scholarly journals MEASURES OF THE BASIS EFFICIENCY IN THE INTERNAL ROTATION PROBLEM

2020 ◽  
pp. 338-347
Author(s):  
Александр Николаевич Белов ◽  
Владимир Владимирович Туровцев ◽  
Юрий Дмитриевич Орлов
Keyword(s):  
Internal Rotation ◽  
Basis Functions ◽  
Basis Sets ◽  
Equation Solution ◽  
Straight Line ◽  
Planar Wave ◽  
Definition Of ◽  
Variational Limit

Рассмотрено понятие вариационного предела при численном решении торсионного уравнения Шрёдингера и определены значения энергий состояний и переходов между ними на вариационном пределе в зависимости от размера базиса. На большом числе модельных потенциалов показано, что количество достоверно вычисляемых уровней линейно зависит от числа базисных функций. Данное число уровней (номер наибольшего достоверного состояния) рекомендовано в качестве меры эффективности базиса. Для базиса плоских волн найдено, что коэффициент углового наклона линейной зависимости составляет ≈ 1,03. Definition of the variational limit for the Schrodinger torsion equation solution was considered. Energies of levels and transitions at the variational limits were calculated for different basis sets. With many modeling potentials it was shown that the quantity of reliable calculated levels linearly depends on the number of the basis functions. This number (the number of the maximum reliable state) was recommended as a measure of the basis efficiency. The slope of the straight line for the planar wave basis dependence is approximately equal to 1,03.

Some Features in the Spectra of Extragalactic Radio Sources

1981 ◽  
Vol 4 (2) ◽  
pp. 184-187 ◽  
Author(s):  
O. B. Slee
Keyword(s):  
Spectral Index ◽  
Recent Analysis ◽  
Radio Sources ◽  
Usual Definition ◽  
Extragalactic Radio Sources ◽  
Flux Data ◽  
Straight Line ◽  
Consistent Manner ◽  
Definition Of ◽  
Second Degree

A recent analysis of the spectra of about 2000 sources in the Culgoora-3 list (Slee 1977) of radio sources (Slee et al. 1981) has revealed some interesting features which may be the result of source evolution. The Culgoora-3 spectra were obtained by combining the 80 and 160 MHz flux densities from the Culgoora radioheliograph with other published flux data between 10 and 10,000 MHz; this is probably the most accurate set of spectra yet derived for a large number of sources selected for observation in a reasonably consistent manner. In addition to fitting the log S-log v data for each source with a straight line (its slope is the usual definition of spectral index) Slee et al. also fitted second-degree and third-degree polynomials to search for curvature in the spectra.

A quantitative measure of nonlinearity

1993 ◽  
Vol 39 (5) ◽  
pp. 766-772 ◽  
Author(s):  
K Emancipator ◽  
M H Kroll
Keyword(s):  
Analytical Method ◽  
Response Curve ◽  
Polynomial Regression ◽  
Quantitative Measure ◽  
Square Root ◽  
Straight Line ◽  
The Mean ◽  
The Difference ◽  
Definition Of ◽  
Fitting In

Abstract Quantitative measures of the nonlinearity of an analytical method are defined as follows: the "(dimensional) nonlinearity" of a method is the square root of the mean of the square of the deviation of the response curve from a straight line, where the straight line is chosen to minimize the nonlinearity. The "relative nonlinearity" is defined as the dimensional nonlinearity divided by the difference between the maximum and minimum assayed values. These definitions may be used to develop practical criteria for linearity that are still objective. Calculation of the nonlinearity requires a method of curve-fitting. In this article, we use polynomial regression to demonstrate calculations, but the definition of nonlinearity also accommodates alternative nonlinear regression procedures.

scholarly journals Evaluation of Nonlinearity Testing Procedures on Simulated Data

1997 ◽  
Vol 80 (1) ◽  
pp. 79-88 ◽  
Author(s):  
Max H Feinberg ◽  
Arnauld J De La Rochette
Keyword(s):  
Prediction Error ◽  
Model Fitting ◽  
Simulated Data ◽  
Relative Difference ◽  
Application Range ◽  
Testing Procedures ◽  
Detection Techniques ◽  
Straight Line ◽  
Definition Of ◽  
Linearity Test

Abstract When calibrating a method, use of a straight line is highly favorable because it is easy to compute sensitivity and the blank to be used to predict an unknown concentration. Therefore, when validating an analytical method, it is necessary to check whether linearity is acceptable over the method’s whole application range before trying another model. Available procedures for checking linearity are reviewed by using a simulation model that gives a complete family of curved calibration lines. From the simulated data, it is possible to compute the prediction error generated by the model curva ture as the relative difference between the linear extrapolated value and the observed value. It appears that the power of the classical “linearity test” depends on experimental design and that at least 25 measurements are necessary to detect curvature for an acceptable prediction error. An alternative model-fitting criterion, based on the χ2 probability law, also was evaluated. It is also applicable but seems less stable and more sensitive to data size. The question of the definition of nonlinearity is also raised because it is directly connected to the comparison of nonlinearity detection techniques.

