scholarly journals COMBINED NEWTON’S THIRD-ORDER CONVERGENCE METHOD FOR MINIMIZE ONE VARIABLE FUNCTIONS

2021 ◽  
pp. 48-55
Author(s):  
V. A. Kodnyanko ◽  
O. A. Grigorieva ◽  
L. V. Strok
Keyword(s):  
Numerical Optimization ◽  
Combined Method ◽  
Third Order ◽  
Unimodal Function ◽  
Actual Problem ◽  
The Third ◽  
Calculation Results ◽  
Convergence Method ◽  
Newtonian Method ◽  
Brent's Method

Contex. The article deals with the actual problem of numerical optimization of slowly computed unimodal functions of one variable. The analysis of existing methods of minimization of the first and second orders of convergence, which showed that these methods can be used to quickly solve these problems for functions, the values of which can be obtained without difficulty. For slowly computed functions, these methods give slow algorithms; therefore, the problem of developing fast methods for minimizing such functions is urgent. Objective. Development of a combined third-order Newtonian method of convergence to minimize predominantly slowly computed unimodal functions, as well as the development of a database, including smooth, monotonic and partially constant functions, to test the method and compare its effectiveness with other known methods. Method. A technique and an algorithm for solving the problem of fast minimization of a unimodal function of one variable by a combined numerical Newtonian method of the third order of convergence presented. The method is capable of recognizing strictly unimodal, monotonic and constant functions, as well as functions with partial or complete sections of a flat minimum. Results. The results of comparison of the proposed method with other methods, including the fast Brent method, presented. 6954 problems were solved using the combined Newtonian method, while the method turned out to be faster than other methods in 95.5% of problems, Brent’s method worked faster in only 4.5% of problems. In general, the analysis of the calculation results showed that the combined method worked 1.64 times faster than the Brent method. Conclusions. A combined third-order Newtonian method of convergence proposed for minimizing predominantly slowly computed unimodal functions of one variable. A database of problems developed, including smooth, monotone and partially constant functions, to test the method and compare its effectiveness with other known methods. It is shown that the proposed method, in comparison with other methods, including the fast Brent method, has a higher performance.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

THE FACTORS OF CAREER SELF-DETERMINATION OF STUDENTS OF HIGHER EDUCATION INSTITUTIONS

2019 ◽  
Vol 7 (1) ◽  
pp. 9-20
Author(s):  
Inna Yeung
Keyword(s):  
Higher Education ◽  
Higher Education Institutions ◽  
Well Being ◽  
Young Person ◽  
Self Determination ◽  
Full Time ◽  
Actual Problem ◽  
The Third ◽  
The Right

Choice of profession is a social phenomenon that every person has to face in life. Numerous studies convince us that not only the well-being of a person depends on the chosen work, but also his attitude to himself and life in general, therefore, the right and timely professional choice is very important. Research about factors of career self-determination of students of higher education institutions in Ukraine shows that self-determination is an important factor in the socialization of young person, and the factors that determine students' career choices become an actual problem of nowadays. The present study involved full-time and part-time students of Institute of Philology and Mass Communications of Open International University of Human Development "Ukraine" in order to examine the factors of career self-determination of students of higher education institutions (N=189). Diagnostic factors of career self-determination of students studying in the third and fourth year were carried out using the author's questionnaire. Processing of obtained data was carried out using the Excel 2010 program; factorial and comparative analysis were applied. Results of the study showed that initial stage of career self-determination falls down on the third and fourth studying year at the university, when an image of future career and career orientations begin to form. At the same time, the content of career self-determination in this period is contradictory and uncertain, therefore, the implementation of pedagogical support of this process among students is effective.

scholarly journals Ultrafast Third-Order Nonlinear Optical Response Excited by fs Laser Pulses at 1550 nm in GaN Crystals

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3194
Author(s):  
Adrian Petris ◽  
Petronela Gheorghe ◽  
Tudor Braniste ◽  
Ion Tiginyanu
Keyword(s):  
Harmonic Generation ◽  
Nonlinear Optical ◽  
Laser Pulses ◽  
Third Harmonic Generation ◽  
High Repetition Rate ◽  
Third Order ◽  
Third Harmonic ◽  
The Third ◽  
High Repetition ◽  
Gan Crystal

The ultrafast third-order optical nonlinearity of c-plane GaN crystal, excited by ultrashort (fs) high-repetition-rate laser pulses at 1550 nm, wavelength important for optical communications, is investigated for the first time by optical third-harmonic generation in non-phase-matching conditions. As the thermo-optic effect that can arise in the sample by cumulative thermal effects induced by high-repetition-rate laser pulses cannot be responsible for the third-harmonic generation, the ultrafast nonlinear optical effect of solely electronic origin is the only one involved in this process. The third-order nonlinear optical susceptibility of GaN crystal responsible for the third-harmonic generation process, an important indicative parameter for the potential use of this material in ultrafast photonic functionalities, is determined.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Direct integration of the third-order two point and multipoint Robin type boundary value problems

2021 ◽  
Vol 182 ◽  
pp. 411-427
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Direct Integration ◽  
Third Order ◽  
The Third ◽  
Type Boundary
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