共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider K3 surfaces which are double covers of rational elliptic surfaces. The former are endowed with a natural elliptic fibration, which is induced by the latter. There are also other elliptic fibrations on such K3 surfaces, which are necessarily induced by special linear systems on the rational elliptic surfaces. We describe these linear systems. In particular, we observe that every conic bundle on the rational surface induces a genus 1 fibration on the K3 surface and we classify the singular fibers of the genus 1 fibration on the K3 surface it terms of singular fibers and special curves on the conic bundle on the rational surface. 相似文献
2.
HU Qianqian & WANG Guojin Department of Mathematics Zhejiang University Hangzhou China State Key Laboratory of CAD&CG Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2005,48(9):1209-1222
Using algebraic and geometric methods,functional relationships between a point on a conic segment and its corresponding parameter are derived when the conic segment is presented by a rational quadratic or cubic Bézier curve.That is,the inverse mappings of the mappings represented by the expressions of rational conic segments are given.These formulae relate some triangular areas or some angles,determined by the selected point on the curve and the control points of the curve,as well as by the weights of the rational Bézier curve.Also,the relationship can be expressed by the corresponding parametric angles of the selected point and two endpoints on the conic segment,as well as by the weights of the rational Bézier curve.These results are greatly useful for optimal parametrization,reparametrization,etc.,of rational Bézier curves and surfaces. 相似文献
3.
We obtain bilinear restriction estimates for surfaces with vanishing curvatures. As application we also prove new linear restriction estimates for some class of conic surfaces. 相似文献
4.
The surfaces of constant Gaussian curvature bearing conjugate networks of conic lines are found.Translated from Ukrainskií Geometricheskií Sbornik, Issue 29, 1986, pp. 3–5. 相似文献
5.
Projective surfaces with bi-elliptic hyperplane sections 总被引:1,自引:0,他引:1
We study projective surfaces X which have a bi-elliptic curve (i.e. 2∶1 covering of an elliptic curve) among their hyperplane
sections . We give a complete characterization of those surfaces when their degree d is d≥17 (only conic bundles and scrolls
if d≥19, three possible exception otherwise) and when d≤8. A conjecture is given for the remaining cases. The main tool we
use is the study of the adjunction mapping on X. 相似文献
6.
Alan P. Wang 《Applied mathematics and computation》1975,1(3):263-277
A technique is developed here to estimate an unknown curve joining two points in a three dimensional Euclidean space. A special application presented here is a computer procedure to determine the intersection of two arbitrary given smooth surfaces. The method used is to assume that y is a function of x and the set (x,y(x)) lies on the projection of the intersection of two surfaces. The function y is determined by least square curve fitting on a Latin square of experimental values. The procedure is written in APL (A Programming Language). A set of preliminary results is presented. The results indicate that this is a successful procedure for some simple surfaces, including some conic surfaces. 相似文献
7.
《高等学校计算数学学报》2016,(3)
The construction of trigonometric B-spline curves with shape parameters has become the hotspot in computer aided geometric design.However,the shape parameters of the curves and surfaces are all global parameters and only meet with C~2 continuity in some previous papers.In order to provide more flexible approaches for designers,the algebraic and trigonometric spline(AT-spline) curves and surfaces are constructed as a generalization of the traditional cubic uniform B-spline curves and surfaces.AT-spline curves and surfaces not only inherit the properties of trigonometric B-spline curves,but also exhibit better performance when adjusting its local shapes through two shape parameters.Particularly,the AT-spline rotational surfaces with two local shape parameters are presented.When the shape parameters take special value,it can accurately represent the conic curve and surface. 相似文献
8.
A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical
learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by
second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral
conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that
solve either second-order conic programming or linear programming relaxations of conic integer programs at the nodes of the
branch-and-bound tree. Central to our approach is a reformulation of the second-order conic constraints with polyhedral second-order
conic constraints in a higher dimensional space. In this representation the cuts we develop are linear, even though they are
nonlinear in the original space of variables. This feature leads to a computationally efficient implementation of nonlinear
cuts for conic mixed-integer programming. The reformulation also allows the use of polyhedral methods for conic integer programming.
We report computational results on solving unstructured second-order conic mixed-integer problems as well as mean–variance
capital budgeting problems and least-squares estimation problems with binary inputs. Our computational experiments show that
conic mixed-integer rounding cuts are very effective in reducing the integrality gap of continuous relaxations of conic mixed-integer
programs and, hence, improving their solvability.
This research has been supported, in part, by Grant # DMI0700203 from the National Science Foundation. 相似文献
9.
Wendelin Degen 《manuscripta mathematica》1986,55(1):9-38
A surface in projective space generated by a one parameter family of conics is called a conic surface of Blutel if the tangent planes of taken along a generating conic, envelop a quadratic cone. If the conjugate curves (with respect to the generating conics) are conics, too, we call a two-fold Blutel's conic surface. In an earlier paper [4] it was shown that the planes of both conic families, the generating and the conjugate one, belong to a pencil, each. The present paper completes these investigations by integrating the derivative equations (3), (8), (9), (10). As a final result, a complete classification of all these surfaces is given. They are all algebraic of at most fourth order and furthermore—besides the quadrics and certain degenerate cases—they are complex projectively equivalent to the cyclides of Dupin. 相似文献
10.
