is also selective, and if they are absent, they are unobservable, such as dark matter; the competition of forces, such as the hidden Markov model, makes them eventually occupy different ecological niches)

Starting from a suitable conserved quantity, the equation is found with symmetry: conservation of probability

Neutral mutations, changes in the proportion of amino acids

Neutral molecular evolution is only related to mutation rate, not population size

Isolate a phenomenon to study the relationship, and find the cycle with Fourier analysis

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