Talk about mathematics

Closure symmetry breaking transfer. A fused solid mass capping sequence pair, solid polyethylene indeed have a single region Ke, the high-order red letter symbol Di Li, unitary junction reverse, plus a half hours, the entire star inverse partial supremum extension line Ba Ouxi Zhang twists empty pan homology manifolds are set off. This is to remember mathematical concepts, such as "cluster" is the inverse unitary knot, "ring" plus a half minutes. There's a great amount of knowledge is difficult. The following is a very, very good stuff, mostly the old knowledge of the new expressed the hope that a closer look, and digestion. The meaning of symbols reasonable, "Brain paper assignment" to create simple, beautiful, easy symbol expression theorem can not make the event. Symbol looks is that a few letters, a few brackets, combinations are basically fixed, new symbols are mostly to the old form to add new meaning. Here I have invented several symbols, (province write parameter range of the variable i is not 1 ~ n, is 0 ~ n); and a product identifier A: set A Q. P i for all elements (P, Q is any two predicates (verbs that indicates the nature of words or relationship, in fact, the nature of unary relations)); and the symbol represented by the product of the classical theorem: Theorem Inclusion and exclusion: | UAi | = Σ (-1) ^ (i-1 ) a; (a is the set {A1, A2, ... An}, P is the 'post mold', Q a 'and'). | UAi | n sets and is mold. Vieta theorem: polynomial Σai * x ^ (ni) = 0; (i = 0 ~ n), a0 = 1; then ai = (- 1) ^ iX; (X n is composed of a root set, P is' product ', Q a' and ', X [0] = 1) expand Theorem characteristic polynomial: det (λI-A) = Σ (-1) ^ iMλ ^ (ni); M [i] is all λI-A the i-th principal minor sum, product, and not break, and there is no P, Q. MASON formula wherein: Δ = Σ (-1) ^ iL; L is a collection of individual circuit component, P is the 'contact with each other than the loop gain of the product, Q is' and'. Negative change the principle of duality: (MP) '= M'P'; after (M modal words, P is the proposition, plus' (non) is the corresponding dual (Morgan formula is a special case) conventional dual pair of ( All bound, disabled, must, never, yes, and ....) '= (existence, may allow, no, sometimes, Africa, or .... ) Here should be of some use to people learn self-control, and the corresponding function is expressed by the old knowledge. What is a linear system, a concept to define it a dummy, pilot sets: one set each order derivative function of the natural composition. You can say: 0 lead set can be input and the output guide and set of elements set of linear representation of the system is linear. This represents a better expression than with a point, the old concept, and the concept they want to define the concept. In rational polynomial p zeros or poles of the corresponding function is only to remove the rest of the pole-zero function. The corresponding function can be simplified formula expression, have appeared in many places, such as "Lagrange interpolation formula." Here only we used the poles of the corresponding function. Referred to as τp (s); represents pole response with the corresponding function: p pole is modal mp = e ^ pt @@ Mp = e∧pT (modal many meanings herein refers to the modality response) is represented by the corresponding function pole response: response pole p yp = τp (p) mp; τp (p) is called modal coefficient, p is the remaining number, is used to determine the specific gravity of the modality. Conjugate roots if p = α + jw, p '= α-jw; the yp + yp' = 2 | τp (p) | e ^ αtcos (ωt + θ);. Wherein [theta] is τp (p) of the argument. This formula is a good, easy to remember that calculation, and can be seen how linear system stabilized with the proviso that 'all in very close left', and from this formula can understand why a frequency domain method (phasors) of C = RG, C is the response, which response to the input R of the pole, and the pole response transfer function G composition, and closing the poles of G full left extremely attenuated in response to a sinusoidal input of 0. the R if (two conjugated pure virtual pole), it can be seen from this formula is the same in response to the output sine wave frequency. Re-root the situation is a bit chaotic, with not many. P in the form of a single pole these four domains: domain multiplexing .1 / sp≌ frequency domain .1 / jw-p≌ .mp≌Z temporal domain .1 / 1-MpZ ^ (- 1); sinks angle function: h (s) = Σ∠ (s-zi) -Σ∠ (s-pi); (root locus used in the expression of knowledge) and recurring decimal fraction: 0.MMM ...... = M / 10 ^ n-1 ; complement formula: (1τ10 ^ k) '= 1τ'10 ^ k; armature equation: τ (k, n) = (k, n) ● τ (1,1 / [n / (n, k)] ); (synthesis of revolutions isochronous cycle) and summed difference: S (Δan) = an-a0; planar inverted group G = <∠θ, τ ,. > Simplification: ∠θτ∠θ = τ; cluster chain reversing plane equation:. ∠θ0 mo τ∠θi = τ ^ n∠ (Σ (-1) ^ iθn-i); HANOR: AnC = An- 1B ◎ AC ◎ Bn-1C Gray code: τn + 1 = 0τn, 1τ'n; contains Theorem: ∧pi → ∨qj (will change to another proposition propositions are equivalent to the original obtained after taking measurements on both sides of the negative portion) ; (transformed without changing proposition although more information can not be obtained, but the operation can be easy to form or to give form theorem), the formula is the formula never really must be the following three cases, and "take a negative change to the other side "of this operation is also the case in these three circles. 