A natural interpolation formula for Prandtl's singular integrodifferential equation

1984 ◽  
Vol 4 (3) ◽  
pp. 283-290 ◽  
Author(s):  
N. I. Ioakimidis
Keyword(s):  
Integrodifferential Equation ◽  
Interpolation Formula ◽  
Singular Integrodifferential Equation

Deformations and Stress Intensities Due to a Craze in an Extended Elastic Material

1984 ◽  
Vol 51 (1) ◽  
pp. 84-92 ◽  
Author(s):  
J. R. Walton ◽  
Y. Weitsman
Keyword(s):  
Analytical Solution ◽  
Elastic Medium ◽  
Finite Length ◽  
Elastic Material ◽  
Integrodifferential Equation ◽  
Numerical Scheme ◽  
Time Dependent ◽  
Stress Fields ◽  
Singular Integrodifferential Equation

This paper presents an analytical solution, accompanied by a numerical scheme, to determine the displacement and stress fields in an extended elastic medium due to a thin craze of finite length directed transversely to the load at infinity. Crazes are thin elongated defects containing fine fibrils that connect their opposite interfaces. These fibrils are modeled as a distributed spring, leading to a formulation in terms of a singular integrodifferential equation. The paper also contains a treatment of central cracks within the craze and time-dependent craze response, and includes a discussion of “tip zone” correction.

THE INFLUENCE OF THE WIND SPEED PREDICTION ERROR ON THE SIZE OF THE STORAGE CONTROLLED OPERATION ZONE IN THE SYSTEM WITH THE WIND GENERATOR

2020 ◽  
Vol 2020 (57) ◽  
pp. 35-41
Author(s):  
K.S. Klen ◽  
◽  
M.K. Yaremenko ◽  
V.Ya. Zhuykov ◽  
◽  
...  
Keyword(s):  
Wind Speed ◽  
Prediction Error ◽  
Average Energy ◽  
Interpolation Formula ◽  
Wind Speed Prediction ◽  
Wind Generator ◽  
Prediction Horizon ◽  
Speed Prediction ◽  
Using Data ◽  
Predictor Corrector

The article analyzes the influence of wind speed prediction error on the size of the controlled operation zone of the storage. The equation for calculating the power at the output of the wind generator according to the known values of wind speed is given. It is shown that when the wind speed prediction error reaches a value of 20%, the controlled operation zone of the storage disappears. The necessity of comparing prediction methods with different data discreteness to ensure the minimum possible prediction error and determining the influence of data discreteness on the error is substantiated. The equations of the "predictor-corrector" scheme for the Adams, Heming, and Milne methods are given. Newton's second interpolation formula for interpolation/extrapolation is given at the end of the data table. The average relative error of MARE was used to assess the accuracy of the prediction. It is shown that the prediction error is smaller when using data with less discreteness. It is shown that when using the Adams method with a prediction horizon of up to 30 min, within ± 34% of the average energy value, the drive can be controlled or discharged in a controlled manner. References 13, figures 2, tables 3.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

scholarly journals Visualizing Profiles of Large Datasets of Weighted and Mixed Data

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 891
Author(s):  
Aurea Grané ◽  
Alpha A. Sow-Barry
Keyword(s):  
Multidimensional Scaling ◽  
Random Sample ◽  
Simulation Study ◽  
Clustering Algorithm ◽  
Computational Cost ◽  
Interpolation Formula ◽  
Large Datasets ◽  
Mixed Data ◽  
Multivariate Techniques ◽  
High Computational Cost

This work provides a procedure with which to construct and visualize profiles, i.e., groups of individuals with similar characteristics, for weighted and mixed data by combining two classical multivariate techniques, multidimensional scaling (MDS) and the k-prototypes clustering algorithm. The well-known drawback of classical MDS in large datasets is circumvented by selecting a small random sample of the dataset, whose individuals are clustered by means of an adapted version of the k-prototypes algorithm and mapped via classical MDS. Gower’s interpolation formula is used to project remaining individuals onto the previous configuration. In all the process, Gower’s distance is used to measure the proximity between individuals. The methodology is illustrated on a real dataset, obtained from the Survey of Health, Ageing and Retirement in Europe (SHARE), which was carried out in 19 countries and represents over 124 million aged individuals in Europe. The performance of the method was evaluated through a simulation study, whose results point out that the new proposal solves the high computational cost of the classical MDS with low error.

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