Boundedness by 3 of the Whitney Interpolation Constant

Let the function fC[0,1] satisfy f( . We prove the estimate

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平面有界调和函数的B1och常数估计

得到了一个平面有界调和函数系数的精确估计式,由此改进了平面有界调和映照的Bloch常数估计,并相应地改进了双调和映照的单叶半径估计.这些结果是Grigoryan,Huang和Abdulhadi等所得结论的推广.     

On Bachet's diophantine equationx 3=y 2=k

Using Eisenstein's law of cubic reciprocity we investigate cases in whichx ³=y ²+k is unsolvable in the ring of rational integers In particular we show, that for all primesp ± 1 (mod 9),p3, the equationx ³=y ²+3p(p±9) has no solutions in .     

关于Lucas三角形猜想的一个结果

运用初等方法,证明k=7时Lucas三角形不存在.     

On equidistant binary codes of lengthn=4k+1 with distanced=2k

The aim of this paper is to provide a short proof of the main result (Theorem 2.12) of [3], using standard methods from the theory of combinatorial designs. This paper was submitted to Combinatorica at the request of the editors.     

Existence of (q,k, 1) difference families with q a prime power and k = 4, 5

The existence of a (q, k, 1) difference family in GF(q) has been completely solved for k = 3. For k = 4, 5 partial results have been given by Bose, Wilson, and Buratti. In this article, we continue the investigation and show that the necessary condition for the existence of a (q, k, 1) difference family in GF(q), i.e., q ≡ 1 (mod k(k − 1)) is also sufficient for k = 4, 5. For general k, Wilson's bound shows that a (q, k, 1) difference family in GF(q) exists whenever q ≡ 1 (mod k(k − 1)) and q > [k(k − 1)/2]^k(k−1). An improved bound on q is also presented. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 21–30, 1999     

Class number 5, 6 and 7

We outline the determination of all imaginary quadratic fields with class number 5, 6 or 7.

     

关于Fibonacci三角形猜想k=6的证明

运用初等方法,证明k=6时Fibonacci三角形不存在.     

Linear relations on LLT polynomials and their k-Schur positivity for $$k=2$$ k = 2

Journal of Algebraic Combinatorics - LLT polynomials are q-analogs of products of Schur functions that are known to be Schur positive by Grojnowski and Haiman. However, there is no known...     

Some new bibds with k = 6 and λ = 1

(v, 6,1) BIBDs are given for several new values of v. This reduces to 55 the number of v values for which existence of a (v,6,1) BIBD is in doubt. A new resolvable (565,5,1) BIBD is also given. © 1995 John Wiley & Sons, Inc.     

Entropy estimates for some C-endomorphisms

In this paper we compute the non-commutative topological entropy in the sense of Voiculescu for some endomorphisms of stationary inductive limits of circle algebras. These algebras are groupoid C*-algebras, and the endomorphisms restricted to the canonical diagonal are induced by some expansive maps, whose entropies provide a lower bound. For the upper bound, we use a result of Voiculescu, similar to the classical Kolmogorov-Sinai theorem. The same technique is used to compute the entropy of a non-commutative Markov shift.

     

An algebraic study of BIB designs: A complete solution for v = 6 and k = 3

The set of all distinct blocks of a BIB design is referred to as the support of the design. The family of BIB designs with v = 6 and k = 3 is studied in depth from the view of possible support sizes. Via a linear algebraic technique it is shown that: (i) a BIB design with v = 6 and k = 3 exists if and only if the support size belongs to {10, 14, 16, 17, 18, 19, 20}; (ii) the minimum block size, b, needed to obtain a BIB design with support size $\text{b}{}^1$ is given by:

     

16.

猜想M(2k,k+1)=3k-1+[(k-1)/2]的反例          下载免费PDF全文

游林  王天明 《数学研究及应用》2002,22(2):194-196

Brualdi与Jung在[1]中研究了一类具有固定线和k的n×n矩阵上的最大跳跃数M(n,k),并提出猜想M(2k, k + 1) = 3k - 1 + [(k-1)/2].本文给出了这一猜想的两个反例．     

17.

The diophantine equationx 2+2 k =y n     

J. H. E. Cohn 《Archiv der Mathematik》1992,59(4):341-344

The author wishes to thank the referee most sincerely for the observation immediately following the statement of the theorem.     

18.

Effective primality tests for integers of the formsN=k3 n +1 andN=k2 m 3 n +1     

Andreas Guthmann 《BIT Numerical Mathematics》1992,32(3):529-534

Using third roots of unity Proth's theorem for primality testing is generalized to integers of the formN=k3 ⁿ +1, avoiding the use of Lucas sequences which are more suitable ifN+1 is factored instead ofN–1. This approach has the advantage of being easily combined with Proth's test and gives polynomial time algorithms for testing integers of the formN=k2 ^m 3 ⁿ +1.     

19.

Discrete Interpolation of G01 Codes in 2D Machining under Bounded Accelerations     

Hongbo Li  Xiaoshan Gao  Lixian Zhang  Ruiyong Sun 《Mathematics in Computer Science》2012,6(3):327-344

In this paper, a new algorithm is proposed to interpolate G01 codes in 2D milling. Without resorting to smooth curve approximation, the algorithm makes full use of the acceleration bounds to change directions with optimal velocities at the cutter location points designated by the G01 codes, and then makes global lookahead and optimization to generate time-optimal interpolation of the G01 codes. The algorithm is realized and tested on NC wood carving machine, showing that when compared with the classical equal-velocity corner-turning method, the current method can reduce the machining time by 14?C115 %, while maintaining better details than the classical method.     

20.

On an infinite class of steiner systems with t = 3 and k = 6     

《Journal of Combinatorial Theory, Series A》1986,42(1):55-60

     

$\text{b}{}^1$	10	14	16	17	18	19	20
$\text{b}$	10	20	20	30	40	30	20

猜想M(2k,k+1)=3k-1+[(k-1)/2]的反例

Brualdi与Jung在[1]中研究了一类具有固定线和k的n×n矩阵上的最大跳跃数M(n,k),并提出猜想M(2k, k + 1) = 3k - 1 + [(k-1)/2].本文给出了这一猜想的两个反例．     

The diophantine equationx 2+2 k =y n

The author wishes to thank the referee most sincerely for the observation immediately following the statement of the theorem.     

Effective primality tests for integers of the formsN=k3 n +1 andN=k2 m 3 n +1

Using third roots of unity Proth's theorem for primality testing is generalized to integers of the formN=k3 ⁿ +1, avoiding the use of Lucas sequences which are more suitable ifN+1 is factored instead ofN–1. This approach has the advantage of being easily combined with Proth's test and gives polynomial time algorithms for testing integers of the formN=k2 ^m 3 ⁿ +1.     

Discrete Interpolation of G01 Codes in 2D Machining under Bounded Accelerations

In this paper, a new algorithm is proposed to interpolate G01 codes in 2D milling. Without resorting to smooth curve approximation, the algorithm makes full use of the acceleration bounds to change directions with optimal velocities at the cutter location points designated by the G01 codes, and then makes global lookahead and optimization to generate time-optimal interpolation of the G01 codes. The algorithm is realized and tested on NC wood carving machine, showing that when compared with the classical equal-velocity corner-turning method, the current method can reduce the machining time by 14?C115 %, while maintaining better details than the classical method.