A Unique Year, a Unique Solution: GetFTR Streamlines Access to Research

2020 ◽  
Author(s):  
Erin Wiringi ◽  
Ralph Youngen ◽  
Lisa Janicke Hinchliffe
Keyword(s):  
Unique Solution

A Unique Solution for Flight Body Angular Histories

2007 ◽  
Author(s):  
Thomas E. Harkins
Keyword(s):  
Unique Solution

scholarly journals Dynamical system of the growth of COVID-19 with controller

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Dania Altulea ◽  
Rafida M. Elobaid
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Growth Rate ◽  
Dynamic System ◽  
Unique Solution ◽  
Population Dynamic ◽  
Integral Control ◽  
The Social ◽  
Social Separation ◽  
Strong Control

AbstractRecently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel.

A unique solution for the exact differential equation of nonuniform lines

1968 ◽  
Vol 56 (12) ◽  
pp. 2181-2182 ◽  
Author(s):  
A.G.J. Holt ◽  
K.U. Ahmed
Keyword(s):  
Differential Equation ◽  
Unique Solution

scholarly journals Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 851
Author(s):  
Robert Stegliński
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Weak Solution ◽  
Variational Methods ◽  
Unique Solution ◽  
Continuous Dependence ◽  
Fractional Laplacian ◽  
Unique Weak Solution ◽  
Fractional Partial Differential Equation ◽  
Integrodifferential Operator

In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the continuous dependence of the solution on parameters. In proofs we use monotonicity and variational methods.

scholarly journals The core inverse and constrained matrix approximation problem

2020 ◽  
Vol 18 (1) ◽  
pp. 653-661 ◽  
Author(s):  
Hongxing Wang ◽  
Xiaoyan Zhang
Keyword(s):  
Unique Solution ◽  
Approximation Problem ◽  
Frobenius Norm ◽  
Matrix Approximation ◽  
The Core ◽  
Core Inverse

Abstract In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse: ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M), where M\in {{\mathbb{C}}}_{n}^{\text{CM}} . We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.

scholarly journals Characterization of Degenerate Configurations in Attitude Determination of Three-Vehicle Heterogeneous Formations

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4631
Author(s):  
Pedro Cruz ◽  
Pedro Batista
Keyword(s):  
Unique Solution ◽  
Multiple Solutions ◽  
Attitude Determination ◽  
Line Of Sight ◽  
Number Of Solutions ◽  
Relative Line ◽  
Heterogeneous Formations ◽  
Heterogeneous Formation

The existence of multiple solutions to an attitude determination problem impacts the design of estimation schemes, potentially increasing the errors by a significant value. It is therefore essential to identify such cases in any attitude problem. In this paper, the cases where multiple attitudes satisfy all constraints of a three-vehicle heterogeneous formation are identified. In the formation considered herein, the vehicles measure inertial references and relative line-of-sight vectors. Nonetheless, the line of sight between two elements of the formation is restricted, and these elements are denoted as deputies. The attitude determination problem is characterized relative to the number of solutions associated with each configuration of the formation. There are degenerate and ambiguous configurations that result in infinite or exactly two solutions, respectively. Otherwise, the problem has a unique solution. The degenerate configurations require some collinearity between independent measurements, whereas the ambiguous configurations result from symmetries in the formation measurements. The conditions which define all such configurations are determined in this work. Furthermore, the ambiguous subset of configurations is geometrically interpreted resorting to the planes defined by specific measurements. This subset is also shown to be a zero-measure subset of all possible configurations. Finally, a maneuver is simulated to illustrate and validate the conclusions. As a result of this analysis, it is concluded that, in general, the problem has one attitude solution. Nonetheless, there are configurations with two or infinite solutions, which are identified in this work.

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