Topological conditions for a resistive circuit containing negative non-linear resistors to have a unique solution

The use of a branching process argument in complex queueing situations often leads to a discussion of a non-linear matrix integral equation of Volterra type. By the use of a fixed point theorem we show these equations have a unique solution.

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A Single CCD Algorithm to Determine the Position and Attitude during Rolling Phase of Rendezvous and Docking

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.190-191.813 ◽

2012 ◽

Vol 190-191 ◽

pp. 813-818 ◽

Cited By ~ 1

Author(s):

Li Li Zheng ◽

Yu Xian Jiang

Keyword(s):

Unique Solution ◽

Relative Position ◽

Linear Equations ◽

Euler Angles ◽

Non Linear ◽

Rendezvous And Docking ◽

Non Linear Equations ◽

Application Scope

Propose a new algorithm that use Euler angles to calculate directly large relative position and attitude of rendezvous and docking. By analyzing the feasibility of using Euler angles to solve instead of using quaternion and deriving the relations between the coordinates of the identification-points and the coordinates of point-images, a group of non-linear equations including relative position and attitude is established. It is proved that three non-collinear points are sufficient and required to determine the position and attitude uniquely. The whole deriving process does not mention any assumption and simplification in theory. Simulations indicate that the algorithm is high-accurate, unique-solution and wide application scope.

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On existence of unique solution to non-linear integral equations of the second kind

Applied Mathematics and Computation ◽

10.1016/j.amc.2004.04.011 ◽

2005 ◽

Vol 163 (2) ◽

pp. 801-809

Author(s):

A. Abd El-Shafy ◽

Mamdouh Elkady

Keyword(s):

Unique Solution ◽

Integral Equations ◽

Non Linear ◽

Linear Integral ◽

Linear Integral Equations

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Non-linear matrix integral equations of Volterra type in queueing theory

Journal of Applied Probability ◽

10.2307/3212783 ◽

1973 ◽

Vol 10 (3) ◽

pp. 644-651 ◽

Cited By ~ 6

Author(s):

Peter Purdue

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Unique Solution ◽

Queueing Theory ◽

Branching Process ◽

Linear Matrix ◽

Volterra Type ◽

Matrix Integral ◽

Non Linear

The use of a branching process argument in complex queueing situations often leads to a discussion of a non-linear matrix integral equation of Volterra type. By the use of a fixed point theorem we show these equations have a unique solution.

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On the Estimation of Permeabilities and Draw Resistances of Cigarette Components

Beiträge zur Tabakforschung International/Contributions to Tobacco Research ◽

10.2478/cttr-2013-0768 ◽

2004 ◽

Vol 21 (1) ◽

pp. 25-31

Author(s):

B Eitzinger

Keyword(s):

Flow Velocity ◽

Linear Model ◽

Unique Solution ◽

Condition Number ◽

Noise Levels ◽

Estimation Task ◽

Experimental Conditions ◽

Non Linear ◽

High Bias ◽

Cigarette Paper

AbstractThe goal of this study is to investigate whether the permeability of the tipping/plugwrap system, the permeability of the cigarette paper and the draw resistances of the filter and tobacco rod can be calculated from measurements of the degree of filter ventilation and of the open and closed draw resistance. This issue is investigated for a linear and a non-linear model of the flow in unlit cigarettes. At first it is proven that there exist experimental conditions to which the cigarette can be exposed such that the problem has at least a unique solution. The problem is then solved by least-squares optimisation for a linear and a non-linear model of the air flow in unlit cigarettes with various noise levels on the output quantities. The error sensitivity of the optimisation problem is estimated by calculation of the condition number.From the simulation several facts can be concluded. Firstly, for the linear model varying the flow velocity at the mouth end of the cigarette does not provide enough information to uniquely determine the properties of the cigarette's components. Secondly, estimates of these properties from the linear model have low standard deviations but a high bias, which makes the linear model useless for the estimation task. Thirdly, estimates from the non-linear model are more reliable if the pressure at the cigarette tip is varied instead of the flow velocity at the mouth end. Fourthly, the measurements of the degree of filter ventilation and of the open and closed draw resistance need to be at least 10 to 20 times more accurate than the desired accuracy of the estimate. Several methods to improve this situation are proposed.

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B. The Non-Linear Calculations for Pulsating Stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900019008 ◽

1967 ◽

Vol 28 ◽

pp. 105-176

Author(s):

Robert F. Christy

Keyword(s):

Major Part ◽

Afternoon Session ◽

Discussion Session ◽

Pulsating Stars ◽

Fourth Symposium ◽

Non Linear ◽

Considerable Discussion ◽

Informal Approach ◽

Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

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