Ismail mirumbe - Academia.edu (original) (raw)
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Papers by Ismail mirumbe
arXiv (Cornell University), Dec 28, 2023
Malaysian Journal of Mathematical Sciences, Jun 1, 2023
We state and prove a condition for the local stability of a certain class of two dimensional syst... more We state and prove a condition for the local stability of a certain class of two dimensional system of polynomial differential equations. We give some examples of polynomial differential systems of equations to demonstrate that this local stability condition established for the trivial equilibrium point (0, 0) is quite sharp and compare our result with the well known Lyapunov local stability criterion (Lyapunov's second method).
Let (N n) n≥0 be the Narayana's cow sequence defined by a third-order recurrence relation N 0 = 0... more Let (N n) n≥0 be the Narayana's cow sequence defined by a third-order recurrence relation N 0 = 0, N 1 = N 2 = 1, and N n+3 = N n+2 + N n for all n ≥ 0. In this paper, we determine all Narayana numbers that are concatenations of two repdigits. The proof of our main theorem uses lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in Diophantine approximation.
Mathematics, 2019
In this paper, we use the Laplace transform technique to examine the generalized solutions of the... more In this paper, we use the Laplace transform technique to examine the generalized solutions of the nth order Cauchy–Euler equations. By interpreting the equations in a distributional way, we found that whether their solution types are classical, weak or distributional solutions relies on the conditions of their coefficients. To illustrate our findings, some examples are exhibited.
Journal of Mathematical Sciences: Advances and Applications, 2018
We consider an m-th order constant coefficient locally Fuchsian ordinary differential equation at... more We consider an m-th order constant coefficient locally Fuchsian ordinary differential equation at the origin
Annales Academiae Scientiarum Fennicae Mathematica, 2020
It was shown in Björn-Björn-Korte ("Minima of quasisuperminimizers", Nonlinear Anal. 155 (2017), ... more It was shown in Björn-Björn-Korte ("Minima of quasisuperminimizers", Nonlinear Anal. 155 (2017), 264-284) that u := min{u1, u2} is a Q-quasisuperminimizer if u1 and u2 are Q-quasisuperminimizers and Q = 2Q 2 /(Q + 1). Moreover, one-dimensional examples therein show that Q is close to optimal. In this paper we give similar examples in higher dimensions. The case when u1 and u2 have different quasisuperminimizing constants is considered as well.
arXiv (Cornell University), Dec 28, 2023
Malaysian Journal of Mathematical Sciences, Jun 1, 2023
We state and prove a condition for the local stability of a certain class of two dimensional syst... more We state and prove a condition for the local stability of a certain class of two dimensional system of polynomial differential equations. We give some examples of polynomial differential systems of equations to demonstrate that this local stability condition established for the trivial equilibrium point (0, 0) is quite sharp and compare our result with the well known Lyapunov local stability criterion (Lyapunov's second method).
Let (N n) n≥0 be the Narayana's cow sequence defined by a third-order recurrence relation N 0 = 0... more Let (N n) n≥0 be the Narayana's cow sequence defined by a third-order recurrence relation N 0 = 0, N 1 = N 2 = 1, and N n+3 = N n+2 + N n for all n ≥ 0. In this paper, we determine all Narayana numbers that are concatenations of two repdigits. The proof of our main theorem uses lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in Diophantine approximation.
Mathematics, 2019
In this paper, we use the Laplace transform technique to examine the generalized solutions of the... more In this paper, we use the Laplace transform technique to examine the generalized solutions of the nth order Cauchy–Euler equations. By interpreting the equations in a distributional way, we found that whether their solution types are classical, weak or distributional solutions relies on the conditions of their coefficients. To illustrate our findings, some examples are exhibited.
Journal of Mathematical Sciences: Advances and Applications, 2018
We consider an m-th order constant coefficient locally Fuchsian ordinary differential equation at... more We consider an m-th order constant coefficient locally Fuchsian ordinary differential equation at the origin
Annales Academiae Scientiarum Fennicae Mathematica, 2020
It was shown in Björn-Björn-Korte ("Minima of quasisuperminimizers", Nonlinear Anal. 155 (2017), ... more It was shown in Björn-Björn-Korte ("Minima of quasisuperminimizers", Nonlinear Anal. 155 (2017), 264-284) that u := min{u1, u2} is a Q-quasisuperminimizer if u1 and u2 are Q-quasisuperminimizers and Q = 2Q 2 /(Q + 1). Moreover, one-dimensional examples therein show that Q is close to optimal. In this paper we give similar examples in higher dimensions. The case when u1 and u2 have different quasisuperminimizing constants is considered as well.