scholarly journals On a theory of the second order longitudinal spherical aberra­tion for a symmetrical optical system

1920 ◽  
Vol 97 (683) ◽  
pp. 196-198
Keyword(s):  
Optical System ◽  
Spherical Aberration ◽  
Empirical Method ◽  
Second Order ◽  
Point Of View ◽  
Axial Plane ◽  
First Order ◽  
Usual Theory ◽  
Semi Empirical

1. The object of this investigation is to establish a formula for the longitudinal spherical aberration of rays which traverse a symmetrical optical system in an axial plane that shall be capable of fairly easy computation for any combination of lenses, and at the same time shall be accurate to the second order and free from certain important difficulties of convergency which occur in certain neighbourhoods when we attempt to use for the longitudinal aberration the method of aberration of successive orders. From the point of view of the optical designer, the usual theory of aberrations, which, for all practical purposes, is largely restricted to the first order, is known to give an unsatisfactory approximation. In practice, the designer adopts a semi-empirical method of tracing a number of rays through the system by means of the trigonometrical equations, a method which is laborious and lengthy, and which can at best give only incomplete informa­tion and very limited guidance for effecting improvements.

THE INVESTIGATION OF ELECTRONIC PROPERTIES AND MICROSCOPIC SECOND-ORDER NONLINEAR OPTICAL BEHAVIOR OF 1-SALICYLIDENE-3-THIO-SEMICARBAZONE

2007 ◽  
Vol 16 (01) ◽  
pp. 91-99 ◽  
Author(s):  
ASLI KARAKAS ◽  
HUSEYIN UNVER ◽  
AYHAN ELMALI
Keyword(s):  
Molecular Orbital ◽  
Electronic Transition ◽  
Nonlinear Optical ◽  
Dipole Moments ◽  
Empirical Method ◽  
Second Order ◽  
Nlo Properties ◽  
Calculation Results ◽  
Moller Plesset ◽  
Semi Empirical

To investigate the microscopic second-order nonlinear optical (NLO) behavior of the 1-salicylidene-3-thio-semicarbazone Schiff base compound, the electric dipole moments (μ), linear static polarizabilities (α) and first static hyperpolarizabilites (β) have been calculated using finite field second-order Møller-Plesset perturbation (FF MP2) theory. The ab-initio results on (hyper)polarizabilities show that the investigated molecule might have microscopic NLO properties with non-zero values. To understand the NLO behavior in the context of molecular orbital structure, we have also examined the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and the HOMO-LUMO gap in the same theoretical framework as the (hyper)polarizability calculations. In addition to the NLO properties, the electronic transition spectra have been computed using a semi-empirical method (ZINDO). ZINDO calculation results show that the electronic transition wavelengths have been estimated to be shorter than 400 nm.

Higher-Order Multilevel Solvers for the EHL Line and Point Contact Problem

1994 ◽  
Vol 116 (4) ◽  
pp. 741-750 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Contact Problem ◽  
Computing Time ◽  
Point Contact ◽  
Higher Order ◽  
Second Order ◽  
Point Of View ◽  
First Order ◽  
Fundamental Point ◽  
Numerical Solver ◽  
Circular Contact

This paper addresses the development of efficient numerical solvers for EHL problems from a rather fundamental point of view. A work-accuracy exchange criterion is derived, that can be interpreted as setting a limit to the price paid in terms of computing time for a solution of a given accuracy. The criterion can serve as a guideline when reviewing or selecting a numerical solver and a discretization. Earlier developed multilevel solvers for the EHL line and circular contact problem are tested against this criterion. This test shows that, to satisfy the criterion a second-order accurate solver is needed for the point contact problem whereas the solver developed earlier used a first-order discretization. This situation arises more often in numerical analysis, i.e., a higher order discretization is desired when a lower order solver already exists. It is explained how in such a case the multigrid methodology provides an easy and straightforward way to obtain the desired higher order of approximation. This higher order is obtained at almost negligible extra work and without loss of stability. The approach was tested out by raising an existing first order multilevel solver for the EHL line contact problem to second order. Subsequently, it was used to obtain a second-order solver for the EHL circular contact problem. Results for both the line and circular contact problem are presented.

scholarly journals All the existences that there are

Disputatio ◽  
2012 ◽  
Vol 4 (32) ◽  
pp. 361-383 ◽  
Author(s):  
Alberto Voltolini
Keyword(s):  
Second Order ◽  
Point Of View ◽  
Order Property ◽  
First Order

Abstract In this paper, I will defend the claim that there are three existence properties: the second-order property of being instantiated, a substantive first-order property (or better a group of such properties) and a formal, hence universal, first-order property. I will first try to show what these properties are and why we need all of them for ontological purposes. Moreover, I will try to show why a Meinong-like option that positively endorses both the former and the latter first-order property is the correct view in ontology. Finally, I will add some methodological remarks as to why this debate has to be articulated from the point of view of reality, i.e., by speaking of properties, rather than from the point of view of language, i.e., by speaking of predicates (for such properties).