1. 2. The right has left false 3. true on both sides of contradiction (it's proved to be very simple, but a lot of it is a special case, such as CP rule, Morgan formula, reductio ad absurdum, all inference rules can be introduced by this theorem, as long as the 1 → p, p → 0,0Vp, etc. can also be seen as a propositional formula, the theorem is really best ah, truly this theorem, "Ya, ∧, V, →" four conjunctions link up, this is one of the most beautiful theorems. I would like to place it in the middle of a semantic model of public toilets for men and women have a sex change operation, a person from one toilet to another toilet, it degeneration, no matter how degeneration, will not change this sentence is true or false. "If the men's room of people, all men, then the women's room inside man" contains theorems, simple, symmetrical, wide, pure, clean, beautiful, bring endless imagination, it would be a broader, more simple, special case of a more abstract theorem false set:. S = {a | a does not belong to a}, reverse puzzle ring empty, full degree even Euler FIG different London K5, K3,3 of plan. ∧pi → ∨qj (after taking a portion of the negative sides of the transducer to another proposition measurements obtained with the original proposition equivalent); (does not change the conversion Proposition although more information can not be obtained, but the operation can be obtained to facilitate form or in the form obtained theorem), the formula is the formula never really must be the following three cases, and "take a negative change to the other side" of this operation is also the case in these three circles. 1. 2. The right has left false 3. true on both sides of contradiction (it's proved to be very simple, but a lot of it is a special case, such as CP rule, Morgan formula, reductio ad absurdum, all inference rules can be introduced by this theorem, as long as the 1 → p, p → 0,0Vp, etc. can also be seen as a propositional formula, the theorem is really best ah, truly this theorem, "Ya, ∧, V, →" four conjunctions link up, this is one of the most beautiful theorems. I would like to place it in the middle of a semantic model of public toilets for men and women have a sex change operation, a person from one toilet to another toilet, it degeneration, no matter how degeneration, will not change this sentence is true or false. "If the men's room of people, all men, then the women's room inside man" contains theorems, simple, symmetrical, wide, pure, clean, beautiful, bring endless imagination, it would be a broader, more simple, special case of a more abstract theorem false set:. S = {a | a does not belong to a}, reverse puzzle ring empty, full degree even Euler FIG different London K5, K3,3 of plan. ∧pi → ∨qj (after taking a portion of the negative sides of the transducer to another proposition measurements obtained with the original proposition equivalent); (does not change the conversion Proposition although more information can not be obtained, but the operation can be obtained to facilitate form or in the form obtained theorem), the formula is the formula never really must be the following three cases, and "take a negative change to the other side" of this operation is also the case in these three circles. 1. 2. The right has left false 3. true on both sides of contradiction (it's proved to be very simple, but a lot of it is a special case, such as CP rule, Morgan formula, reductio ad absurdum, all inference rules can be introduced by this theorem, as long as the 1 → p, p → 0,0Vp, etc. can also be seen as a propositional formula, the theorem is really best ah, truly this theorem, "Ya, ∧, V, →" four conjunctions link up, this is one of the most beautiful theorems. I would like to place it in the middle of a semantic model of public toilets for men and women have a sex change operation, a person from one toilet to another toilet, it degeneration, no matter how degeneration, will not change this sentence is true or false. "If the men's room of people, all men, then the women's room inside man" contains theorems, simple, symmetrical, wide, pure, clean, beautiful, bring endless imagination, it would be a broader, more simple, special case of a more abstract theorem false set:. S = {a | a does not belong to a}, reverse puzzle ring empty, full degree even Euler FIG different London K5, K3,3 of plan.