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A class of Kukles differential systems of degree five having an invariant conic is examined. We show the coexistence of small
amplitude limit cycles, large amplitude limit cycles, under perturbations of the coefficients of the systems.
Financed partially by: USM Grant No. 12.06.28 and 12.06.27. 相似文献
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1 IntroductionBy definition a complex (respectively reao planar polynomial differentialsystem or simply a polynomial system is a differential system of the formdx. da.~ = i = p(x,y), ac = i = Q(x,y), (l)dt dt ~ y = Q(x,y), (l)where the dependent variables x and y are complex (respectively real), theindependent one (the time) t is real, and P and Q are polynomials in thevariables x and y with complex (respectively real) coefficients. In all thispaper m = ma-c{deg P, deg Q} denote the degree o… 相似文献
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As is well known, the Witten deformation dh of the De Rham complex computes the De Rham cohomology. In this paper, we study the Witten deformation on noncompact manifolds and restrict it on differential forms which behave polynomially near infinity. Such polynomial differential forms naturally appear on manifolds with the cylindrical structure. We prove that the cohomology of the Witten deformation dh acting on the complex of the polynomially growing forms (depends on h and) can be computed as the cohomology of the negative remote fiber of
h. We show that the assumptions of our main theorem are satisfied in a number of interesting special cases, including generic real polynomials on Rn. 相似文献
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In Geometriae Dedicata 79 (2000), 101–108, Rudolf Winkel conjectured: for a given algebraic curve f=0 of degree m 4 there is in general no polynomial vector field of degree less than 2m -1 leaving invariant f=0 and having exactly the ovals of f=0 as limit cycles. Here we show that this conjecture is not true.
Mathematics Subject Classifications (2000). Primary 14P25, 34C05, 34A34. 相似文献
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Yu. Yu. Kochetkov 《Functional Analysis and Its Applications》2002,36(3):240-243
Some special systems of polynomial equations (anti-Vandermonde systems) and the definition fields of their solutions are studied. In the case of four variables it is proved that a definition field is an extension of a real quadratic field of degree 12. 相似文献
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设Pn(x)为[0,∞)上次数不超过n的代数多项式,则有‖p′n(x)e-x‖[0,∞)≤(6.3n+1)‖pn(x)e-x‖[0,∞).若pn(x)同时又是奇函数或偶函数,则有‖p′n(x)e-x‖[0,∞)≤(1.8+7n1/2)‖p相似文献
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Roland Pulch 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(4):315-330
In radio frequency (RF) applications, slowly varying signals often modulate the amplitude and frequency of fast carrier waves. Thus a numerical simulation of the differential algebraic equations (DAEs) modelling the electric circuit becomes tedious. Alternative models are required to achieve efficient simulations. A multivariate formulation of signals yields a suitable representation via decoupling the widely separated time scales. Consequently, the circuit's DAEs change into warped multirate partial DAEs. On the other hand, the transient behaviour of the circuit can also be approximated by a parameter-dependent DAE model including a multivariate structure. The properties of this alternative strategy are investigated. In particular, the two multidimensional approaches are compared with respect to the simulation of RF signals. 相似文献
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庄圻泰 《纯粹数学与应用数学》1996,(1)
在这篇论文中,研究了一般形式的代数微分方程的亚纯解的增长性并得到一些结果,研究的方法是根据一个关于亚纯函数组的定理。这个定理是Borel的一个关于整函数组的定理的一个推广。 相似文献
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用有理数域或特征p的素域上的有n个独立变量的有理函数域的有限代数扩张域上的多项式的不可约分解,建议了一类密码系统. 相似文献
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We study conditions under which a partial differential operator of arbitrary order n in two variables or an ordinary linear
differential operator admits a factorization with a first-order factor on the left.The process of factoring consists of recursively
solving systems of linear equations subject to certain differential compatibility conditions.In the general case of partial
differential operators, it is not necessary to solve a differential equation. In special degenerate cases, such as an ordinary
differential operator, the problem eventually reduces to solving some Riccati equation(s). We give the factorization conditions
explicitly for the second and third orders and in outline form for higher orders.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 165–180, November, 2005. 相似文献
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In this paper the Charpit system of partial differential equations with algebraic constraints is considered. So, first the compatibility conditions of a system of algebraic equations and also of the Charpit system of partial differential equations are separately considered. For the combined system of equations of both types sufficient conditions for the existence of a solution are found. They lead to an algorithm for reducing the combined system to a Charpit system of partial differential equations of dimension less than the initial system and without algebraic constraints. Moreover, it is proved that this system identically satisfies the compatibility conditions if so does the initial system. 相似文献
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关于代数体函数的微分多项式 总被引:1,自引:0,他引:1
本文证明υ值代数函数的微分多项式是一λ值(1≤λ≤υ)代数体函数,即υ值代数体函数ω=ω(z)的微分多项式p(ω)可以被如下方程确定:[ελ(z)p^λ ελ-1(z)p^λ-1 … ε0(z)]^k=0这里ε0(z),ε1(z),…,ελ(z)为整函数且无公共零点,λ和k为正整数且λk=υ。 相似文献
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Andrei Minchenko 《代数通讯》2013,41(12):5094-5100
For a partial differential field K, we show that the triviality of the first differential Galois cohomology of every linear differential algebraic group over K is equivalent to K being algebraically, Picard–Vessiot, and linearly differentially closed. This cohomological triviality condition is also known to be equivalent to the uniqueness up to an isomorphism of a Picard–Vessiot extension of a linear differential equation with parameters. 相似文献
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E. A. Volkov 《Mathematical Notes》1999,66(2):139-141
It is proved that an equilateral triangle is the unique polygon on which the solution of the equation Δu=1 with homogeneous boundary conditions is an algebraic polynomial, and moreover, the degree of this polynomial is equal to
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Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 178–180, August, 1999. 相似文献