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1.
高阶半线性椭圆型方程奇摄动边值问题   总被引:83,自引:5,他引:78  
莫嘉琪  S.Shao 《数学进展》2001,30(2):141-148
本文研究了一类高阶半线性椭圆型方程奇摄动边值问题,利用比较定理,证明了渐近解的一致有效性。  相似文献
2.
倒向随机微分方程及其应用   总被引:41,自引:1,他引:40  
彭实戈 《数学进展》1997,26(2):97-112
本文将介绍一类新的议程:倒向随机微分方程,为了便于理解,我们将首先通过与常微分方程和经典的随机微分方程的对比,并通过数理经济和数学金融学中的一个典型的例子来引入倒向随机微分方程。  相似文献
3.
The State of Elliptic Curve Cryptography   总被引:40,自引:0,他引:40  
Since the introduction of public-key cryptography by Diffie and Hellman in 1976, the potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized. Although the discrete logarithm problem as first employed by Diffie and Hellman was defined explicitly as the problem of finding logarithms with respect to a generator in the multiplicative group of the integers modulo a prime, this idea can be extended to arbitrary groups and, in particular, to elliptic curve groups. The resulting public-key systems provide relatively small block size, high speed, and high security. This paper surveys the development of elliptic curve cryptosystems from their inception in 1985 by Koblitz and Miller to present day implementations.  相似文献
4.
The State of Elliptic Curve Cryptography   总被引:39,自引:0,他引:39  
Since the introduction of public-key cryptography by Diffie and Hellman in 1976, the potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized. Although the discrete logarithm problem as first employed by Diffie and Hellman was defined explicitly as the problem of finding logarithms with respect to a generator in the multiplicative group of the integers modulo a prime, this idea can be extended to arbitrary groups and, in particular, to elliptic curve groups. The resulting public-key systems provide relatively small block size, high speed, and high security. This paper surveys the development of elliptic curve cryptosystems from their inception in 1985 by Koblitz and Miller to present day implementations.  相似文献
5.
We consider the following boundary value problem ill the unbounded donain Liui = fi(x,u, Tu), i = 1, 2,' ! N,x E fl, (1) olLi "i0n Pi(x)t'i = gi(x,u), i = l, 2,',N,x E 0fl, (2) where x = (x i,', x.), u = (u1,' f uN), Th = (T1tti,', TNi'N) and [ n. 1 L, = -- I Z ajk(X)the i0j(X)C], Li,k=1' j=1 J] l Ltti = / K(x,y)ui(y)dy, x E n. jn K(x, y)ui(y)dy, x E n. Q denotes an unbounded dolllain in R", including the exterior of a boullded doinain and 0…  相似文献
6.
Efficient Arithmetic on Koblitz Curves   总被引:22,自引:0,他引:22  
It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation.Koblitz introduced a family of curves which admit especially fast elliptic scalar multiplication. His algorithm was later modified by Meier and Staffelbach. We give an improved version of the algorithm which runs 50 than any previous version. It is based on a new kind of representation of an integer, analogous to certain kinds of binary expansions. We also outline further speedups using precomputation and storage.  相似文献
7.
Efficient Arithmetic on Koblitz Curves   总被引:22,自引:0,他引:22  
It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation.Koblitz introduced a family of curves which admit especially fast elliptic scalar multiplication. His algorithm was later modified by Meier and Staffelbach. We give an improved version of the algorithm which runs 50 than any previous version. It is based on a new kind of representation of an integer, analogous to certain kinds of binary expansions. We also outline further speedups using precomputation and storage.  相似文献
8.
The method of fundamental solutions for elliptic boundary value problems   总被引:22,自引:0,他引:22  
The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over the last three decades. Several applications of MFS-type methods are presented. Techniques by which such methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are also outlined. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献
9.
椭圆外区域上的自然边界元法   总被引:15,自引:5,他引:10       下载免费PDF全文
邬吉明  余德浩 《计算数学》2000,22(3):355-368
1.引言 二十年来,自然边界元法已在椭圆问题求解方面取得了许多研究成果。它可以直接用来解决圆内(外)区域、扇形区域、球内(外)区域及半平面区域等特殊区域上的椭圆边值问题[1,2,5],也可以结合有限元法求解一般区域上的椭圆边值问题,例如基于自然边界归化的耦合算法及区域分解算法就是处理断裂区域问题及外问题的一种有效手段[2-4,6]。 人们在设计求解外问题的耦合算法或者区域分解算法时,通常选取圆周或球面作人工边界。但对具有长条型内边界的外问题,以圆周或球面作人工边界显然并非最佳选择,它将会导致大量的…  相似文献
10.
余德浩  贾祖朋 《计算数学》2002,24(3):375-384
1.引 言为求解微分方程的外边值问题常需要引进人工边界(见[1-4]),对人工边界外部区域作自然边界归化得到的自然积分方程即Dirichlet-Neumann映射,正是人工边界上的准确的边界条件(见[2-6]),这是一类非局部边界条件.自然积分算子即Dirichlet-Neumann算子,  相似文献
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