scholarly journals Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions

2011 ◽  
Vol 7 (10) ◽  
pp. 3027-3034 ◽  
Author(s):  
Ewa Papajak ◽  
Jingjing Zheng ◽  
Xuefei Xu ◽  
Hannah R. Leverentz ◽  
Donald G. Truhlar
Keyword(s):  
Basis Functions ◽  
Basis Sets

Homeomeric Lines in Greek Mathematics

2010 ◽  
Vol 23 (1) ◽  
pp. 1-37 ◽  
Author(s):  
Fabio Acerbi
Keyword(s):  
Companion Paper ◽  
Future Issue ◽  
Property A ◽  
Straight Line ◽  
Key Issues ◽  
The Subject ◽  
Cosmological Debate ◽  
Greek Mathematics ◽  
Definition Of ◽  
Cylindrical Helix

ArgumentThis article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context.

scholarly journals CALCULATION OF DEFLECTIONS OF HOLLOW CONCRETE-FILLED STEEL TUBULAR MEMBERS OF THREE-HINGE SUSPENSION STRUCTURE/KABAMOSIOS TRILANKSTĖS BETONŠERDŽZIŲ TUŠČIAVIDURIŲ VAMZDINIŲ PLIENO STRYPŲ KONSTRUKCIJOS ĮLINKIŲ SKAIČIAVIMAS

2001 ◽  
Vol 7 (2) ◽  
pp. 99-105
Author(s):  
Viačeslavas Šaraškinas ◽  
Audronis Kazimieras Kvedaras
Keyword(s):  
Composite Structures ◽  
Theoretical Data ◽  
Bending Stiffness ◽  
Flexural Stiffness ◽  
Vertical Deflection ◽  
Cross Sectional ◽  
Straight Line ◽  
Deformation Properties ◽  
Definition Of ◽  
Suspended Roof

Recently, in scientific literature, information on a new type of suspended straight-line 3-hinged roof structures has considerably increased. It was stressed that straight-line elements are easily manufactured and erected, roof decking service conditions are good. In the world building practice during last 30 years very effective composite structures have been introduced, even hollow concrete-filled steel tubular members. But no information on the application of such members for suspended roofs was obtained. In some sources very simple straight-line suspended roofs structures were analysed, and for those shapes an effective centrifuged hollow concrete-filled steel tubular members may be successfully applied. These members do not require additional roof stabilisation. These composite ropes may be attributed to the elements of final flexural stiffness, and they are effective and simple to decrease deflections of the suspended roof. However, for these composite ropes the methods of their deflection calculations must be developed because it is necessary to estimate their composite cross-section and interaction between components. This paper deals with analysis of these ropes' behaviour and their deflection calculation, which was made by exact I. Kalminzer's and other simplified methods. The vertical deflections in the middle of elements of the straight-line three-hinge composite suspended structure may be calculated as consisting of two parts depending on their bending and tension. The part of vertical deflection at mid-span of a composite member connected with its bending may be calculated as for hollow concrete-filled steel tubular beam taking into account the sum of flexural bending stiffness of its cross-sectional components (EJ) c . The I.Kalminzer's or other simplified methods taking into account the sum of flexural bending stiffness of cross-sectional components may calculate the vertical deflection called by tension of element as the member of final flexural stiffness (EJ) c . Comparison of experimental and theoretical data shows a good satisfaction when deflection calculation for the straight-line composite rope is made by dividing it into two parts depending on bending and tension. Investigation made into the deformation properties and methods of deflection definition of straight-line circular hollow concrete-filled steel tubular members allows declaring the possibility of useful application of such members as the ones of final flexural stiffness in suspended roof structures.

scholarly journals Street space design for bendi in the urban area of a ternate city

2020 ◽  
Vol 9 (2) ◽  
pp. 494
Author(s):  
Andi Arifah Pasri ◽  
Sabaruddin . ◽  
Abdul Gaus ◽  
Mufti Amir Sultan ◽  
Najamuddin .
Keyword(s):  
Public Space ◽  
Spatial Planning ◽  
Descriptive Analysis ◽  
Space Design ◽  
Road Users ◽  
Straight Line ◽  
Street Space ◽  
Qualitative Descriptive ◽  
Definition Of ◽  
Physical Order

Spatial planning is very important because it is a public space so whether or not a street space will affect all road users. Structuring street space is to increase user experience so that the best place of public space is achieved.To get the best place, we need to accommodate and clearly define each user of the space. Bendi as a mode of transportation certainly uses street space as a means of motion space. And it requires a clear definition of the movement of the bendi in a physical order that can prevent violations of the rights of other street users both pedestrians and motorized vehicles.The purpose of this study is how the standard of road spatial planning for bendi. The method used in this study is the collection of field data through qualitative descriptive analysis with several indicators, namely Characteristics and space for bendi, spatial planning standards, street space settings. The design concept of bendi lane is proposed in 2 types, namely a special lane with a straight line divider on the Hasan Esa street, the Pahlawan revolusi street, and the Djabar Syah street and integration on the Ahmad Yani street and the Nukila street. 

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