共查询到19条相似文献,搜索用时 62 毫秒
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众所周知,给定微分或差分域上一组元素,它们在常数域上线性相关当且仅当它们所对应的Wronskian行列式或者Casoratian行列式为零.文章将这个结果推广到具有微分导子和差分导子的微分差分域;同时基于Okugawa的工作,还将结果推广到特征非0的微分差分域. 相似文献
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《数学的实践与认识》2015,(24)
讨论了一类具有耦合边界条件的左定四阶微分算子,利用具有耦合边界条件的左定四阶微分算子和其相应的右定四阶微分算子的关系,最终给出左定四阶微分算子特征值的计算方法. 相似文献
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本文在研究一类高阶微分算子谱的离散性的基础上研究了2n阶实系数Euler微分算式生成的对称微分算子,进一步完善了自伴Euler微分算子的谱是离散的充分必要条件. 相似文献
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《数学的实践与认识》2020,(9)
研究了具有转移条件的四阶正则微分算子自共轭边界条件的统一规范型.在标准型的基础上通过对自共轭边界条件矩阵左乘非奇异矩阵和右乘辛矩阵给出了四阶微分算子自共轭边界条件的统一规范型.结果表明具有转移条件的四阶自共轭微分算子的边界条件的统一规范型不仅与边界条件矩阵的秩有关,而且与转移条件矩阵的行列式有关. 相似文献
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《复变函数与椭圆型方程》2012,57(1):83-94
This article studies the problem on the fixed points and hyper-order of differential polynomials generated by solutions of two type of second order differential equations. Because of the control of differential equation, we can obtain some precise estimates of their hyper-order and fixed points. 相似文献
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In this paper, we propose algorithms for computing differential Chow forms for ordinary prime differential ideals which are given by characteristic sets. The algorithms are based on an optimal bound for the order of a prime differential ideal in terms of a characteristic set under an arbitrary ranking, which shows the Jacobi bound conjecture holds in this case. Apart from the order bound, we also give a degree bound for the differential Chow form. In addition, for a prime differential ideal given by a characteristic set under an orderly ranking, a much simpler algorithm is given to compute its differential Chow form. The computational complexity of the algorithms is single exponential in terms of the Jacobi number, the maximal degree of the differential polynomials in a characteristic set, and the number of variables. 相似文献
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关于高阶整函数系数微分方程解的超级 总被引:5,自引:0,他引:5
研究两种类型的高阶线性齐次整函数系数微分方程解的增长性问题。对于这两种类型的方程,当存在某个系数对方程的解的性质起主要支配作用时,得到了方程解的超级的估计,特别是对零点收敛指数是有穷的解,得到了解的超级的精确估计。 相似文献
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刘其林 《高校应用数学学报(A辑)》1993,(3):231-238
本文研究一类非线性微分方程的非线性边值问题的奇摄动,应用边界层校正法构造出解的形式渐近展开式,并借助于上,下解及微分不等式理论研究解及其一阶导数的有关余项估计。 相似文献
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I.-G. E. Kordonis Ch. G. Philos 《Proceedings of the American Mathematical Society》1998,126(6):1661-1667
An oscillation criterion is given for a certain form of nonlinear two-dimensional differential systems. This criterion originated in a well-known oscillation result due to Coles (as extended and improved by Wong) concerning second order nonlinear differential equations with alternating coefficients.
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Ravi P. Agarwal 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):2859-124
We consider a differential equation of fractional order with uncertainty and present the concept of solution. It extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty. Some examples are presented. 相似文献
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We consider fourth order ordinary differential operators on the half-line and on the line, where the perturbation has compactly supported coefficients. The Fredholm determinant for this operator is an analytic function in the whole complex plane without zero. We describe the determinant at zero. We show that in the generic case it has a pole of order 4 in the case of the line and of order 1 in the case of the half-line. 相似文献
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Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal approximations of uncertain inputs, updates on the affine approximation bounds and a generalized formula for the analytical error. The approach proposed is able to achieve higher order convergence with respect to the current state-of-the-art. We implemented the methodology in Ariadne, a library for the verification of continuous and hybrid systems. For evaluation purposes, we introduce ten systems from the literature, with varying degrees of nonlinearity, number of variables and uncertain inputs. The results are hereby compared with two state-of-the-art approaches to time-varying uncertainties in nonlinear systems. 相似文献
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Differential equations of different types and orders are of utmost importance for mathematical modeling of control system problems. State variable method uses the concept of expressing n number of first order differential equations in vector matrix form to model and analyze/synthesize control systems.The present work proposes a new set of orthogonal hybrid functions (HF) which evolved from synthesis of sample-and-hold functions (SHF) and triangular functions (TF). This HF set is used to approximate a time function in a piecewise linear manner with the mean integral square error (MISE) much less than block pulse function based approximation which always provides staircase solutions.The operational matrices for integration and differentiation in HF domain are also derived and employed for solving non-homogeneous and homogeneous differential equations of the first order as well as state equations. The results are compared with exact solutions, the 4th order Runge-Kutta method and its further improved versions proposed by Simos [6]. The presented HF domain theory is well supported by a few illustrations. 相似文献