* * * Yokes appear in mathematics, physics and chemistry. Intention: The frame on the back of two cows is called yoke, so that the two cows can walk synchronously. * * * yoke is a pair that matches according to certain rules. In layman's terms, twins.

* * * The two real parts of a complex number of a yoke are equal, and the complex number with the opposite imaginary part is a conjugate complex number. (When the imaginary part is not equal to 0, it is also called * * * yoke imaginary number. ) The * * * yoke of the complex number Z is marked as z(z plus a horizontal).

According to the definition, if z=a+ib(a, b∈R), then z*** yoke = a-ib (a, b ∈ r), usually expressed as z(z plus a bar). * * * The point corresponding to the complex number of the yoke is symmetrical about the real axis. (as shown on the right)

Edit this paragraph * * * Yoke Roots When A, B, C and D are rational numbers, and at least one of √B and √D is irrational, it is said that A√B+C√D and A √ B-C √ D are mutually "* * * Yoke Roots". The product of these two formulas is a rational number.

(√: quadratic root sign)

Edit the concept of hyperbola of yoke in this paragraph: hyperbola H: (x 2)/(a 2)-(y 2)/(b 2) = 1 and hyperbola H': (y 2)/(b 2)-(x 2)/(a).

(a & gt0，b & gt0,c=√a^2+b^2)

The main properties are: they have the same asymptote, their four focus circles, and the sum of the squares of their reciprocal eccentricity is equal to 1.

Edit this paragraph * * * Yoke Matrix * * Yoke Matrix is also called Hermite Matrix. In Hermite matrix, every element in row I and column J is equal to the * * * yoke of the elements in row J and column I..

Edit the yoke transposition of the matrix in this paragraph. After transposing the matrix, each number is converted into its complex number.

[1] In the physical extreme value problem, one physical quantity (set as y) can obtain the maximum or minimum value. When another physical quantity (set as x) related to it increases continuously, y is a nonmonotonic function of x ... When the physical quantity y is equal to a value other than the extreme value, the physical quantity x can take two different values corresponding to it. When the sum or product of these two different values is a constant value, this phenomenon is called * * * yoke phenomenon. This * * * yoke phenomenon is reflected in mechanics, electromagnetism and optics (see "Resources" for details).

In addition, there is the concept of * * * yoke physical quantity in physics-the physical quantity with uncertain relationship is called * * * yoke physical quantity. For example, angular momentum and angle are a pair of yoke physical quantities in quantum mechanics.

Edit the normal * * * yoke effect in this paragraph, also known as π-π * * yoke. Refers to the dislocation of electrons when two or more double bonds (or triple bonds) are connected by a single bond. Ingold, C.K. called this effect intermediate effect, and thought that the displacement of this electron in the * * * yoke system was determined by the electronegativity of each atom and the size (or principal quantum number) of the p orbit. Therefore, if the following electronic dislocations occur in a simple normal yoke system: (for example: CH2═ch-ch2═ch-ch ═ch2═ch-ch o). The greater the electronegativity of Y atom, the greater its P orbital radius, and the greater its ability to attract electrons, which is more conducive to the * * * yoke effect of the group -—X Y attracting electrons from the reference double bond AB (as shown by the arrow on the right). On the contrary, if the electronegativity of atom A and its P orbital radius are larger, its ability to release electrons to move to atom Y is smaller, which is not conducive to giving the * * * yoke effect of electrons in the direction of -XY group. The properties of intermediate atoms B and X are also directly related to the yoke effect.

Edit the multi-electron * * * yoke effect in this paragraph, also called p-π*** yoke. In a simple multi-electron yoke system, Z is an atom or group with P electron pairs (or N electrons). In this * * * yoke system, in addition to the case that Z can form a p-π*** yoke, there is also a * * yoke effect in the reference double bond A B- (for example,

Wait here. ). The function of a pair of P electrons of Z atom is similar to that of -XY group in normal yoke system.

The super-* * yoke effect in this paragraph is also called-* * * yoke, which is a kind of bond electron of C-H bond of alkyl group and adjacent bond electron (carbon atom of alkyl group combines with tiny hydrogen atom, which has little shielding effect on electron cloud, and a pair of electrons of C-H bond of alkyl group are attracted by nuclear action, and when a certain distance is reached, several electrons on alkyl group attract each other. According to the multi-electron * * * yoke theory, a C-H bond or the whole CH group can be regarded as a pseudo atom, just like the Z atom in the structural formula: (for example, CH2 ═ CH-CH3, O CH-CH3, etc. ). Super-yoke effect exists in compounds with alkyl groups linked to unsaturated bonds. The size of super-* * yoke effect depends on the number of -H atoms in alkyl, with methyl being the strongest and tert-butyl the weakest. Super * * * yoke effect is much weaker than ordinary * * * yoke effect and multi-electron * * * yoke effect. (It can be divided into σ-π and σ-P, with σ-π being the most common)

Edit this paragraph with * * * yoke effect, which is also called the overlapping of P-rings and P-rings. In addition to the super * * yoke effect, alkyl groups with methyl groups or more may have the same * * yoke effect.

All isomorphic yoke effects initially refer to the interaction between C-H bonds on carbon atoms and adjacent bonds. A large number of chemical activity and electronic spectrum data show that there is a special p- or-* * * yoke phenomenon between propenyl ions and similar alkenylcarbonyl groups, that is, the so-called same yoke effect:

In propylene-based ions, it is the P orbital on the carbon atom of olefin, which partially overlaps with the empty P orbital on the carbocation (). In similar alkenylcarbonyl groups, the p orbitals of carbonyl carbon atoms and alkene carbon atoms partially overlap: