scholarly journals Protection numbers in simply generated trees and Pólya trees

2021 ◽  
pp. 10-10
Author(s):  
Bernhard Gittenberger ◽  
Zbigniew Gołębiewski ◽  
Isabella Larcher ◽  
Małgorzata Sulkowska
Keyword(s):  
Numerical Computation ◽  
High Accuracy ◽  
Expected Value ◽  
Binary Trees ◽  
Polya Trees ◽  
Simply Generated Trees

We determine the limit of the expected value and the variance of the protection number of the root in simply generated trees, in P?lya trees, and in unlabelled non-plane binary trees, when the number of vertices tends to infinity. Moreover, we compute expectation and variance of the protection number of a randomly chosen vertex in all those tree classes. We obtain exact formulas as sum representations, where the obtained sums are rapidly converging thus allowing an efficient numerical computation of high accuracy.

scholarly journals A Least Squares Computational Method for the Scattering Amplitude

1988 ◽  
Vol 41 (1) ◽  
pp. 47 ◽  
Author(s):  
JN Das
Keyword(s):  
Least Squares ◽  
Numerical Computation ◽  
Scattering Amplitude ◽  
High Accuracy ◽  
Computational Method ◽  
Partial Support ◽  
Numerical Instabilities

A new least squares computational method for the scattering amplitude is proposed. This may be applied without difficulty to atomic and other scattering computations. The approach is expected to give converged results of high accuracy and also to be free from major numerical instabilities. As an example a numerical computation is carried out following the method and some results are presented in partial support of the claim.

scholarly journals On the number of transversals in random trees

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Bernhard Gittenberger ◽  
Veronika Kraus
Keyword(s):  
Generating Functions ◽  
Singularity Analysis ◽  
Random Trees ◽  
Alternative Proof ◽  
Fixed Size ◽  
Random Subset ◽  
Polya Trees ◽  
Vertex Set ◽  
International Audience ◽  
Simply Generated Trees

International audience We study transversals in random trees with n vertices asymptotically as n tends to infinity. Our investigation treats the average number of transversals of fixed size, the size of a random transversal as well as the probability that a random subset of the vertex set of a tree is a transversal for the class of simply generated trees and for Pólya trees. The last parameter was already studied by Devroye for simply generated trees. We offer an alternative proof based on generating functions and singularity analysis and extend the result to Pólya trees.

A New 1,000 kV Electron Microscope

1967 ◽  
Vol 25 ◽  
pp. 260-261
Author(s):  
M. Nishigaki ◽  
S. Katagiri ◽  
H. Kimura ◽  
B. Tadano
Keyword(s):  
Electron Microscope ◽  
High Voltage ◽  
Basic Research ◽  
Chromatic Aberration ◽  
High Accuracy ◽  
Biological Specimen ◽  
Voltage Electron ◽  
High Voltage Electron Microscope ◽  
High Voltage Electron

The high voltage electron microscope has many advantageous features in comparison with the ordinary electron microscope. They are a higher penetrating efficiency of the electron, low chromatic aberration, high accuracy of the selected area diffraction and so on. Thus, the high voltage electron microscope becomes an indispensable instrument for the metallurgical, polymer and biological specimen studies. The application of the instrument involves today not only basic research but routine survey in the various fields. Particularly for the latter purpose, the performance, maintenance and reliability of the microscope should be same as those of commercial ones. The authors completed a 500 kV electron microscope in 1964 and a 1,000 kV one in 1966 taking these points into consideration. The construction of our 1,000 kV electron microscope is described below.

Application Of BIM-Technology In The Restoration Of Buildings

2020 ◽  
pp. 42-48
Keyword(s):  
Chinese Communist Party ◽  
Laser Scanning ◽  
High Accuracy ◽  
Information Environment ◽  
Information Modeling ◽  
Structural Scheme ◽  
Traditional Design ◽  
Information Interaction ◽  
Heritage Buildings ◽  
Effective Organization

The paper describes the main trends in the development of BIM technologies in the field of restoration and reconstruction of historical and cultural heritage buildings. The practical part of the paper presents the experience in using information modeling technologies when restoring the building, where the VI Congress of the Chinese Communist Party in Moscow took place. The use of laser scanning technologies made it possible to reproduce with high accuracy in the information model the original appearance of the building using Autodesk RevitR software. It is shown, how the use of information modeling technologies affects the duration of restoration process, taking into account the calculation of the structural scheme and bearing structures of the building, ensuring the identity of the decoration and the effective organization of electromechanical installation. Operating in a single BIM information environment makes it possible to continuously obtain reliable information on the project, which provides more effective information interaction and communication of participants compared to using traditional design methods.

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