Extended goursat normal form: a geometric characterization

2007 ◽  
pp. 323-338
Author(s):  
Witold Respondek ◽  
William Pasillas-Lépine
Keyword(s):  
Normal Form ◽  
Geometric Characterization

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Radioscopic Images Segmentation by “Edge and Area” Combined Approach for Weld Geometric Characterization

2000 ◽  
Vol 12 (1) ◽  
pp. 179-189
Author(s):  
C. Gueudre ◽  
J. Moysan ◽  
G. Corneloup
Keyword(s):  
Geometric Characterization ◽  
Combined Approach

A 3D Field Expression in Multilayered Structures using Jordan Normal Form

2012 ◽  
Vol 132 (8) ◽  
pp. 698-699 ◽  
Author(s):  
Hideaki Wakabayashi ◽  
Jiro Yamakita
Keyword(s):  
Normal Form ◽  
Jordan Normal Form ◽  
Multilayered Structures

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

Analysis of a 2DOF Nonlinear Mechanical System Using the Normal Form Method

2019 ◽  
Author(s):  
David Julian Gonzalez Maldonado ◽  
Peter Hagedorn ◽  
Thiago Ritto ◽  
Rubens Sampaio ◽  
Artem Karev
Keyword(s):  
Normal Form ◽  
Mechanical System ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Normal Form Method

Classification of IC Process Deformation Characteristics Using Memory Fail Bitmaps

2004 ◽  
Author(s):  
T. Zanon ◽  
W. Maly
Keyword(s):  
Geometric Characterization ◽  
Deformation Characteristics ◽  
Analysis Study ◽  
Preliminary Results ◽  
Failure Patterns ◽  
Yield Learning ◽  
Sram Memory ◽  
Viable Approach ◽  
Ic Technology

Abstract Building a portfolio of deformations is the key step for building better defect models for the test and yield learning domain. A viable approach to achieve this goal is through geometric characterization and classification of failure patterns found on memory fail bitmaps. In this paper, we present preliminary results on how to build such a portfolio of deformations for an IC technology of interest based on a fail bitmap analysis study conducted on large, modern SRAM memory products.

Normal form method in search for periodic solutions of ordinary differential equations. Case of the fourth order

2018 ◽  
pp. 24-34
Author(s):  
V. F. Edneral ◽  
O. D. Timofeevskaya
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Computational Time ◽  
Resonant Normal Form ◽  
Normal Form Method

Introduction:The method of resonant normal form is based on reducing a system of nonlinear ordinary differential equations to a simpler form, easier to explore. Moreover, for a number of autonomous nonlinear problems, it is possible to obtain explicit formulas which approximate numerical calculations of families of their periodic solutions. Replacing numerical calculations with their precalculated formulas leads to significant savings in computational time. Similar calculations were made earlier, but their accuracy was insufficient, and their complexity was very high.Purpose:Application of the resonant normal form method and a software package developed for these purposes to fourth-order systems in order to increase the calculation speed.Results:It has been shown that with the help of a single algorithm it is possible to study equations of high orders (4th and higher). Comparing the tabulation of the obtained formulas with the numerical solutions of the corresponding equations shows good quantitative agreement. Moreover, the speed of calculation by prepared approximating formulas is orders of magnitude greater than the numerical calculation speed. The obtained approximations can also be successfully applied to unstable solutions. For example, in the Henon — Heyles system, periodic solutions are surrounded by chaotic solutions and, when numerically integrated, the algorithms are often unstable on them.Practical relevance:The developed approach can be used in the simulation of physical and biological systems.

The Logic of Normal-Form Games

2015 ◽  
Author(s):  
Gabriel Frahm
Keyword(s):  
Normal Form ◽  
Normal Form Games

Box-Cox Transformations

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Maximum Likelihood ◽  
Normal Form ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimate ◽  
Grouped Data ◽  
Numerical Example ◽  
Alternative Method ◽  
Modified Likelihood

This chapter examines the well-known Box-Cox method, which transforms a sample of non-normal observations into approximately normal form. Two non-standard aspects are highlighted. First, the likelihood of the transformed sample has an unbounded maximum, so that the maximum likelihood estimate is not consistent. The usually suggested remedy is to assume grouped data so that the sample becomes multinomial. An alternative method is described that uses a modified likelihood similar to the spacings function. This eliminates the infinite likelihood problem. The second problem is that the power transform used in the Box-Cox method is left-bounded so that the transformed observations cannot be exactly normal. This biases estimates of observational probabilities in an uncertain way. Moreover, the distributions fitted to the observations are not necessarily unimodal. A simple remedy is to assume the transformed observations have a left-bounded distribution, like the exponential; this is discussed in detail, and a numerical example given.

Sign in / Sign up

Export Citation Format

Share Document