Results 11 to 20 of about 240,101 (314)
Differential Equations for Algebraic Functions [PDF]
Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007 It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions.
Bostan, Alin +4 more
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On algebraic integrals of a differential equation
Discrete and Continuous Models and Applied Computational Science, 2019 We consider the problem of integrating a given differential equation in algebraic functions, which arose together with the integral calculus, but still is not completely resolved in finite form.
Mikhail D Malykh +2 more
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Singularities of algebraic differential equations [PDF]
Advances in Applied Mathematics, 2021 There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of ordinary or partial differential equations.
Lange-Hegermann, Markus +3 more
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Solutions of algebraic differential equations
Journal of Differential Equations, 1983 This paper may be considered as a mathematical essay on the question “What is a solution of an algebraic differential equation?” Many theorems in differential algebra are proved by differentiating an algebraic differential equation several times, and then eliminating certain quantities, say, by the use of resultants.
Lee A. Rubel
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Algebraic and differential operator equations
Linear Algebra and its Applications, 1988 Let H be a complex separable Hilbert space and let L(H) be the algebra of all bounded linear operators on H. The boundary value problem (1) \(X^{(n)}+A_{n-1}X^{(n-1)}+...+A_ 0X=0\), (2) \(EX(b)-X(0)F=G\), where \(A_ i,E,F,G\in L(H)\) and b is a positive real number is considered.
L. Jódar
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Irreducible Systems of Algebraic Differential Equations [PDF]
Transactions of the American Mathematical Society, 1939 Let 7 be a domain of rationality, and let yi, , Yn be a set of indeterminates. Then the set of prime ideals in the ring of polynomials j7 [yi, , yn] satisfies a divisor-chain condition for decreasing sequences as well as for increasing sequences. That is, a sequence of prime ideals 11, 12, in 7[yi, , y.] must be of finite length not only if 2;i1 ...
Walter Strodt
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Differential Algebraic Equations [PDF]
, 2021 AbstractLet H be a Hilbert space and $$\nu \in \mathbb {R}$$ ν ∈ ℝ . We saw in the previous chapter how initial value problems can be formulated within the framework of evolutionary equations.
Christian Seifert +2 more
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Differential Equivalence for Linear Differential Algebraic Equations [PDF]
IEEE Transactions on Automatic Control, 2022 Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering.
Stefano Tognazzi +3 more
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Algebras and differential equations [PDF]
Nagoya Mathematical Journal, 1977 One purpose of this paper is a purely algebraic study of (systems of) ordinary differential equations of the typewhere the coefficients are taken from a fixed associative, commutative, unital ring R, such as the field R of real or C of complex numbers or a commutative, unital Banach algebra.
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Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator [PDF]
, 2009 A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out.
Bayram Tekin +12 more
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