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1.
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler's classical result in the theory of forcing. 相似文献
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Debra J. Knisley 《Journal of Graph Theory》1994,18(1):59-71
A graph G of order n satisfies the neighborhood condition NCk > s if any collection of k independent vertices is collectively adjacent to more than s vertices. Given a family H of graphs, the decomposition class β(H) is the family of graphs B with the property that for some H ∈ H of chromatic number d, H contains B as an induced subgraph and l?V(H) ? V(B)? is (d ? 2) colorable. Let H be a family of d-chromatic graphs, B an element of β(H) such that B contains an s-matching as an induced subgraph. Thus the cardinality of one of the partite sets of B is s + r for some integer r ≥ 0. We show that if t is a fixed positive integer, G is a graph of sufficiently large order n that satisfies the neighborhood condition then G contains B + K(d - 2; t) as a subgraph. 相似文献
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Jose Pujol 《International Journal of Mathematical Education in Science & Technology》2018,49(5):778-792
Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our proof we consider the plane generated by a linear combination of uand v. When looking for the coefficients in the linear combination required to reach a desired point on the plane, the solution involves the existence of a normal vector n = u × v. Our results have a bearing on the history of vector analysis, as a product similar to the cross product but without the perpendicularity requirement existed at the same time. These competing products originate in the work of two major nineteen-century mathematicians, W. Hamilton, and H. Grassmann. These historical aspects are discussed in some detail here. We also address certain aspects of the teaching of u × v to undergraduate students, which is known to carry some difficulties. This includes the algebraic and geometric denitions of u × v, the rule for the direction of u × v, and the pseudovectorial nature of u × v. 相似文献
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Noboru Osuga 《Mathematical Logic Quarterly》2006,52(4):351-358
Let f, g ∈ ω ω . We will denote by g ? f that for every k < ω, f (n k ) ≤ g (n ) except for finitely many n . The ideal ?f on ω 2 is the collection of sets X such that, for some g ? f and τ ∈ ∏n <ω g (n )2, every x ∈ X satisfies τ (n ) ? x for infinitely many n . In the present paper, we will prove the consistency of cov(?f ) < ?? and non(?f ) < ??. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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In this paper, we focus on a special class of ideal projectors. With the aid of algebraic geometry, we prove that for this special class of ideal projectors, there exist “good” error formulas as defined by C. de Boor. Furthermore, we completely analyze the properties of the interpolation conditions matched by this special class of ideal projectors, and show that the ranges of this special class of ideal projectors are the minimal degree interpolation spaces with regard to their associated interpolation conditions. 相似文献
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Shiyou Weng Haiyin Gao Daqing Jiang Xuezhang Hou 《Journal of Mathematical Sciences》2011,177(3):466-473
The singular boundary-value problemis studied. The singularity may appear at u?=?0, and the function g may change sign. An existence theorem for solutions to the above boundary-value problem is proposed, and it is proved via the method of upper and lower solutions.
相似文献
$ \left\{ {\begin{array}{*{20}{c}} {{u^{\prime\prime}} + g\left( {t,u,{u^{\prime}}} \right) = 0\quad {\text{for}}\quad t \in \left( {0,1} \right),} \hfill \\ {u(0) = u(1) = 0} \hfill \\ \end{array} } \right. $
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Y. Abe 《Proceedings of the American Mathematical Society》1999,127(3):847-849
We use a variant of the diamond principle to show many ideals on are not -saturated if is large. For instance, the -indescribable ideal is not -saturated if is almost ineffable.
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The aim of this article is to give necessary and sufficient conditions for the existence
of Cartan connections on principal bundles. For this purpose we recall the definition of abstract
soldering forms and introduce the notion of geometrizable principle bundles.Received: 13 November 2003 相似文献
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N. V. Medvedev 《Mathematical Notes》1968,4(1):551-554
The equation d2x/dt2=Ax +f(t, x) is considered in a Banach space E, where A is a fixed unbounded linear operator, andf(t, x) is a nonlinear operator which is periodic in t and satisfies a Lipschitz condition with respect to x E. Existence conditions have been obtained for a well defined generalized periodic solution of this equation, and also when this solution coincides with the true solution. Similar results have been obtained for the first order equation.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 105–112, July, 1968. 相似文献
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Weigu Li 《中国科学A辑(英文版)》1999,42(7):699-703
A method of identifying the existence of horseshoe for a two-dimension diffeomorphism is introduced and utilized to generalize
the Birkhoff-Smale Theorem to the saddle-node case.
Project supported by the National Natural Science Foundation of China (Grant No. 19531070). 相似文献
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Franco Obersnel Pierpaolo Omari 《Proceedings of the American Mathematical Society》2007,135(7):2055-2058
We extend a result of J. Andres and K. Pastor concerning scalar time-periodic first order ordinary differential equations without uniqueness, by proving that the existence of just one subharmonic implies the existence of large sets of subharmonics of all given orders. Since these periodic solutions must coexist with complicated dynamics, we might paraphrase T. Y. Li and J. A. Yorke by loosely saying that in this setting even period two implies chaos. Similar results are obtained for a class of differential inclusions.
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We introduce a monomial ideal whose standard monomials encode the vertices of all fibers of a lattice. We study the minimal generators, the radical, the associated primes and the primary decomposition of this ideal, as well as its relation to initial ideals of lattice ideals. 相似文献
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Using methods of nonlinear functional analysis, we define the structure of an evolution operator equation of second order that can be formulated in direct variational terms. 相似文献
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The conditions are formulated for the existence of a temperature-time analogy in stationary temperature fields for hereditary viscoelastic media which are described by Volterra equations of the second kind with a singular relaxation kernel. A time transformation has been found for a nonstationary temperature field which results in the heredity equation becoming invariant with respect to temperature.The M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 2, pp. 217–222, March–April, 1970. 相似文献
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Charles R. Johnson 《Discrete Mathematics》2006,306(23):3130-3135
Among those real symmetric matrices whose graph is a given tree T, the maximum multiplicity is known to be the path cover number of T. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are 1. 相似文献
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Vladimir V. Andrievskii 《Arkiv f?r Matematik》2004,42(2):217-238
We investigate local properties of the Green function of the complement of a compact setEυ[0,1] with respect to the extended complex plane. We demonstrate, that if the Green function satisfies the 1/2-Hölder condition locally at the origin, then the density ofE at 0, in terms of logarithmic capacity, is the same as that of the whole interval [0, 1].. 相似文献