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The Wayback Machine - https://web.archive.org/web/20250805015049/https://hiast.academia.edu/OmranKouba
Self-excited systems (SES) arise in numerous applications, such as fluid-structure interaction, c... more Self-excited systems (SES) arise in numerous applications, such as fluid-structure interaction, combustion, and biochemical systems. In support of system identification and digital control of SES, this paper analyzes discrete-time Lur'e models with affinely constrained, piecewise-C 1 feedback nonlinearities. The main result provides sufficient conditions under which a discrete-time Lur'e model is self-excited in the sense that its response is 1) bounded for all initial conditions, and 2) nonconvergent for almost all initial conditions.
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. Th... more Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is done by parameterizing the angular velocity vector in terms of 3-2-1 and 3-1-3 Euler angles as well as Euler parameters, that is, unit quaternions.
Using the expansion in a Fourier-Gegenbauer series, we prove several identities that extend and g... more Using the expansion in a Fourier-Gegenbauer series, we prove several identities that extend and generalize known results. In particular, it is proved among other results, that ∞ n=0 1 4 n 2n n z − 2n z−1/2 n z n 3 = tan(πz) π for all complex numbers z such that (z) > − 1 2 and z / ∈ 1 2 + Z.
Bollettino Dell'unione Matematica Italiana, Dec 20, 2017
Consider a sequence (a n) n≥1 of complex numbers such that for some positive number p we have lim... more Consider a sequence (a n) n≥1 of complex numbers such that for some positive number p we have lim n→∞ 1 n p n k=1 a k = ∈ C. We prove that, under some mild conditions on the sequence (positivity or absolute boundedness in the mean, etc.), we have lim n→∞ 1 n q n k=1 k q− p a k f k n = p 1 0 x q−1 f (x)dx for all q > 0 and all Riemann integrable functions f : [0, 1] → C. Some applications to probability theory and to number theory are also discussed. Keywords Stolz-Cesàro lemma • Continuous functions • Riemann integrable functions • Convergence in the mean • Euler's totient function • The law of large numbers
Euler’s equation relates the change in angular momentum of a rigid body to the applied torque. Th... more Euler’s equation relates the change in angular momentum of a rigid body to the applied torque. This paper uses Lagrangian dynamics to derive Euler’s equation in terms of generalized coordinates. This is done by parameterizing the angular velocity vector in terms of 3-2-1 and 3-1-3 Euler angles as well as Euler parameters, that is, quaternions. This paper fills a gap in the literature by using generalized coordinates to parameterize the angular velocity vector and thereby transform the dynamics obtained from Lagrangian dynamics into Euler’s equation for rigid-body rotation.
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials... more In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications to these polynomials are presented, including a unified approach to the asymptotic expansion of the error term in many numerical quadrature formulae, and many new and sharp inequalities, that bound some trigonometric sums.
Self-excited systems (SES) arise in numerous applications, such as fluid-structure interaction, c... more Self-excited systems (SES) arise in numerous applications, such as fluid-structure interaction, combustion, and biochemical systems. In support of system identification and digital control of SES, this paper analyzes discrete-time Lur'e models with affinely constrained, piecewise-C 1 feedback nonlinearities. The main result provides sufficient conditions under which a discrete-time Lur'e model is self-excited in the sense that its response is 1) bounded for all initial conditions, and 2) nonconvergent for almost all initial conditions.
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. Th... more Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is done by parameterizing the angular velocity vector in terms of 3-2-1 and 3-1-3 Euler angles as well as Euler parameters, that is, unit quaternions.
Using the expansion in a Fourier-Gegenbauer series, we prove several identities that extend and g... more Using the expansion in a Fourier-Gegenbauer series, we prove several identities that extend and generalize known results. In particular, it is proved among other results, that ∞ n=0 1 4 n 2n n z − 2n z−1/2 n z n 3 = tan(πz) π for all complex numbers z such that (z) > − 1 2 and z / ∈ 1 2 + Z.
Bollettino Dell'unione Matematica Italiana, Dec 20, 2017
Consider a sequence (a n) n≥1 of complex numbers such that for some positive number p we have lim... more Consider a sequence (a n) n≥1 of complex numbers such that for some positive number p we have lim n→∞ 1 n p n k=1 a k = ∈ C. We prove that, under some mild conditions on the sequence (positivity or absolute boundedness in the mean, etc.), we have lim n→∞ 1 n q n k=1 k q− p a k f k n = p 1 0 x q−1 f (x)dx for all q > 0 and all Riemann integrable functions f : [0, 1] → C. Some applications to probability theory and to number theory are also discussed. Keywords Stolz-Cesàro lemma • Continuous functions • Riemann integrable functions • Convergence in the mean • Euler's totient function • The law of large numbers
Euler’s equation relates the change in angular momentum of a rigid body to the applied torque. Th... more Euler’s equation relates the change in angular momentum of a rigid body to the applied torque. This paper uses Lagrangian dynamics to derive Euler’s equation in terms of generalized coordinates. This is done by parameterizing the angular velocity vector in terms of 3-2-1 and 3-1-3 Euler angles as well as Euler parameters, that is, quaternions. This paper fills a gap in the literature by using generalized coordinates to parameterize the angular velocity vector and thereby transform the dynamics obtained from Lagrangian dynamics into Euler’s equation for rigid-body rotation.
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials... more In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications to these polynomials are presented, including a unified approach to the asymptotic expansion of the error term in many numerical quadrature formulae, and many new and sharp inequalities, that bound some trigonometric sums.
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