共查询到20条相似文献,搜索用时 46 毫秒
1.
Rubén A. Hidalgo Maximiliano Leyton-Álvarez 《Journal of Pure and Applied Algebra》2019,223(7):3057-3070
Let be a generalized Fermat pair of the type . If is the set of fixed points of the non-trivial elements of the group H, then F is exactly the set of hyperosculating points of the standard embedding . We provide an optimal lower bound (this being sharp in a dense open set of the moduli space of the generalized Fermat curves) for the Weierstrass weight of these points. 相似文献
2.
Vladimir Matveev 《Acta Appl Math》1994,36(1-2):187-210
A brief exposition of applications of the methods of algebraic geometry to systems integrable by the IST method with variable spectral parameters is presented. Usually, theta-functional solutions for these systems are generated by some deformations of algebraic curves. The deformations of algebraic curves are also related with theta-functional solutions of Yang-Mills self-duality equations which contain special systems with a variable spectral parameter as a special reduction. Another important situation in which the deformations of algebraic curves naturally occur is the KdV equation with string-like boundary conditions. Most important concrete examples of systems integrable by the IST method with variable spectral parameter having different properties within a framework of the behavior of moduli of underlying curves, analytic properties of the Baker-Akhiezer functions, and the qualitative behavior of the solutions, are vacuum axially symmetric Einstein equations, the Heisenberg cylindrical magnet equation, the deformed Maxwell-Bloch system, and the cylindrical KP equation.Dedicated to the memory of J.-L. Verdier 相似文献
3.
The Severi variety parameterizes plane curves of degree d with δ nodes. Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov–Witten invariants of CP2. Fomin and Mikhalkin (2010) [10] proved the 1995 conjecture that for fixed δ, Severi degrees are eventually polynomial in d. 相似文献
4.
We obtain new examples and the complete list of the rational cuspidal plane curvesC with at least three cusps, one of which has multiplicitydegC-2. It occurs that these curves are projectively rigid. We also discuss the general problem of projective rigidity of rational
cuspidal plane curves. 相似文献
5.
Let σ be a nontrivial automorphism of a compact connected Riemann surface X of genus at least two. Assume that σ fixes each of the theta characteristics of X. We prove that X is hyperelliptic, and σ is the unique hyperelliptic involution of X. 相似文献
6.
Nonconforming mixed finite element approximation to the stationary Navier-Stokes equations on anisotropic meshes 总被引:1,自引:0,他引:1
The main aim of this paper is to study the error estimates of a rectangular nonconforming finite element for the stationary Navier-Stokes equations under anisotropic meshes. That is, the nonconforming rectangular element is taken as approximation space for the velocity and the piecewise constant element for the pressure. The convergence analysis is presented and the optimal error estimates both in a broken H1-norm for the velocity and in an L2-norm for the pressure are derived on anisotropic meshes. 相似文献
7.
Francesca Vetro 《manuscripta mathematica》2008,125(3):353-368
Let Y be a smooth, connected, projective complex curve. In this paper, we study the Hurwitz spaces which parameterize branched
coverings of Y whose monodromy group is a Weyl group of type D
d
and whose local monodromies are all reflections except one. We prove the irreducibility of these spaces when and successively we extend the result to curves of genus g ≥ 1. 相似文献
8.
T. Le Tat 《Journal of Pure and Applied Algebra》2003,177(3):253-285
The postulation of a space curve is a classifying invariant which computes for any integer n the dimension of the family of surfaces of degree n containing the curve. We prove that for any integers d and g satisfying d−3?g?2d−9, there exists a smooth connected curve of degree d and genus g with the minimal postulation expected by the Riemann-Roch theorem. 相似文献
9.
In this paper we study the homeomorphic properties of the solutions to one dimensional backward stochastic differential equations under suitable assumptions, where the terminal values depend on a real parameter. Then, we apply them to the solutions for a class of second order quasilinear parabolic partial differential equations. 相似文献
10.
A fictitious domain approach to the numerical solution of PDEs in stochastic domains 总被引:1,自引:0,他引:1
We present an efficient method for the numerical realization of elliptic PDEs in domains depending on random variables. Domains
are bounded, and have finite fluctuations. The key feature is the combination of a fictitious domain approach and a polynomial
chaos expansion. The PDE is solved in a larger, fixed domain (the fictitious domain), with the original boundary condition
enforced via a Lagrange multiplier acting on a random manifold inside the new domain. A (generalized) Wiener expansion is
invoked to convert such a stochastic problem into a deterministic one, depending on an extra set of real variables (the stochastic
variables). Discretization is accomplished by standard mixed finite elements in the physical variables and a Galerkin projection
method with numerical integration (which coincides with a collocation scheme) in the stochastic variables. A stability and
convergence analysis of the method, as well as numerical results, are provided. The convergence is “spectral” in the polynomial
chaos order, in any subdomain which does not contain the random boundaries. 相似文献
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15.
Jichun Li 《Journal of Computational and Applied Mathematics》2011,236(5):950-961
The discontinuous Galerkin method has proved to be an accurate and efficient way to numerically solve many differential equations. In this paper, we extend this method to solve the time-dependent Maxwell’s equations when metamaterials and perfectly matched layers are involved. Numerical results are presented to demonstrate that our method is not only simple to implement, but also quite effective in solving Maxwell’s equations in complex media. 相似文献
16.
17.
The Navier-Stokes equations for a compressible barotropic fluid in 1D with zero velocity boundary conditions are considered. We study the case of large initial data in H1 as well as the mass force such that the stationary density is uniquely determined but admits vacua. Missing uniform lower bound for the density is compensated by a careful modification of the construction procedure for a Lyapunov functional known for the case of solutions which are globally away from zero [I. Straškraba, A.A. Zlotnik, On a decay rate for 1D-viscous compressible barotropic fluid equations, J. Evol. Equ. 2 (2002) 69-96]. An immediate consequence of this construction is a decay rate estimate for this highly singular problem. The results are proved in the Eulerian coordinates for a large class of increasing state functions including p(ρ)=aργ with any γ>0 (a>0 a constant). 相似文献
18.
Juliana Coelho 《Journal of Pure and Applied Algebra》2010,214(8):1319-1333
Recently, the first Abel map for a stable curve of genus g≥2 has been constructed. Fix an integer d≥1 and let C be a stable curve of compact type of genus g≥2. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the second Abel map. 相似文献
19.
Global properties of solutions to 1D-viscous compressible
barotropic fluid equations with density dependent viscosity 总被引:4,自引:0,他引:4
The Navier-Stokes equations for compressible barotropic fluid in 1D with the mass
force under zero velocity boundary conditions are studied. We prove the uniform upper and
lower bounds for the density as well as the uniform in time L
2()-estimates for
x
and
u
x
(u is the velocity).
Moreover, a collection of the decay rate estimates for -
(with
being the stationary density) and u
in 2()-norm and
H
1()-norm as time
t are
established. The results are given for general state function
p() (but mainly monotone) and
viscosity coefficient
µ() of arbitrarily fast (or slow) growth as well as for the large data. 相似文献
20.
We reconsider the classical problem of representing a finite number of
forms of degree d in the polynomial ring
over n + 1 variables as scalar combinations
of powers of linear forms.
We define a geometric construct called a grove, which,
in a number of cases, allows us to determine the dimension of the space of
forms which can be so represented for a fixed number of summands.
We also present two new examples, where this dimension turns out to
be less than what a naïve parameter count would predict. 相似文献