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1.
Contrary to published results, it is shown that there do not exist ‘strongest’ (or ‘best possible’) homogeneous quadratic polynomial triangle inequalities of the form $$q(R,r) \leqslant s^2 \leqslant Q(R,r)$$ without further restrictions. Also, several best inequalities for symmetric functions of three positive variables are considered.  相似文献   

2.
Brezzi  F.  Cornalba  M.  Di Carlo  A. 《Numerische Mathematik》1986,48(4):417-427
Summary We analyse from a theoretical point of view a computational technique previously introduced [2, 5] for tracing branches of solutions of nonlinear equations near simple quadratic folds.Supported in part by an M.P.I. 40% grantSupported in part by a C.N.R. grant  相似文献   

3.
Consider a compact, connected Lie group G acting isometrically on a sphere Sn of radius 1. The quotient of Sn by this group action, Sn/G, has a natural metric on it, and so we may ask what are its diameter and q-extents. These values have been computed for cohomogeneity one actions on spheres. In this paper, we compute the diameters, extents, and several q-extents of cohomogeneity two orbit spaces resulting from such actions, and we also obtain results about the q-extents of Euclidean disks. Additionally, via a simple geometric criterion, we can identify which of these actions give rise to a decomposition of the sphere as a union of disk bundles. In addition, as a service to the reader, we give a complete breakdown of all the isotropy subgroups resulting from cohomogeneity one and two actions.  相似文献   

4.
Let be a triangle in and let be the set of its three medians. We construct interpolants to smooth functions using transfinite (or blending) interpolation on The interpolants are of type f(1)+g(2)+h(3), where (1,2,3) are the barycentric coordinates with respect to the vertices of . Based on an error representation formula, we prove that the interpolant is the unique best L1-approximant by functions of this type subject the function to be approximated is from a certain convexity cone in C3().Received: 17 December 2003  相似文献   

5.
This paper proved the following three facts about the Lipschitz continuous property of Bernstein polynomials and Bezier nets defined on a triangle: suppose f(P) is a real valued function defined on a triangle T, (1) If f(P) satisfies Lipschitz continuous condition, i.e. f(P)∃LipAα, then the corresponding Bernstein Bezier net fnLip Asec αφα, here φ is the half of the largest angle of triangle T; (2) If Bernstein Bezier net fnLip Bα, then its elevation Bezier net EfnLip Bα; and (3) If f(P)∃Lip Aα, then the corresponding Bernstein polynomials Bn(f;P)∃Lip Asec αφα, and the constant Asecαφ is best in some sense. Supported by NSF and SF of National Educational Committee  相似文献   

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An extension of the traditional geometry of the triangle is derived through the construction of two 30-points particular cubics. Two generation procedures founded on triangular quadratic transformations and dual associate properties of the two cubics are presented.  相似文献   

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A precise definition of a fractalF p r 1 derived from Pascal's triangle modulop r (p prime) is given. The number of nonzero terms in the firstp s lines of Pascal's triangle modulop r is computed. From this result the Hausdorff dimension and Hausdorff measure ofF p r 1 are deduced. The nonself-similarty ofF p r 1,r2, is also discussed.  相似文献   

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The triangle conjecture sets a bound on the cardinality of a code formed by words of the form aibaj. A counterexample exceeding that bound is given. This also disproves a stronger conjecture that every code is commutatively equivalent to a prefix code.  相似文献   

11.
We prove that if the three angles of a triangleT in the plane are different from (60°, 60°, 60°), (30°, 30°, 120°), (45°,45°,90°),(30°,60°,90°), then the set of vertices of those triangles which are obtained fromT by repeating ‘edge-reflection’ is everywhere dense in the plane.  相似文献   

12.
There exists a triangle T and a number \frac{1}{2}$$ " align="middle" border="0"> such that any sequence of triangles similar to T with total area not greater than times the area of T can be packed into T.  相似文献   

13.
Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with certain families of lattice-free sets are polyhedra. For a long time, the only result known was the celebrated theorem of Cook, Kannan and Schrijver who showed that the split closure is a polyhedron. Although some fairly general results were obtained by Andersen et al. (Math Oper Res 35(1):233–256, 2010) and Averkov (Discret Optimiz 9(4):209–215, 2012), some basic questions have remained unresolved. For example, maximal lattice-free triangles are the natural family to study beyond the family of splits and it has been a standing open problem to decide whether the triangle closure is a polyhedron. In this paper, we show that when the number of integer variables $m=2$ the triangle closure is indeed a polyhedron and its number of facets can be bounded by a polynomial in the size of the input data. The techniques of this proof are also used to give a refinement of necessary conditions for valid inequalities being facet-defining due to Cornuéjols and Margot (Math Program 120:429–456, 2009) and obtain polynomial complexity results about the mixed integer hull.  相似文献   

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Lattice dynamics of a Sierpinski triangle submitted to different levels of disorder was studied via atomistic Green’s functions. It was found that there is a critical level of disorder that separates two regions of thermal transport. The first is characterized by a fast destruction of fracton states and the formation of spatially extended phonon states. The second region is characterized by a transition from extended to localized phonon states as predicted by the Anderson model.  相似文献   

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On the principal centers of a triangle

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20.
Let T denote the triangle with vertices (ui, vi) i = 1, 2, 3. The purpose of this paper is to present a family of cubature rules for approximating the double integral of f(u, v) over T. A FORTRAN implementation of the method is given.  相似文献   

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