In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes of surfaces in the four-dimensional Euclidean space, determined by conditions on their invariants, can be interpreted in terms of the properties of two geometric figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We construct a family of surfaces with flat normal connection. 相似文献
11.
A. Alzati 《Annali dell'Universita di Ferrara》1994,40(1):55-70
In this paper we show that there are no smooth rational 3-folds in ?5 (C) which are rational conic bundles, over minimal surfaces, whose generic fibre is embedded as a rational curve of degreeh≥3, (ifh=2 there is a complete classification for these 3-folds as well as for the case of ?1-bundles). Except for conic bundles, we also give the complete list of rational 3-folds in ?5 which are minimal according to Mori’s theory. These are little steps towards the classification of all smooth 3-folds in ?5 not of general type. 相似文献
12.
A strong conic quadratic reformulation for machine-job assignment with controllable processing times
We describe a polynomial-size conic quadratic reformulation for a machine-job assignment problem with separable convex cost. Because the conic strengthening is based only on the objective of the problem, it can also be applied to other problems with similar cost functions. Computational results demonstrate the effectiveness of the conic reformulation. 相似文献
13.
14.
《高等学校计算数学学报》2016,(2)
The trust region(TR) method for optimization is a class of effective methods.The conic model can be regarded as a generalized quadratic model and it possesses the good convergence properties of the quadratic model near the minimizer.The Barzilai and Borwein(BB) gradient method is also an effective method,it can be used for solving large scale optimization problems to avoid the expensive computation and storage of matrices.In addition,the BB stepsize is easy to determine without large computational efforts.In this paper,based on the conic trust region framework,we employ the generalized BB stepsize,and propose a new nonmonotone adaptive trust region method based on simple conic model for large scale unconstrained optimization.Unlike traditional conic model,the Hessian approximation is an scalar matrix based on the generalized BB stepsize,which resulting a simple conic model.By adding the nonmonotone technique and adaptive technique to the simple conic model,the new method needs less storage location and converges faster.The global convergence of the algorithm is established under certain conditions.Numerical results indicate that the new method is effective and attractive for large scale unconstrained optimization problems. 相似文献
15.
Lifting is a procedure for deriving valid inequalities for mixed-integer sets from valid inequalities for suitable restrictions
of those sets. Lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming
and it has been successfully used to solve such problems with branch-and-cut algorithms. Here we generalize the theory of
lifting to conic integer programming, i.e., integer programs with conic constraints. We show how to derive conic valid inequalities
for a conic integer program from conic inequalities valid for its lower-dimensional restrictions. In order to simplify the
computations, we also discuss sequence-independent lifting for conic integer programs. When the cones are restricted to nonnegative
orthants, conic lifting reduces to the lifting for linear integer programming as one may expect. 相似文献
16.
Wen-yuSun Jin-yunYuan Ya-xiangYuan 《计算数学(英文版)》2003,21(3):295-304
In this paper we present a trust region method of conic model for linearly constrained optimization problems.We discuss trust region approaches with conic model subproblems.Some equivalent variation properties and optimality conditions are given.A trust region algorithm based on conic model is constructed.Global convergence of the method is established. 相似文献
17.
18.
In this article we present a simple and elegant algebraic proof of Pascal’s hexagon theorem which requires only knowledge
of basics on conic sections without theory of projective transformations. Also, we provide an efficient algorithm for finding
an equation of the conic containing five given points and a criterion for verification whether a set of points is a subset
of the conic. 相似文献
19.
It is not straightforward to find a new feasible solution when several conic constraints are added to a conic optimization
problem. Examples of conic constraints include semidefinite constraints and second order cone constraints. In this paper,
a method to slightly modify the constraints is proposed. Because of this modification, a simple procedure to generate strictly
feasible points in both the primal and dual spaces can be defined. A second benefit of the modification is an improvement
in the complexity analysis of conic cutting surface algorithms. Complexity results for conic cutting surface algorithms proved
to date have depended on a condition number of the added constraints. The proposed modification of the constraints leads to
a stronger result, with the convergence of the resulting algorithm not dependent on the condition number.
Research supported in part by NSF grant number DMS-0317323. Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. 相似文献
20.
Leanne D. Holder 《Journal of Geometry》2004,80(1-2):95-105
Define a conic blocking set to be a set of lines in a Desarguesian projective plane such that all conics meet these lines. Conic blocking sets can be used in determining if a collection of planes in projective three-space forms a flock of a quadratic cone. We discuss trivial conic blocking sets and conic blocking sets in planes of small order. We provide a construction for conic blocking sets in planes of non-prime order, and we make additional comments about the structure of these conic blocking sets in certain planes of even order. 相似文献