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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...
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...
Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained.
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...
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 ...
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...
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...
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, ...
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...
Studying expressions of the form (f(x)D)p, where D = d dx is the derivation operator, goes back to Scherk’s Ph.D.
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.
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...
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...

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