scholarly journals Geometric approximation of the sphere by triangular polynomial spline patches

2021 ◽  
pp. 102061
Author(s):  
Aleš Vavpetič ◽  
Emil Žagar
Keyword(s):  
Polynomial Spline ◽  
Geometric Approximation

scholarly journals Development of means for experimental identification of navigator attention in ergatic systems of maritime transport

2020 ◽  
Vol 97 (1) ◽  
pp. 58-69
Author(s):  
P.S. Nosov ◽  
◽  
I.V. Palamarchuk ◽  
S.M. Zinchenko ◽  
Ya.A. Nahrybelnyi ◽  
...  
Keyword(s):  
Maritime Transport ◽  
Negative Consequences ◽  
Experimental Identification ◽  
System A ◽  
Geometric Approximation ◽  
Literary Sources ◽  
Special Means ◽  
Software And Hardware ◽  
Port Areas ◽  
Critical Situations

The article discusses the issues of identification of models of analysis of the navigational situation by the navigator during the passage in narrow places and port areas; this is especially relevant in critical situations. As part of the research, an analysis of literary sources was carried out, which made it possible to characterize this direction as actual for the development of special means of an experimental nature. As the main goal, the article presents formal-logical approaches to the development of software and hardware means for determining the areas of attention of the navigator as a subject of an ergatic system. A mechanism was determined for the formation the indexes of the analytical activities of the navigator during assessing the situation, mathematical models, and means for clarifying the position of the navigator on the navigation bridge. A geometric approximation of indexes was proposed, the metric of which can significantly reduce the identification time of critical situations and prevent negative consequences. The carried experiments by using the certified navigation simulator Navi Trainer 5000 confirmed the effectiveness and practical value of the proposed approaches, which will greatly improve the retraining of marine crew.

scholarly journals QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems

2021 ◽  
Vol 2000 (1) ◽  
pp. 012007
Author(s):  
A Sunarto ◽  
P Agarwal ◽  
J V L Chew ◽  
H Justine ◽  
J Sulaiman
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Polynomial Spline ◽  
Point Boundary ◽  
Spline Method

scholarly journals Stein's Method for Compound Geometric Approximation

2010 ◽  
Vol 47 (1) ◽  
pp. 146-156 ◽  
Author(s):  
Fraser Daly
Keyword(s):  
Generating Functions ◽  
Analytical Approach ◽  
Geometric Distribution ◽  
Stein’S Method ◽  
Hitting Times ◽  
Stein's Method ◽  
Geometric Approximation ◽  
Compound Geometric Distribution ◽  
Probabilistic Approximation ◽  
Sequence Patterns

We apply Stein's method for probabilistic approximation by a compound geometric distribution, with applications to Markov chain hitting times and sequence patterns. Bounds on our Stein operator are found using a complex analytical approach based on generating functions and Cauchy's formula.

scholarly journals Numerical Approach of Linear Volterra Integro-Differential Equations Using Generalized Spline Functions

2012 ◽  
Vol 9 (4) ◽  
pp. 734-740
Author(s):  
Baghdad Science Journal
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Approach ◽  
Polynomial Spline ◽  
Spline Functions

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

scholarly journals Computation of the Added Masses of an Unconventional Airship

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Naoufel Azouz ◽  
Said Chaabani ◽  
Jean Lerbet ◽  
Azgal Abichou
Keyword(s):  
Mathematical Analysis ◽  
Potential Flow ◽  
Velocity Potential ◽  
Special Focus ◽  
System Of Equations ◽  
Approximation Methods ◽  
Numerical Studies ◽  
Geometric Approximation ◽  
Elliptic Cone ◽  
Added Masses

This paper presents a modelling of an unmanned airship. We are studying a quadrotor flying wing. The modelling of this airship includes an aerodynamic study. A special focus is done on the computation of the added masses. Considering that the velocity potential of the air surrounding the airship obeys the Laplace's equation, the added masses matrix will be determined by means of the velocity potential flow theory. Typically, when the shape of the careen is quite different from that of an ellipsoid, designers in preprocessing prefer to avoid complications arising from mathematical analysis of the velocity potential. They use either complete numerical studies, or geometric approximation methods, although these methods can give relatively large differences compared to experimental measurements performed on the airship at the time of its completion. We tried to develop here as far as possible the mathematical analysis of the velocity potential flow of this unconventional shape using certain assumptions. The shape of the careen is assumed to be an elliptic cone. To retrieve the velocity potential shapes, we use the spheroconal coordinates. This leads to the Lamé's equations. The whole system of equations governing the interaction air-structure, including the boundary conditions, is solved in an analytical setting.

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