scholarly journals Correction: Kiskinov et al. Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays. Mathematics 2021, 9, 150

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1282
Author(s):  
Hristo Kiskinov ◽  
Ekaterina Madamlieva ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Fundamental Matrix ◽  
Distributed Delays ◽  
Absolutely Continuous ◽  
Fractional System ◽  
The Right

We have found that, in the right side of Equation (35) in our paper [...]

scholarly journals Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 150
Author(s):  
Hristo Kiskinov ◽  
Ekaterina Madamlieva ◽  
Magdalena Veselinova ◽  
Andrey Zahariev
Keyword(s):  
Integral Representation ◽  
Differential System ◽  
Fundamental Matrix ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Absolutely Continuous ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Fractional System

The goal of the present paper is to obtain sufficient conditions that guaranty the existence and uniqueness of an absolutely continuous fundamental matrix for a retarded linear fractional differential system with Caputo type derivatives and distributed delays. Some applications of the obtained result concerning the integral representation of the solutions are given too.

On Finite Part Integrals and Hadamard-Type Fractional Derivatives

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Li Ma ◽  
Changpin Li
Keyword(s):  
Fractional Derivative ◽  
Singular Integral ◽  
Fractional Derivatives ◽  
Continuous Functions ◽  
Finite Part ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Fundamental Properties ◽  
Logarithmic Series ◽  
The Right

This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.

ON SUFFICIENT CONDITIONS OF EXPONENTIAL STABILITY FOR SYSTEMS OF LINEAR AUTONOMOUS DIFFERENTIAL EQUATIONS WITH AFTEREFFECT

2021 ◽  
Vol 28 (28) ◽  
pp. 73-83
Author(s):  
T. SABATULINA SABATULINA
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Fundamental Matrix ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Comparison System ◽  
System A ◽  
Differential Equa ◽  
Functional Differential ◽  
Autonomous Differential Equations

We consider systems of linear autonomous functional differential equa-tion with aftereffect and propose an approach to obtain effective sufficient conditions of exponential stability for these systems. In the approach we use the positiveness of the fundamental matrix of an auxiliary system (a comparison system) with concentrated and distributed delays.

The fundamental matrix for a certain random walk

1999 ◽  
Vol 36 (02) ◽  
pp. 320-333
Author(s):  
Howard M. Taylor
Keyword(s):  
Random Walk ◽  
Green Function ◽  
Explicit Formula ◽  
Fundamental Matrix ◽  
Simple Random Walk ◽  
Limiting Behavior ◽  
Point Of Entry ◽  
Discrete Lattices ◽  
The Green Function ◽  
The Right

Consider the random walk {Sn} whose summands have the distributionP(X=0) = 1-(2/π), andP(X= ±n) = 2/[π(4n2−1)], forn≥ 1. This random walk arises when a simple random walk in the integer plane is observed only at those instants at which the two coordinates are equal. We derive the fundamental matrix, or Green function, for the process on the integral [0,N] = {0,1,…,N}, and from this, an explicit formula for the mean timexkfor the random walk starting fromS0=kto exit the interval. The explicit formula yields the limiting behavior ofxkasN→ ∞ withkfixed. For the random walk starting from zero, the probability of exiting the interval on the right is obtained. By lettingN→ ∞ in the fundamental matrix, the Green function on the interval [0,∞) is found, and a simple and explicit formula for the probability distribution of the point of entry into the interval (−∞,0) for the random walk starting fromk= 0 results. The distributions for some related random variables are also discovered.Applications to stress concentration calculations in discrete lattices are briefly reviewed.

scholarly journals Deteksi Tungkai Bayi Pada Image Sequence Berbasis Vector Depth Estimation

2021 ◽  
Vol 7 (3) ◽  
pp. 35-42
Author(s):  
Faisal Lutfi Afriansyah ◽  
Niyalatul Muna
Keyword(s):  
Image Processing ◽  
Pattern Recognition ◽  
3D Reconstruction ◽  
Reference Frame ◽  
Fundamental Matrix ◽  
Motion Vector ◽  
Depth Estimation ◽  
Image Sequence ◽  
Image Sequences ◽  
The Right

