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11.
We show that for any possible Weierstrass gap sequence L on a non-singular curve of genus 8 with twice the smallest positive non-gap is less than the largest gap there exists a pointed
non-singular curve (C, P) over an algebraically closed field of characteristic 0 such that the Weierstrass gap sequence at P is L. Combining this with the result in [6] we see that every possible Weierstrass gap sequence of genus 8 is attained by some
pointed non-singular curve.
*Partially supported by Grant-in-Aid for Scientific Research (17540046), Japan Society for the Promotion of Science.
**Partially supported by Grant-in-Aid for Scientific Research (17540030), Japan Society for the Promotion of Science. 相似文献
12.
In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model. 相似文献
13.
Kilian Kilger 《The Ramanujan Journal》2008,17(3):321-330
Generally it is unknown, whether or not ∞ is a Weierstrass point on the modular curve X
0(N) if N is squarefree. A classical result of Atkin and Ogg states that ∞ is not a Weierstrass point on X
0(N), if N=pM with p prime, p
∤
M and the genus of X
0(M) zero. We use results of Kohnen and Weissauer to show that there is a connection between this question and the p-adic valuation of cusp forms under the Atkin–Lehner involution. This gives, in a sense, a generalization of Ogg’s Theorem
in some cases.
相似文献
14.
Giuseppe Saccomandi 《International Journal of Non》2004,39(2):331-339
By an extension of the usual Weierstrass discussion for first-order differential equations, we determine a simple criterion which allows us to determine when compact structures are possible in second-order wave equations. For higher-order wave equations, such as the modified improved Boussinesq equation, this criterion may still be used, but the appearance of an overdetermined system of differential equations which is not trivially satisfied, unlike in the second-order case, renders the possibility of compact structures a happenstance. 相似文献
15.
Kotarski W.; El-Saify H. A.; Bahaa G. M. 《IMA Journal of Mathematical Control and Information》2002,19(4):461-476
A distributed control problem for the parabolic operator withan infinite number of variables and time delay is considered.The performance index has an integral form. Constraints on controlsare imposed. To obtain optimality conditions for the Neumannproblem, the generalization of the DubovitskiiMilyutintheorem given by Walczak in WALCZAK, S. Folia Mathematics, 1,187196 and WALCZAK, S. J. Optim. Theory Appl., 42, 561582was applied. 相似文献
16.
The Fractional Derivatives of a Fractal Function 总被引:2,自引:0,他引:2
Kui YAO Wei Yi SU Song Ping ZHOU 《数学学报(英文版)》2006,22(3):719-722
The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function. 相似文献
17.
Weierstrass不等式的新推广 总被引:2,自引:0,他引:2
石焕南 《数学的实践与认识》2002,32(1):132-135
利用控制不等式理论将 Weierstrass不等式 ∏ni=1( 1± xi) >1± ∑ni=1xi推广到一般初等对称函数上 ,并且给出一个上界估计 . 相似文献
18.
Clifford分析中双正则函数的Taylor展式及其性质 总被引:1,自引:0,他引:1
首先借助实Clifford分析中双正则函数的累次积分的换序公式,给出了双正则函数的Cauchy积分公式,然后由特征边界的Cauchy积分公式,得到了双正则函数的Taylor展式,并由此给出了双正则函数的唯一性定理,柯西不等式和Weierstrass定理. 相似文献
19.
Andrea Del Centina 《Annali dell'Universita di Ferrara》2008,54(1):37-59
In this note we give a historical account of the origin and the development of the concept of Weierstrass point. We also explain
how Weierstrass points have contributed to the study of compact Riemann surfaces and algebraic curves in the century from
Weierstrass’ statement of the gap theorem to the 1970s. In particular, we focus on the seminal work of Hürwitz that raised
questions which are at the center of contemporary research on this topic.
相似文献
20.
N. Kjurkchiev 《BIT Numerical Mathematics》1996,36(1):182-186
We give an alternative formulation of Le Verrier-Fadeev's method in terms of the Weierstrass root-finding method. Some computational aspects are discussed.This paper is partially supported by the Bulgarian Ministry of Science and Education, Contract MM-515/95. 相似文献