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宿迁 2015 3 SQC 航模提高课程 Model Aircraft Colloquia 3.27.2015 Friday Millennium Prize Puzzle Jun Steed Huang [email protected] 宿迁 2015 3

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宿迁 2015年 3月

SQC

航模提高课程

Model Aircraft Colloquia

3.27.2015 Friday

Millennium Prize Puzzle

Jun Steed Huang

[email protected]

宿迁 2015年 3月

宿迁 2015年 3月

SQC

航模提高课程

Millennium 7 Prize Problems

1. P=NP Can the dispatcher be lazy ? 1970s

2. Hodge Can high dim space be decomposed ?1930s

3. Poincare Apple is not same as donut ! 1900s

4. Riemann Is prime distribution regular ? 1850s

5. Yang-Mills There is always a ghost !?1950s

6. Navier-Stokes How many solutions ? 1820s

7. Birch Swinnerton-Dyer : Only oval fly! 1960s

宿迁 2015年 3月

SQC

航模提高课程

NP up bound \NP/ != P

1. P=NP? Can the dispatcher be lazy ?

If there is an algorithm (such as a Turing machine, or a LISP or Pascal program with unlimited memory), the correct answer can be given for a string of length n inputs in the most n ^ k steps, where k is an independent In the input string of constants, then we call the problem can be solved in the polynomial time, and it is placed in class P. Most computer scientists believe that P ≠ NP. No one can find a polynomial time algorithm for a non-deterministic (non-deterministic) Polynomial complete problem.

宿迁 2015年 3月

SQC

航模提高课程

NP lower bound /NP\ = P

1971 by UoT Professor Stephen A. Cook et al

宿迁 2015年 3月

SQC

航模提高课程

2. Hodge Can high dim space be decomposed ?

Whether the shape of a given object can be formed by bonding a simple geometric building block with increasing numbers of dimensions. In this promotion, the geometric starting point of the program becomes blurred and must be added without any geometric interpretation of the parts. Hodge's conjecture that Hodge's closed-chain components are a rational combination of geometric components called algebraic closed chains for the particularly perfect spatial type of projective algebra clusters.

1935 by W. V. D. Hodge

Shinichi MochizukiIUT \HC/ != Q

宿迁 2015年 3月

SQC

航模提高课程

Shinichi MochizukiIUT /HC\ = Q

宿迁 2015年 3月

SQC

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道生一,一生二

3. Poincare Apple is not same as donut !

In 1904, Poincare put forward a seemingly simple topology of the conjecture: in a three-dimensional space, if each closed curve can shrink to a little, then this space must be a three-dimensional ball. But in 1905 found the error, modified as: "Any n-dimensional spherical with n-dimensional closed manifold must be homologous in the n-dimensional sphere." Later, this conjecture was extended to more than three-dimensional space, known as the "high-dimensional Poincare guess. "

宿迁 2015年 3月

SQC

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二生三,三生万

More than equal to the five - dimensional Poincaré conjecture proved by Stephen Smell;The four-dimensional Poincaré conjecture was confirmed by Michael Friedman;Three-dimensional Poincare conjecture proved by the Russian mathematician Perelman;They were awarded the 1961, 1986 and 2006 Fields Award respectively.

亏格 0 1 2 3

宿迁 2015年 3月

SQC

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Our Integel Complexity\n/ > /n\ > log2(n)

4. Riemann Is prime distribution regular ?!

German mathematician Riemann (1826 ~ 1866) observes that the frequency of prime numbers is closely related to the structure of a well-constructed Riemannian zeta function ζ (s). The Riemann hypothesis asserts that all meaningful solutions of the equation ζ (s) = 0 are on a 1/2 line: Root line!

宿迁 2015年 3月

SQC

航模提高课程

Prime FibonacciP(F) = 1 mod(4)

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Space is not empty where ghost particle hide

5. Yang-Mil ls There is always a ghost !?!

In 1954, Yang Zhenning and Mills proposed

Yang - Mills norms theory, put forward the theory of gauge field. The theory will produce particles that carry the force, with charge but no mass! However, the difficulty is that if the charged particles are of no mass, then why is there no experimental evidence? And if the particle is assumed to be of mass, the normative symmetry will be destroyed.

宿迁 2015年 3月

SQC

航模提高课程

Space is made of ghost mass

杨振宁

宿迁 2015年 3月

SQC

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MH370 \Ns/ != S

6. Navier-Stokes How many solutions

French engineer Navier and the British mathematician Stoke, the sticky items are also taken into account is the Navier-Stoke equation. Since 1943 the French mathematician Leray proved that the solution of the whole time after the weak solution, is the solution unique? The result is that the strong solution is unique. So this question becomes: the whole solutions? Is it proof that the solution will burst in a limited time? To solve this problem contribute to the navigation project, especially turbulence killed MH370 (turbulence)!

宿迁 2015年 3月

SQC

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Fractal /Ns\ = S

Navier - Stokes is currently only about a hundred special solution is solved. The nonlinearity is due to convection acceleration (the acceleration associated with the point velocity change), so any convection will involve nonlinearity regardless of whether the turbulence or not.

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All Ellipses \Key/ = 1/0

7. Birch Swinnerton-Dyer Only oval fly ?

Refers to the rank of any elliptic curve on the rational domain, where the L function is equal to the order of the Abel group. When the solution is an Abelian point, Beech and Sternon - Dell guessed that: the rationality of the group size with a related Zeta function z (s) at point s = 1 near the state: If z is equal to 0, then there are infinite number of rational points (solution), on the contrary, if z is not equal to 0, then there are only a limited number of such points. 1960s.

宿迁 2015年 3月

SQC

航模提高课程

ECC /Key\ = p/q

Elliptic encryption algorithm (ECC) is a public key cryptography system, originally proposed by Koblitz and Miller in 1985, whose mathematical basis is to use the rational points on elliptic curves to compute the computational complexity of elliptic discrete logarithms on Abel addition groups The

宿迁 2015年 3月

SQC

航模提高课程

航模 Colloquia

Thank you for watching this

presentation!

谢谢邹青,黄佳敏,姚成,孙晨旭,

韩学波,沙龙,周嘉宇的协助。

宿迁 2015年 3月