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1.
2.
Joël Merker 《Journal of Mathematical Sciences》2008,154(6):817-922
This paper is divided into three parts. Part I develops a general, new theory (inspired by modern CR geometry) of Lie symmetries
of completely integrable pde systems, viewed from their associated submanifolds of solutions. Part II constructs general combinatorial formulas for the
prolongations of vector fields to jet spaces. Part III explicitly characterizes the flatness of some systems of the second
order. The results presented here are original and were not published elsewhere; most formulas of Parts II and III were verified
by means of Maple Release 7.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 47, Complex
Analysis, 2007. 相似文献
3.
Effective algebraic degeneracy 总被引:1,自引:0,他引:1
We show that for every smooth projective hypersurface X⊂ℙ
n+1 of degree d and of arbitrary dimension n
≥2, if X is generic, then there exists a proper algebraic subvariety Y
⊊
X such that every nonconstant entire holomorphic curve f
:ℂ→X has image f(ℂ) which lies in Y, as soon as its degree satisfies the effective lower bound
d\geqslant 2n5d\geqslant 2^{n^{5}}
. 相似文献
4.
5.
Roman Dwilewicz Joë l Merker 《Proceedings of the American Mathematical Society》2002,130(7):1975-1980
Let be a compact, connected, -smooth and globally minimal hypersurface in which divides the projective space into two connected parts and . We prove that there exists a side, or , such that every continuous CR function on extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.
6.
We give necessary conditions for certain real analytic tube generic submanifolds in n to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in n. During the proof, we show that the local CR automorphism group of a minimal, finitely nondegenerate real algebraic generic submanifold is a real algebraic local Lie group. We may state one of the main results as follows. Let M be a real analytic hypersurface tube in n passing through the origin, having a defining equation of the form v= (y), where (z,w)=(x+iy,u+iv)n–1×. Assume that M is Levi nondegenerate at the origin and that the real Lie algebra of local infinitesimal CR automorphisms of M is of minimal possible dimension n, i.e. generated by the real parts of the holomorphic vector fields z1,...,z n–1,w. Then M is locally algebraizable only if every second derivative 2yky l; is an algebraic function of the collection of first derivatives y1,,ym.Mathematics Subject Classification (2000): 32V40, 32V25, 32H02, 32H40, 32V10 相似文献
7.
Joël Merker 《Acta Appl Math》2006,92(2):125-207
We treat the problem of linearizability of a system of second order ordinary differential equations. The criterion we provide has applications to nonlinear Newtonian mechanics, especially in three-dimensional space. Let or , let , let , let and let
be a collection of m analytic second order ordinary differential equations, in general nonlinear. We obtain a new and applicable necessary and sufficient condition in order that this system is equivalent, under a point transformation
to the Newtonian free particle system .Strikingly, the explicit differential system that we obtain is of first order in the case , whereas according to a classical result due to Lie, it is of second order the case of a single equation . 相似文献
8.
We prove existence of weak solutions to doubly degenerate diffusion equations
[(u)\dot] = Dp um - 1 + f(m,p \geqslant 2)\dot u = \Delta _p u^{m - 1} + f(m,p \geqslant 2) 相似文献
9.
Albertson, Berman, Hutchinson, and Thomassen showed in 1990 that there exist highly connected graphs in which every spanning tree contains vertices of degree 2. Using a result of Alon and Wormald, we show that there exists a natural number such that every graph of minimum degree at least contains a spanning tree without adjacent vertices of degree 2. Moreover, we prove that every graph with minimum degree at least 3 has a spanning tree without three consecutive vertices of degree 2. 相似文献
10.
We introduce the notion of bounded diameter arboricity. Specifically, the diameter- arboricity of a graph is the minimum number such that the edges of the graph can be partitioned into forests each of whose components has diameter at most . A class of graphs has bounded diameter arboricity if there exists a natural number such that every graph in the class has diameter- arboricity at most . We conjecture that the class of graphs with arboricity at most has bounded diameter arboricity at most . We prove this conjecture for by proving the stronger assertion that the union of a forest and a star forest can be partitioned into two forests of diameter at most 18. We use these results to characterize the bounded diameter arboricity for planar graphs of girth at least for all . As an application we show that every 6-edge-connected planar (multi)graph contains two edge-disjoint -thin spanning trees. Moreover, we answer a question by Mütze and Peter, leading to an improved lower bound on the density of globally sparse Ramsey graphs. 相似文献
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