共查询到20条相似文献,搜索用时 33 毫秒
1.
在解析几何中有二次曲线与直线位置关系的讨论、二次曲面与直线位置关系的讨论,而二次曲面与平面相关位置关系的探讨较少.本文给出二次曲面a11x2+a22y2+a33z2+2a12xy+2a13xz+2a23yz+2a14x+2a24y+2a34z+a44=0(1)和平面Ax+By+Cz+D=0(2)的相对位置的判别式Δ=a11a12a13a14Aa21a22a23a24Ba31a32a33a34Ca41a42a43a44DA B C D0(aij=aji).(3)并证明了:若Δ>0,则二次曲面(1)与平面(2)相交;若Δ=0,则(1)和(2)相切;若Δ<0,则(1)和(2)相离. 相似文献
2.
Scalarization of Henig Proper Efficient Points in a Normed Space 总被引:1,自引:0,他引:1
In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base. 相似文献
3.
B. Lemaire 《Set-Valued Analysis》2001,9(1-2):111-121
This paper deals with a variant of a dynamical selection scheme introduced by Attouch and Cominetti for ill-posed convex minimization which combines approximation with the steepest descent method by mean of a suitable parameterization of the approximation parameter as a function of the time. This variant applies to a general inclusion with a maximal monotone operator by mean of a staircase parameterization. A discrete analogue is also considered. Applications to selecting a particular zero of a maximal monotone operator or a particular fixed point of a nonexpansive mapping via regularization techniques are presented. Finally, the alternative use of well-posedness by perturbations is discussed. 相似文献
4.
Takesi Kawasaki 《Transactions of the American Mathematical Society》2002,354(1):123-149
The Rees algebra is the homogeneous coordinate ring of a blowing-up. The present paper gives a necessary and sufficient condition for a Noetherian local ring to have a Cohen-Macaulay Rees algebra: A Noetherian local ring has a Cohen-Macaulay Rees algebra if and only if it is unmixed and all the formal fibers of it are Cohen-Macaulay. As a consequence of it, we characterize a homomorphic image of a Cohen-Macaulay local ring. For non-local rings, this paper gives only a sufficient condition. By using it, however, we obtain the affirmative answer to Sharp's conjecture. That is, a Noetherian ring having a dualizing complex is a homomorphic image of a finite-dimensional Gorenstein ring.
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《Optimization》2012,61(1-4):369-385
In this paper, we are concerned with global efficiency in multiobjective optimization. After exposing a property of a cone-subconvexlike function, we prove that a local weakly efficient solution, a local efficient solution and a local properly efficient solution are respectively a global weakly efficient solution, a global efficient solution and a global properly efficient solution of a multiobjective programming problem if cone- subconvexlikeness or cone-pre-invexity is assumed 相似文献
7.
In this paper a barrier function method is proposed for approximating a solution of the nonconvex quadratic programming problem with box constraints. The method attempts to produce a solution of good quality by following a path as the barrier parameter decreases from a sufficiently large positive number. For a given value of the barrier parameter, the method searches for a minimum point of the barrier function in a descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. When all the diagonal entries of the objective function are negative, the method converges to at least a local minimum point of the problem if it yields a local minimum point of the barrier function for a sequence of decreasing values of the barrier parameter with zero limit. Numerical results show that the method always generates a global or near global minimum point as the barrier parameter decreases at a sufficiently slow pace. 相似文献
8.
Le Thi Hoai An Pham Dinh Tao Nam Nguyen Canh Nguyen Van Thoai 《Journal of Global Optimization》2009,44(3):313-337
We propose a method for finding a global solution of a class of nonlinear bilevel programs, in which the objective function
in the first level is a DC function, and the second level consists of finding a Karush-Kuhn-Tucker point of a quadratic programming
problem. This method is a combination of the local algorithm DCA in DC programming with a branch and bound scheme well known
in discrete and global optimization. Computational results on a class of quadratic bilevel programs are reported. 相似文献
9.
给出了最佳参数α_1,α_2,α_3,β_1,β_2,β_3∈R,使得双向不等式α_1Q(a,b)+(1-α_1)G(a,b)0且a≠b成立.其中A(a,b)=(a+b)/2,H(a,b)=2ab/(a+b),G(a,b)=(ab)~(1/2),Q(a,b)=((a~2+b~2)/2)~(1/2),C(a,b)=(a~2+b~2)/(a+b),T(a,b)=2/π∫_0~(π/2)(a~2cos~2t+b~2sin~2)~(1/2)tdt分别是两个正数a和b的算术平均,调和平均,几何平均,二次平均,反调和平均和Toader平均. 相似文献
10.
Ming Liao 《Journal of Theoretical Probability》2009,22(1):164-185
We study a decomposition of a general Markov process in a manifold invariant under a Lie group action into a radial part (transversal
to orbits) and an angular part (along an orbit). We show that given a radial path, the conditioned angular part is a nonhomogeneous
Lévy process in a homogeneous space, we obtain a representation of such processes and, as a consequence, we extend the well-known
skew-product of Euclidean Brownian motion to a general setting.
