scholarly journals Common solution to the Lyapunov equation for 2×2 complex matrices

2007 ◽  
Vol 420 (2-3) ◽  
pp. 609-624 ◽  
Author(s):  
Thomas J. Laffey ◽  
Helena Šmigoc
Keyword(s):  
Lyapunov Equation ◽  
Complex Matrices ◽  
Common Solution

scholarly journals On the existence of a common solution to the Lyapunov equations

2015 ◽  
Vol 63 (1) ◽  
pp. 163-168 ◽  
Author(s):  
S. Białas ◽  
M. Góra
Keyword(s):  
Sufficient Conditions ◽  
Positive Definite ◽  
Necessary And Sufficient Conditions ◽  
Lyapunov Equations ◽  
Positive Definite Matrices ◽  
Complex Matrices ◽  
Common Solution ◽  
Necessary And Sufficient

Abstract In this paper, a system of Lyapunov equations A*i P + PAi = −Qi (i = 1, . . . ,m), (A) is considered in which Ai are given n × n complex matrices, Qi are unknown n × n Hermitian positive definite matrices and P, if any, is a common solution to the Lyapunov equations (A). Both sufficient and necessary and sufficient conditions are derived for the existence of such a matrix P. Examples are presented to illustrate the results.

THE ROLE OF POLYETHYLENIMINE IN ENHANCING PERFORMANCE OF GLUTAMATE BIOSENSORS

2018 ◽  
Vol 8 (3) ◽  
pp. 36-41
Author(s):  
Diep Do Thi Hong ◽  
Duong Le Phuoc ◽  
Hoai Nguyen Thi ◽  
Serra Pier Andrea ◽  
Rocchitta Gaia
Keyword(s):  
First Generation ◽  
Good Reproducibility ◽  
Complex Matrices ◽  
Long Term Stability ◽  
In Vitro Characterization ◽  
Glutamate Oxidase

Background: The first biosensor was constructed more than fifty years ago. It was composed of the biorecognition element and transducer. The first-generation enzyme biosensors play important role in monitoring neurotransmitter and determine small quantities of substances in complex matrices of the samples Glutamate is important biochemicals involved in energetic metabolism and neurotransmission. Therefore, biosensors requires the development a new approach exhibiting high sensibility, good reproducibility and longterm stability. The first-generation enzyme biosensors play important role in monitoring neurotransmitter and determine small quantities of substances in complex matrices of the samples. The aims of this work: To find out which concentration of polyethylenimine (PEI) exhibiting the most high sensibility, good reproducibility and long-term stability. Methods: We designed and developed glutamate biosensor using different concentration of PEI ranging from 0% to 5% at Day 1 and Day 8. Results: After Glutamate biosensors in-vitro characterization, several PEI concentrations, ranging from 0.5% to 1% seem to be the best in terms of VMAX, the KM; while PEI content ranging from 0.5% to 1% resulted stable, PEI 1% displayed an excellent stability. Conclusions: In the result, PEI 1% perfomed high sensibility, good stability and blocking interference. Furthermore, we expect to develop and characterize an implantable biosensor capable of detecting glutamate, glucose in vivo. Key words: Glutamate biosensors, PEi (Polyethylenimine) enhances glutamate oxidase, glutamate oxidase biosensors

scholarly journals Light dark matter: A common solution to the lithium and problems

2021 ◽  
Vol 812 ◽  
pp. 136008
Author(s):  
Jailson Alcaniz ◽  
Nicolás Bernal ◽  
Antonio Masiero ◽  
Farinaldo S. Queiroz
Keyword(s):  
Dark Matter ◽  
Common Solution

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

scholarly journals Blur-readable two-dimensional barcode based on blur-invariant shape and geometric features

2021 ◽  
Vol 18 (2) ◽  
pp. 172988142199958
Author(s):  
Shundao Xie ◽  
Hong-Zhou Tan
Keyword(s):  
Circular Disk ◽  
Geometric Features ◽  
Two Dimensional ◽  
Common Solution ◽  
Ringing Artifacts ◽  
2D Barcode ◽  
Defocus Blur ◽  
Blurred Image ◽  
Decoding Accuracy ◽  
Invariant Shape

In recent years, the application of two-dimensional (2D) barcode is more and more extensive and has been used as landmarks for robots to detect and peruse the information. However, it is hard to obtain a sharp 2D barcode image because of the moving robot, and the common solution is to deblur the blurry image before decoding the barcode. Image deblurring is an ill-posed problem, where ringing artifacts are commonly presented in the deblurred image, which causes the increase of decoding time and the limited improvement of decoding accuracy. In this article, a novel approach is proposed using blur-invariant shape and geometric features to make a blur-readable (BR) 2D barcode, which can be directly decoded even when seriously blurred. The finder patterns of BR code consist of two concentric rings and five disjoint disks, whose centroids form two triangles. The outer edges of the concentric rings can be regarded as blur-invariant shapes, which enable BR code to be quickly located even in a blurred image. The inner angles of the triangle are of blur-invariant geometric features, which can be used to store the format information of BR code. When suffering from severe defocus blur, the BR code can not only reduce the decoding time by skipping the deblurring process but also improve the decoding accuracy. With the defocus blur described by circular disk point-spread function, simulation results verify the performance of blur-invariant shape and the performance of BR code under blurred image situation.

scholarly journals On the Perron–Frobenius theory for complex matrices

2012 ◽  
Vol 437 (4) ◽  
pp. 1071-1088 ◽  
Author(s):  
Dimitrios Noutsos ◽  
Richard S. Varga
Keyword(s):  
Complex Matrices

scholarly journals Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ghorban Khalilzadeh Ranjbar ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Solution ◽  
Type Integral ◽  
First Time ◽  
Common Fixed Point Theorems

Abstract The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ α s -admissible, triangular partially triple weakly $\alpha _{s}$ α s -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

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