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91.
In this paper we give an explicit construction of the moduli space of the pointed complete Gorenstein curves of arithmetic genus g with a given quasi-symmetric Weierstrass semigroup, that is, a Weierstrass semigroup whose last gap is equal to 2g – 2. We identify such a curve with its image under the canonical embedding in the (g – 1)-dimensional projective space. By normalizing the coefficients of the quadratic relations and by constructing Gröbner bases of the canonical ideal, we obtain the equations of the moduli space in terms of Buchberger's criterion. Moreover, by analyzing syzygies of the canonical ideal we establish criteria that make the computations less expensive. 相似文献
92.
We consider a canonical Gorenstein curve C of arithmetic genus g in P g-1 (K), that admits a non-singular point P, whose Weierstrass semigroup is quasi-symmetric in the sense that the last gap is equal to 2g-2. By making local considerations at the point P and the second point of the curve C on its osculating hyperplane at P we construct monomial bases for the spaces of higher order regular differentials. We give an irreducibility criterion for the canonical curve in terms of the coefficients of the quadratic relations. We also realize each quasi-symmetric numerical semigroup as the Weierstrass semigroup of a reducible canonical Gorenstein curve, but we give examples of such semigroups that cannot be realized as Weierstrass semigroups of smooth curves. 相似文献
93.
We describe the Weierstrass semigroup of a Galois Weierstrass point with prime degree and the Weierstrass semigroup of a pair of Galois Weierstrass points with prime degree, where a Galois Weierstrass point with degree n means a total ramification point of a cyclic covering of the projective line of degree n.*Supported by Korea Research Foundation Grant (KRF-2003-041-C20010).**Partially supported by Grant-in-Aid for Scientific Research (15540051), JSPS. 相似文献
94.
CHEN Yong WANG Qi LI Biao 《理论物理通讯》2004,42(9)
Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1 1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions. 相似文献
95.
赵德钧 《宁波大学学报(理工版)》2004,17(4):419-423
首先给出了Gauss-Weierstrass算子的一类线性组合在Lp空间加权逼近的正、逆定理和逼近阶的特征刻划的一个一般结果,然后具体给出了一类加Jacobi权逼近的正、逆定理和逼近阶的特征刻划. 相似文献
96.
CHENYong WANGQi LIBiao 《理论物理通讯》2004,42(5):655-660
We generalize the algebraic method presented by Fan [J.Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). As an application of the method, we choose a (2 1)-dimensional asymmetric Nizhnik Novikov Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions‘soliton-like solutions, double-like periodic and trigonometric-like function solutions. 相似文献
97.
V. B. Sherstyukov 《Mathematical Notes》2007,82(3-4):555-563
We obtain a criterion for totally regular growth of canonical products with real symmetric zeros, which involves a generalization of the notion of condensation index of a sequence of positive numbers of a finite upper density. 相似文献
98.
In this paper we investigate from both a theoretical and a practical point of view the following problem: Let s be a function from [0;1] to [0;1] . Under which conditions does there exist a continuous function f from [0;1] to R such that the regularity of f at x , measured in terms of H?lder exponent, is exactly s(x) , for all x ∈ [0;1] ?
We obtain a necessary and sufficient condition on s and give three constructions of the associated function f . We also examine some extensions regarding, for instance, the box or Tricot dimension or the multifractal spectrum. Finally,
we present a result on the ``size' of the set of functions with prescribed local regularity.
November 30, 1995. Date revised: September 30, 1996. 相似文献
99.
The Higher Derivatives of Bianalytic Functions 总被引:1,自引:0,他引:1
Bianalyticfunctionsisanewkif1doffunctionspresentedrecently-PapersL1j'[2Jdls-cussedson1ebaslcpropertiesofbianalyticfunctions-Inthispaper,wewillgetthehigherdt'rivD'-tivesandWeierstrassTheorembytheresultsofpapers[lj.[2j.5l.TheFormulaofHigherDerivativesFromF2j,wehavetherepresentatlonformulaofbianalytlcfu11ctionsProvidedthattheintegralcanbedifferentiatedunderthesignofintegrationwefi11dFronlti1edefinitionofthe(ierivativeofl)ia11alyticfu11ctionlwehaveWearegoingtc)IJrovetlIeaboveformulainfollowi… 相似文献
100.
In this work we study the Liénard differential systems that admit a Weierstrass first integral or a Weierstrass inverse integrating factor. 相似文献