There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Fractional Differential Equations

Theory of fuzzy integrals and its applications

In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness. We first introduce the concept of cyclic (noncyclic) Θ-condensing operator for a pair of sets using the measure of noncompactness and then establish results on the best proximity pair (point) on Banach spaces and strictly Banach spaces. In addition, we have illustrated the considered system of integro-differential equations by three examples and discussed the stability, efficiency, and accuracy of solutions.

/pdf/best-proximity-point-results-and-application-to-a-system-of-s6fbp3bx0b.pdf

Best proximity point results and application to a system of integro-differential equations

In this paper, an adaptive digital implementation of an inverse model based control scheme for a system with parametric uncertainty is proposed using Generalized Sampling and Hold Functions. The implementation of the control law using this kind of holds allows overcoming the difficulties related to the presence of unstable zeros in the continuous-time model and the usual appearance of unstable discretization zeros in the discrete model when a ZOH is applied. The Generalized Sampling and Hold Functions allows obtaining a discrete model of the plant with all its zeros stable which allows performing an exact inverse model of the plant in comparison to the use of a classical ZOH which only allows, in general, an approximate inversion of the plant. The stability and asymptotic properties of the general adaptive scheme are established. Also, simulation examples showing the scope and application of the method are presented.

Adaptive discrete-time inverse model control using generalized holds

In this paper, we prove convergence theorems for viscosity approximation processes involving * −nonexpansive multi-valued mappings in complete convex metric spaces. We also consider finite and infinite families of such mappings and prove convergence of the proposed iteration schemes to common fixed points of them. Our results improve and extend some corresponding results.

https://www.mdpi.com/2075-1680/9/1/10/pdf

Viscosity Approximation Methods for * −Nonexpansive Multi-Valued Mappings in Convex Metric Spaces

This paper establishes sufficient conditions for stability of linear and time-invariant delay differential systems including their various usual sub­ classes (ie, point, distributed and mixed point-distributed delay systems) Suffi­ cient conditions for stability are obtained in terms of the Schur's complement of operators and the frequency domain Lyapunov equation The basic idea in the analysis consists in the use of modified Laplace operators which split the ch~ac­ teristic equation into two separate multiplicative factors whose roots characterize the system stability The method allows a simple derivation of stabilizing control laws

Stability and the matrix Lyapunov equation for differential systems with point, distributed and/or mixed point-distributed delays

In this paper, we establish strong and convergence results for mappings satisfying condition through a newly introduced iterative process called JA iteration process. A nonlinear Hadamard space is used the ground space for establishing our main results. A novel example is provided for the support of our main results and claims. The presented results are the good extension of the corresponding results present in the literature.

/pdf/fixed-point-approximation-for-a-class-of-generalized-4fjfbef116.pdf

Manuel De la Sen

Papers

Best proximity point results and application to a system of integro-differential equations

Adaptive discrete-time inverse model control using generalized holds

Viscosity Approximation Methods for * −Nonexpansive Multi-Valued Mappings in Convex Metric Spaces

Stability and the matrix Lyapunov equation for differential systems with point, distributed and/or mixed point-distributed delays

Fixed Point Approximation for a Class of Generalized Nonexpansive Mappings in Hadamard Spaces