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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Proofs of two or infinity conjectures for Reeb orbits and closed geodesics
Reeb轨道 闭测地线 两个 无穷大猜想
2023/11/29
In this talk, we give a proof of the conjecture of Hofer-Wysocki-Zehnder published in 2003 asserting that a smooth and autonomous Hamiltonian flow on R4 has either two or infinitely many simple period...
Phase Portraits of Planar Vector Fields: Computer Proofs
Computer Proofs Planar Vector Fields
2015/8/25
This paper presents an algorithm for computer veri cation of the
global structure of structurally stable planar vector elds. Constructing
analytical proofs for the qualitative properties of phase p...
NEW PROOFS OF THE TORELLI THEOREMS FOR RIEMANN SURFACES
NEW PROOFS THE TORELLI THEOREMS RIEMANN SURFACES
2018/4/19
In this paper, by using the Kuranishi coordinates on the Teichm¨uller spaceand the explicit deformation formula of holomorphic one-forms on Riemann surface, we
give an explicit expression of the peri...
The proofs of twin prime conjecture and weaker Polignac's conjecture
prime distribution of primes twin primes Polignac's conjecture Goldbach-type problem
2011/9/18
This paper advanced a new method of appointedly covering prime circles with level colors of black degree, and showed twin prime conjecture and weaker Polignac's conjecture to be true with the proof by...
Algebraic proofs over noncommutative formulas
Proof complexity Algebraic proof systems Frege proofs Lower bounds Polynomial calculus
2012/12/4
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege, ...
Proofs of some binomial identities using the method of last squares
binomial identities method of last squares Proofs Combinatorics
2011/8/26
Abstract: We give combinatorial proofs for some identities involving binomial sums that have no closed form.
Direct proofs of the Feigin-Fuchs character formula for unitary representations of the Virasoro algebra
Direct proofs of the Feigin-Fuchs character unitary representations Virasoro algebra
2011/3/1
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary
discrete series of the Virasoro algebra with 0 < c < 1.
WZ-proofs of "divergent" Ramanujan-type series
Hypergeometric series WZ-method Ramanujan-type series for 1/ and 1/2 Barnes Integrals
2011/1/21
We prove some ”divergent” Ramanujan-type series for 1/ and 1/2 applying a Barnes-integrals strategy of the WZ-method.
Proofs of power sum and binomial coefficient congruences via Pascal's identity
binomial coefficient Pascal's identity
2010/11/8
A frequently cited theorem says that for n > 0 and prime p, the sum of the first p n-th powers is congruent to -1 modulo p if p-1 divides n, and to 0 otherwise. We survey the main ingredients in seve...
Proofs of definability of some varieties and sets of varieties of semigroups
Semigroup, variety lattice of varieties first-order formula definable set of varieties
2010/12/1
We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.
Some Proofs on Statistical Magnitudes for Continuous Phenomena
Statistical Magnitudes Continuous Phenomena
2010/4/2
In this work, the proofs concerning the continuity of the disequilibrium, Shannon information and statistical complexity in the space of distributions are presented. Also, some results on the existenc...
Visually Dynamic Presentation of Proofs in Plane Geometry Part 1. Basic Features and the Manual Input Method
Geometry theorem proving Visually dynamic presentation of proof Dynamic geometry Unordered geometry Gelernter Java Geometry Expert Morley’s theorem Feuerbach’s theorem Pythagorean theorem Pedal triangle
2013/9/9
With dynamic mediums such as computer displays, we propose a new kind of visually dynamic presentation of proofs in plane geometry. In asingle diagram for the proof, when the proof text goes on step b...
Visually Dynamic Presentation of Proofs in Plane Geometry
Geometry theorem proving Proof with hierarchical structures Visually dynamic presentation of proof Dynamic geometry Full-angle Deductive database Fixpoint Unordered geometry Hilbert geometry Tarski geometry
2013/9/9
We present the method for automated generation of visually dynamic presentations of plane geometry proofs based on the full-angle method. The proof generated by the full-angle method is organized hier...
Carleman's Inequality - History, Proofs and Some New Generalizations
Inequalities Carleman's inequality Pólya-Knopp's inequality Sharp constants Proofs Weights Historical remarks
2008/7/1
Carleman's Inequality - History, Proofs and Some New Generalizations.
Automated Generation of Readable Proofs with Geometric Invariants II. Theorem Proving With Full-Angles
Automated reasoning automated geometry theorem proving method based on angle forward chaining backward chaining
2013/9/9
We present a set of rules based on full-angles as the basis of automated geometry theorem proving. We extend the idea of eliminating variables and points to the idea of eliminating lines. We also disc...