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141.
142.
研究勾股方程给定正整数N时,方程是否有解,有几组解,怎样求解.在证明N的解与N的因数的基本解和本原解三者之间存在着一一对应关系的基础上,利用素数的本原解和两组本原解的勾股积运算,经逐次递推,导出了计算N的各种不同类型因数的本原解的计算方法,得到了计算任意N的所有解的简捷方法,并给出了计算全部解的组数的初等公式.填补了多年来研究勾股数的一个空白. 相似文献
143.
《代数通讯》2013,41(8):2717-2723
Let R be a local ring and M a finitely generated generalized Cohen-Macaulay R-module such that dim R M = dim R M/αM + heightMα a for all ideals α of R. Suppose that HI j(M) ≠ 0 for an ideal I of R and an integer j > heightM I. We show that there exists an ideal J ? such that a. heightM J = j; b. the natural homomorphism HI j(M) → HI j(M) is an isomorphism, for all i > j; and, c. the natural homomorphism HI j(M) → HI j(M) is surjective. By using this theorem, we obtain some results about Betti numbers, coassociated primes, and support of local cohomology modules. 相似文献
144.
145.
Kamal Bahmanpour Reza Naghipour 《Proceedings of the American Mathematical Society》2008,136(7):2359-2363
In this note we show that if is an ideal of a Noetherian ring and is a finitely generated -module, then for any minimax submodule of the -module is finitely generated, whenever the modules are minimax. As a consequence, it follows that the associated primes of are finite. This generalizes the main result of Brodmann and Lashgari (2000).
146.
On sums of a prime and four prime squares in short intervals 总被引:1,自引:1,他引:0
In this paper, we prove that each sufficiently large integer N ≠1(mod 3) can be written as N=p+p1^2+p2^2+p3^2+p4^2, with
|p-N/5|≤U,|pj-√N/5|≤U,j=1,2,3,4,
where U=N^2/20+c and p,pj are primes. 相似文献
|p-N/5|≤U,|pj-√N/5|≤U,j=1,2,3,4,
where U=N^2/20+c and p,pj are primes. 相似文献
147.
We study generalised prime systems , with tending to infinity) and the associated Beurling zeta function . Under appropriate assumptions, we establish various analytic properties of , including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of . Further we study ‘well-behaved’ g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on . Some of the above results are relevant to the second author’s theory of ‘fractal membranes’, whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.The work of M. L. Lapidus was partially supported by the U. S. National Science Foundation under grant DMS-0070497. 相似文献