Image processing in the image sequence for pattern recognition can be a solution for detecting limb movements in infants after surgery, but the camera is not calibrated. So we need the right method solution to be able to detect these conditions. This happens to cameras that are generally not calibrated and do not have the feature to calculate the vector depth for 3D reconstruction. Because to detect and find limb movement depth is needed to be able to do 3D reconstruction, because it is not only based on the x and y parameters but also z so that with the additional parameters it makes it easier to analyze the motion of the motion axis and the motion vector. This paper discusses a method for detecting 2D motion into a 3D-based motion vector by sequencing the image sequence image then finding the point of transfer of the motion frame destination from the frame reference frame by obtaining the depth (depth vector) using the fundamental matrix from the generated motion vector. This method is recommended because it can perform 3D reconstruction from input in the form of 2D image sequences by calculating the intrinsic parameters so that 3D reconstruction can be carried out. So that the limb vector movement in infants that was originally 2D can be reconstructed into 3D based and makes it easier to carry out the analysis because of the additional parameters.

scholarly journals Addendum to stability analysis of neutral linear fractional system with distributed delays (Filomat 30:3 (2016), 841-851)

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 5013-5017
Author(s):  
Magdalena Veselinova ◽  
Hristo Kiskinov ◽  
Andrey Zahariev
Keyword(s):  
Fractional Integral ◽  
Initial Conditions ◽  
Initial Condition ◽  
Initial Value ◽  
Short Article ◽  
Delayed Argument ◽  
Fractional Differential ◽  
Fractional System ◽  
The Right ◽  
Equations With Delay

In this short article we discuss the initial condition of the initial value problem for fractional differential equations with delayed argument and derivatives in Riemann-Liouville sense. We provide also a new lemma - a ?mirror? analogue of the Kilbas Lemma, concerning the right side Riemann-Liouville fractional integral, which is important for the correct setting of the initial conditions, especially in the case of equations with delay.

Research on Surface Reconstruction from Intersecting Curves

2014 ◽  
Vol 701-702 ◽  
pp. 145-149
Author(s):  
Jun Ting Cheng ◽  
Xin Kuan Liu
Keyword(s):  
Laser Beam ◽  
Surface Reconstruction ◽  
Fundamental Matrix ◽  
Stereo Matching ◽  
Curve Surface ◽  
Matching Method ◽  
The World ◽  
The Cross ◽  
3D Information ◽  
The Right

This paper comes up with an stereo matching method for handy-scanner based on cross light. The handy-scan system with two cameras and one cross laser beam can scan very detail accurately through cross laser. 3D information is gained by dealing with cross laser image. What we do aims at estimating the transformation of the measured objects under the world coordinate. In order to achieve this goal, firstly we use 8-points algorithm to compute fundamental matrix. Then, the points on the left and the right can be matched based on fundamental matrix. The 3D coordinates of the point on the cross laser can be obtained by triangulation and curve surface differential. The experiment proves that this algorithm solves the problem of calculating the matching points in disorder. And in some way, it increases efficiency of matching cross laser stripes.

The fundamental matrix for a certain random walk

1999 ◽  
Vol 36 (2) ◽  
pp. 320-333 ◽  
Author(s):  
Howard M. Taylor
Keyword(s):  
Random Walk ◽  
Green Function ◽  
Explicit Formula ◽  
Fundamental Matrix ◽  
Simple Random Walk ◽  
Limiting Behavior ◽  
Point Of Entry ◽  
Discrete Lattices ◽  
The Green Function ◽  
The Right

Consider the random walk {Sn} whose summands have the distribution P(X=0) = 1-(2/π), and P(X = ± n) = 2/[π(4n2−1)], for n ≥ 1. This random walk arises when a simple random walk in the integer plane is observed only at those instants at which the two coordinates are equal. We derive the fundamental matrix, or Green function, for the process on the integral [0,N] = {0,1,…,N}, and from this, an explicit formula for the mean time xk for the random walk starting from S0 = k to exit the interval. The explicit formula yields the limiting behavior of xk as N → ∞ with k fixed. For the random walk starting from zero, the probability of exiting the interval on the right is obtained. By letting N → ∞ in the fundamental matrix, the Green function on the interval [0,∞) is found, and a simple and explicit formula for the probability distribution of the point of entry into the interval (−∞,0) for the random walk starting from k = 0 results. The distributions for some related random variables are also discovered.Applications to stress concentration calculations in discrete lattices are briefly reviewed.

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