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本文试图从新的角度研究质数的充分条件，给出两个新的三角和公式，明确了计算出S集（特征和）的方法，计算出了前所未知的S集列表，以多项式的形式描述了质数新的必要条件，并进行了初步的验证，期待着能够被进一步加以证明。本文所得出的初步结果，将导致一种全新的数学研究方法的产生，并指向了数学难题NP完全问题的解决路径。
本文通过研究和分析已经获知的质数的S集（特征和），发现其中任意一位的符号Sj都是有规律可寻的，首次系统地揭示出确定S集中符号规律的法则，将会推动数论中特征和、三角和理论的发展。探讨了更加便于应用的新类型的质数充分必要条件，只需要较小的计算量就可以进行大质数识别的多项式公式，给出了数学难题“NP完全问题”的解决路径。在经典的数论中，主要是偏重于对“数”的研究。而在本文中，是把数字的结构分解成由若干位...
Classification of Kac representations in the logarithmic minimal models LM(1,p)
Classification of Kac representations logarithmic minimal models LM(1,p)
2011/3/3
For each pair of positive integers r, s, there is a so-called Kac representation (r, s) associated with a Yang-Baxter integrable boundary condition in the lattice approach to the logarithmic minimal m...
Generalized Compositions of Natural Numbers
optimal control optimal synthesis atom cooling
2011/2/21
Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained.
Cutting Mutually Congruent Pieces from Convex Regions
Cutting Mutually Congruent Pieces Convex Regions
2011/1/21
What is the shape of the 2D convex region P from which, when 2 mutually congruent convex pieces with maximum possible area are cut out, the highest fraction of the area of P is left over? When P is re...
A homology plane of general type can have at most a cyclic quotient singularity
Homology plane of general type BMY inequality Zariski-Fujita decomposition
2011/2/22
We show that a homology plane of general type has at worst a single cyclic quotient singular point. An example of such a surface with a singular point does exist [MS, Theorem 3.1]. We
also show that ...
Expansions of subfields of the real field by a discrete set
Expansions of subfields real field discrete set
2011/2/21
Let K be a subfield of the real field, D K be a closed and discrete set and f : Dn ! K be such that f(Dn) is somewhere dense. Then (K, f) defines Z. We present several applications of this result. W...
Identities and congruences for a new sequence
congruence Euler polynomial identity p-regular function
2011/2/22
Let [x] be the greatest integer not exceeding x. In the paper we introduce the sequence {Un} given by U0 = 1 and Un = −2P[n/2] k=1 n 2kUn−2k (n 1), and establish many recursi...
Some Congruences of Kloosterman Sums and their Minimal Polynomials
Congruences of Kloosterman Sums Minimal Polynomials
2011/1/18
We prove two results on Kloosterman sums over finite fields, using Stickelberger’s theorem and the Gross-Koblitz formula. The first result concerns the minimal polynomial over Q of a Kloosterman sum, ...
Points rationnels sur les quotients d'Atkin-Lehner de courbes de Shimura de discriminant $pq$
Points rationnels quotients d’Atkin-Lehner
2011/2/21
Let p and q be two distinct prime numbers, and Xpq/wq be the quotient of the Shimura curve of discriminant pq by the Atkin-Lehner involution wq. We describe a way to verify in wide generality a criter...
Some remarks about the derivation operator and generalized Stirling numbers
formal power series derivation operator Stirling num-bers
2011/2/22
Studying expressions of the form (f(x)D)p, where D = d dx is the derivation operator, goes back to Scherk’s Ph.D.
Some inversion formulas and formulas for Stirling numbers
Inversion formula Inverse function Stirling number
2011/2/22
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
Let a and b be positive integers and let p be an odd prime such that p =ax2+by2 for some integers x and y.
Toda Molecule and Tomimatsu-Sato Solution $\sim$ Toward the complete proof of Nakamura's conjecture$\sim$
Toda Molecule Tomimatsu-Sato Solution $\sim$
2010/12/28
We discuss the Nakamura’s conjecture stating that the Tomimatsu-Sato black hole solution with deformation parameter n is composed of the special solutions of the Toda molecule equation at the n-th lat...
An inverse problem of Calderon type with partial data
inverse problem of Calderon type partial data
2011/2/24
A generalized variant of the Calder´on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension n 2...