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Nicolae Vulpe 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6553-6582
This article is about weak singularities of quadratic differential systems, that is, non-degenerate singular points with traces of the corresponding linearized systems at such points equal to zero. These could be foci, centers or saddles. Necessary and sufficient conditions for a real quadratic system to possess a fixed number of weak singularities of a specific order are given. The conditions are stated in terms of affine invariant polynomials in the 12-dimensional space of the coefficients. 相似文献
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Yu. S. Chislenko 《Functional Analysis and Its Applications》1988,22(4):297-310
Leningrad Branch, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 22, No. 4, pp. 52–67, October–December, 1988. 相似文献
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《中国科学 数学(英文版)》2017,(6)
In this survey article, we present some known results and also propose some open questions related to the analytic and geometric aspects of Bishop submanifolds in a complex space. We mainly focus on those problems that the author and his coauthors have recently worked on. The article also contains an example of a Bishop submanifold in C~3 of real codimension two, which cannot be quadratically flattened at a CR singular point but is CR non-minimal at any CR point. This provides a counter-example to a question asked in a private communication by Zaistev(2013). 相似文献
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Alexander I. Barvinok 《Discrete and Computational Geometry》1993,10(1):1-13
We consider the problem of deciding whether a given system of quadratic homogeneous equations over the reals has nontrivial
solution. We design an algorithm which, for a fixed number of equations, uses a number of arithmetic operations bounded by
a polynomial in the number of variables only.
A preliminary version of this paper with a weaker result appeared in theProceedings of STOC '92. This research was supported by the Mittag-Leffler Institute and KTH, Stockholm. 相似文献
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We complete the study of first-order structural stability at singular points of positive quadratic differencial forms on two manifolds. For this, we consider the generic 1-parameter bifurcation of a D23-singular point. This situation consists in having, before the bifurcation, two locally stable singular points (one of type D2 and the other of type D3) which collapse at the D23-singular point when the bifurcation parameter is reached, and afterwards disappear. In local (x,y)-coordinates, such a point appears at the origin of a planar differential equation of the form with (b2-ac)(x,y)?0, such that
- (1)
- the first jet of the map (a,b,c) at the origin is T1(a,b,c)(0,0)=(y,0,-y) and
- (2)
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We show that the elements of the ring of integers of real quadratic fields which are sums of integral squares are in fact sums of distinct squares, provided their norm is large enough. 相似文献
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V. V. Lychagin 《Journal of Mathematical Sciences》1990,51(6):2735-2757
The article is devoted to singularities of integral manifolds which realize solutions of nonlinear partial differential equations and to the algebraic geometric and topological questions related to them.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 20, pp. 207–247, 1988. 相似文献
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V. A. Bel’skii 《Differential Equations》2013,49(12):1639-1644
For a two-dimensional quadratic system, we obtain necessary conditions for the existence of a triangular quadratic system with the same Mironenko reflecting function as the original system. We suggest an algorithm that permits establishing the coincidence of the reflecting functions of a quadratic nonstationary system and some stationary system. 相似文献
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The main aim of this paper is to investigate the existence problem for blow-up solutions of quadratic differential systems,
Riccati equations, and Lotka-Volterra systems. For this purpose, we introduce the concept of negative and positive blow-up
times of solutions of the above-mentioned systems and provide upper or lower bounds for these times.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 15, Differential and Functional Differential Equations. Part 1, 2006. 相似文献
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We characterize all the quadratic polynomial differential systems having a polynomial inverse integrating factor and provide explicit normal forms for such systems and for their associated first integrals. We also prove that these families of quadratic systems have no limit cycles. 相似文献
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M. T. Ashordia 《Differential Equations》2010,46(2):167-181
For a linear Kurzweil generalized differential system with singularities, we consider two-point boundary value problems of
two forms. The singularity is understood in the sense that the matrix and vector functions defining the system may have infinite
total variation. 相似文献
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M. T. Ashordia 《Differential Equations》2014,50(8):987-1002
We study a multipoint boundary value problem for systems of Kurzweil generalized linear differential equations with singularities on a finite closed interval of the real line. We assume that the offdiagonal entries of the matrix function corresponding to the system, as well as the elements of the right-hand side of the system, have bounded variation on the entire interval; however, the diagonal entries of the matrix function are not assumed to have bounded variation on the entire interval. This is what we mean by saying that the system is singular. We study the unique solvability of the problem. We prove a general theorem and use it to we obtain efficient optimal (in particular, spectral) solvability conditions for the problem. 相似文献
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We show how some differential geometric ideas help to resolve some singularities of ordinary differential systems. Hence a
singular problem is replaced by a regular one, which facilitates further analysis of the system. The methods employed are
constructive and the regularized systems can also be used for numerical computations.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献