相似文献
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In this paper we obtain the genus field of a general Kummer extension of a global rational function field. We study first the case of a general Kummer extension of degree a power of a prime. Then we prove that the genus field of a composite of two abelian extensions of a global rational function field with relatively prime degrees is equal to the composite of their respective genus fields. Our main result, the genus of a general Kummer extension of a global rational function field, is a direct consequence of this fact. 相似文献
13.
Hideo Ueda 《Annals of Global Analysis and Geometry》1998,16(5):477-495
In this paper a Dirichlet problem for the Laplacian in a domain with a corner in R2 is treated and a new method of construction of a local parametrix for that Dirichlet problem at a corner point is given. In order to construct a parametrix a certain class of operators in a slab domain is introduced and it is shown that that operator class is an algebra. 相似文献
14.
E. Capelas de Oliveira Ary O. Chiacchio 《International Journal of Mathematical Education in Science & Technology》2013,44(4):491-497
The paper considers a class of real integrals performed by using a convenient integral in the complex plane. A complex integral containing a multi-valued function with two branch points is transformed into another integral containing a pole and a unique branch point. As a by-product we obtain a new class of integrals which can be calculated in a very simple way. 相似文献
15.
《Journal of Pure and Applied Algebra》2022,226(11):107116
It was proved in [4] that every group ring of a torsion abelian group over a commutative local ring is a semi-clean ring. It was asked in [4] whether every group ring of a torsion abelian group over a commutative clean ring is a semi-clean ring and whether every group ring of a torsion abelian group over a commutative semi-clean ring is a semi-clean ring. In this paper, we give a positive answer to question 1 and a negative answer to question 2. 相似文献
16.
Based on a study of a minimization problem, we present the following results applicable to possibly nonconvex sets in a Banach space: an approximate projection result, an extended extremal principle, a nonconvex separation theorem, a generalized Bishop-Phelps theorem and a separable point result. The classical result of Dieudonné (on separation of two convex sets in a finite-dimensional space) is also extended to a nonconvex setting. 相似文献
17.
A straight-line planar drawing of a plane graph is called a convex drawing if every facial cycle is drawn as a convex polygon. Convex drawings of graphs is a well-established aesthetic in graph drawing, however not all planar graphs admit a convex drawing. Tutte [W.T. Tutte, Convex representations of graphs, Proc. of London Math. Soc. 10 (3) (1960) 304–320] showed that every triconnected plane graph admits a convex drawing for any given boundary drawn as a convex polygon. Thomassen [C. Thomassen, Plane representations of graphs, in: Progress in Graph Theory, Academic Press, 1984, pp. 43–69] gave a necessary and sufficient condition for a biconnected plane graph with a prescribed convex boundary to have a convex drawing.In this paper, we initiate a new notion of star-shaped drawing of a plane graph as a straight-line planar drawing such that each inner facial cycle is drawn as a star-shaped polygon, and the outer facial cycle is drawn as a convex polygon. A star-shaped drawing is a natural extension of a convex drawing, and a new aesthetic criteria for drawing planar graphs in a convex way as much as possible. We give a sufficient condition for a given set A of corners of a plane graph to admit a star-shaped drawing whose concave corners are given by the corners in A, and present a linear time algorithm for constructing such a star-shaped drawing. 相似文献
18.
In this paper, we introduce the concept of a new nonlinear mapping called demigeneralized in a Banach space. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common fixed point for a family of the new nonlinear mappings in a Banach space. We apply this result to obtain new strong convergence theorems in a Hilbert space and a Banach space, respectively. 相似文献
19.
《Discrete Mathematics》2022,345(5):112803
A squared rectangle is a rectangle dissected into squares. Similarly a rectangled rectangle is a rectangle dissected into rectangles. The classic paper ‘The dissection of rectangles into squares’ of Brooks, Smith, Stone and Tutte described a beautiful connection between squared rectangles and harmonic functions. In this paper we count dissections of a rectangle into a set of integral squares or a set of integral rectangles. Here, some squares and rectangles may have the same size. We introduce a method involving a recurrence relation of large sized matrices to enumerate squared and rectangled rectangles of a given sized rectangle and propose the asymptotic behavior of their growth rates. 相似文献
20.
M. S. Bakre 《Proceedings Mathematical Sciences》1996,106(4):379-401
The article presents two results. (1) Let a be a reductive Lie algebra over ℂ and let b be a reductive subalgebra of a. The
first result gives the formula for multiplicity with which a finite dimensional irreducible representation of b appears in
a given finite dimensional irreducible representation of a in a general situation. This generalizes a known theorem due to
Kostant in a special case. (2) LetG be a connected real semisimple Lie group andK a maximal compact subgroup ofG. The second result is a formula for multiplicity with which an irreducible representation ofK occurs in a generalized representation ofG arising not necessarily from fundamental Cartan subgroup ofG. This generalizes a result due to Enright and Wallach in a fundamental case. 相似文献