Optimal Location of Support Points in the Kirchhoff Plate

2012 ◽  
pp. 93-116 ◽  
Author(s):  
Giuseppe Buttazzo ◽  
Sergey A. Nazarov
Keyword(s):  
Optimal Location ◽  
Kirchhoff Plate ◽  
Support Points

Modern Technology of Education: Support Points of Discussion

2018 ◽  
pp. 7-17
Author(s):  
Elena Viktorovna Tikhomirova ◽  
Anna Gennadievna Samokhvalova ◽  
Anatoly Grigorievich Kirpichnik ◽  
Daria Andreevna Dolotova
Keyword(s):  
Modern Technology ◽  
Support Points ◽  
Education Support

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

Voltage Stability Enhancement with Optimal Placement of IPFC

2019 ◽  
Vol 8 (4) ◽  
pp. 9465-9471
Keyword(s):  
Transmission Line ◽  
Objective Function ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Test System ◽  
Optimal Location ◽  
Optimal Placement ◽  
Utilization Factor ◽  
Location Selection ◽  
Multi Objective

This paper presents a novel technique based on Cuckoo Search Algorithm (CSA) for enhancing the performance of multiline transmission network to reduce congestion in transmission line to huge level. Optimal location selection of IPFC is done using subtracting line utilization factor (SLUF) and CSA-based optimal tuning. The multi objective function consists of real power loss, security margin, bus voltage limit violation and capacity of installed IPFC. The multi objective function is tuned by CSA and the optimal location for minimizing transmission line congestion is obtained. The simulation is performed using MATLAB for IEEE 30-bus test system. The performance of CSA has been considered for various loading conditions. Results shows that the proposed CSA technique performs better by optimal location of IPFC while maintaining power system performance

Impact of plumb location on the determination accuracy of chimney heeling by photographic method

2017 ◽  
Vol 919 (1) ◽  
pp. 55-59
Author(s):  
O.V. Raskatkina
Keyword(s):  
Image Processing ◽  
Experimental Research ◽  
Optimal Location ◽  
Paint System ◽  
Photographic Method ◽  
Round Shape ◽  
Straight Line ◽  
Left And Right

There is a method of using the corded plumb as vertical reference straight line, located in front of the objective of a digital photocamera in the article. When we take picture of the object under study, there will be this straight line in the photo, from which we can carry out all necessary measurements in the Paint system with the following conversion them into metric system. All possible variants of location of the reference straight line relative to it axis are considered by the example of the construction of the tower round shape and it is shown a method of heeling calculation by image processing results. Experimental research to determine the degree of influence of plumb location in the photo relative to it axe on the accuracy of the heeling determination was carried out by shooting the brick chimney with the 30 metres height when the plumb is located on the chimney axis and on different distance from the left and right of the axis. It is set in the result that the plumb location has influence on the accuracy of heeling determination. The optimal location is on the centre of the top section of the chimney and there is shown the method of accounting corrections due to inaccurate location.

scholarly journals The Impact of the Ring Roads on the Location Pattern of Shops in Town and City Centres. A Space Syntax Approach

2021 ◽  
Vol 13 (7) ◽  
pp. 3927
Author(s):  
Akkelies van Nes
Keyword(s):  
Urban Areas ◽  
Space Syntax ◽  
Optimal Location ◽  
Spatial Integration ◽  
Street Network ◽  
Location Pattern ◽  
Ring Road ◽  
Road Projects ◽  
The Impact ◽  
City Centres

This contribution demonstrates how inner ring roads change the location pattern of shops in urban areas with the application of the space syntax method. A market rational behaviour persists, in that shop owners always search for an optimal location to reach as many customers as possible. If the accessibility to this optimal location is affected by changes in a city’s road and street structure, it will affect the location pattern of shops. Initially, case studies of inner ring road projects in Birmingham, Coventry, Wolverhampton, Bristol, Tampere, and Mannheim show how their realisation affect the spatial structure of the street network of these cities and the location pattern of shops. The results of the spatial integration analyses of the street and road network are discussed with reference to changes in land-use before and after the implementation of ring roads, and current space syntax theories. As the results show, how an inner ring road is connected to and the type of the street network it is imposed upon dictates the resulting location pattern of shops. Shops locate and relocate themselves along the most spatially-integrated streets. Evidence on how new road projects influence the location pattern of shops in urban centres are useful for planning sustainable city centres.

scholarly journals An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics

Pharmaceutics ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 42
Author(s):  
Walter M. Yamada ◽  
Michael N. Neely ◽  
Jay Bartroff ◽  
David S. Bayard ◽  
James V. Burke ◽  
...  
Keyword(s):  
Drug Development ◽  
Population Pharmacokinetics ◽  
Empirical Bayes ◽  
Applied Mathematics ◽  
Grid Method ◽  
Bayes Estimation ◽  
Population Pharmacokinetic ◽  
Support Points ◽  
Primal Dual ◽  
Log Normal

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.

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