scholarly journals CONSTRUCTIVE AND PROBABILISTIC ANALYSIS OF EXCAVATED PILES WITH LOST METALLIC SHIRT

Revista EIA ◽  
2021 ◽  
Vol 19 (37) ◽  
Author(s):  
Lucas Eugênio Rodrigues ◽  
Aílton Carlos Dos Santos Brandão ◽  
George Fernandes Azevedo
Keyword(s):  
Load Capacity ◽  
Empirical Method ◽  
Point Of View ◽  
Theoretical Point ◽  
First Order Second Moment ◽  
Probabilistic Study ◽  
Geometrical Data ◽  
Semi Empirical ◽  
Parameter Values

This work brings in its scope some analyzes around the constructive methodology of a case study that refers to the implantation of a dolphin (a structure that in this case has the purpose of mooring ships) at Pier III, located in Ponta da Madeira Maritime Terminal, in the city of São Luís, Maranhão, and with a focus on the process of building its infrastructure, more precisely the adopted foundation. This type of work, being port and in a maritime environment is called offshore, the foundation used in this case is the deep type, more precisely called piles excavated with a lost metallic shirt whose constructional scope will be detailed in this work, from the driving from shirts to concreting the piles that made up the system. The theme is approached from a practical and theoretical point of view, with a probabilistic study of the load capacity of foundations based on geometrical data from surveys carried out in the region, in order to define results that include any variability of the location and guarantee functionality and safety necessary for the foundation to achieve the project's objectives and be optimized throughout its useful life. The analysis of the probability of rupture was made using the semi-empirical method of Aoki-Velloso, combined with the First Order Second Moment method in order to compare the result achieved with the established parameter values. The work also aims to serve as a basis for future guidance and guidance on the topic, which does not have such a vast bibliography, mainly in view of the installation of new similar projects in the region and in other locations.

LOGICAL ASPECTS OF CAYLEY-GRAPHS: THE MONOID CASE

2006 ◽  
Vol 16 (02) ◽  
pp. 307-340 ◽  
Author(s):  
DIETRICH KUSKE ◽  
MARKUS LOHREY
Keyword(s):  
Cayley Graph ◽  
Cayley Graphs ◽  
Order Theory ◽  
Second Order ◽  
Point Of View ◽  
Direct Products ◽  
Graph Products ◽  
Arbitrary Graph ◽  
First Order ◽  
First Order Theory

Cayley-graphs of monoids are investigated under a logical point of view. It is shown that the class of monoids, for which the Cayley-graph has a decidable monadic second-order theory, is closed under free products. This result is derived from a result of Walukiewicz, stating that the decidability of monadic second-order theories is preserved under tree-like unfoldings. Concerning first-order logic, it is shown that the class of monoids, for which the Cayley-graph has a decidable first-order theory, is closed under arbitrary graph products, which generalize both, free and direct products. For the proof of this result, tree-like unfoldings are generalized to so-called factorized unfoldings. It is shown that the decidability of the first-order theory of a structure is preserved by factorized unfoldings. Several additional results concerning factorized unfoldings are shown.

Evaluation of a Correction for Photometric Errors in FT-IR Spectrometry Introduced by a Nonlinear Detector Response

1998 ◽  
Vol 52 (4) ◽  
pp. 565-571 ◽  
Author(s):  
Robert L. Richardson ◽  
Husheng Yang ◽  
Peter R. Griffiths
Keyword(s):  
Empirical Method ◽  
Second Order ◽  
Detector Response ◽  
Ir Spectrometry ◽  
First Order ◽  
Beer's Law ◽  
Ft Ir ◽  
Beer’S Law ◽  
First Order Correction ◽  
Phase Spectra

For strongly absorbing bands measured with a Fourier transform infrared (FT-IR) spectrometer, the effects of a nonlinear detector response must be eliminated before Beer's law linearity can be achieved. An empirical method for greatly reducing the effect of detector nonlinearity on FT-IR Beer's law spectra measured by using an FT-IR spectrometer equipped with a mercury-cadmium-telluride (MCT) detector is investigated. This first-order analytical function has been applied to correct nonlinear vapor-phase spectra and statistically evaluated for validity for spectral regions above the detector cutoff. In addition, a series of second-order functions has been evaluated to investigate the possibility that the transmittance scale is slightly nonlinear even after the first-order correction has been applied. Any improvement caused by the second-order functions was not statistically significant.

scholarly journals A NEW LIE–SYSTEMS APPROACH TO SECOND-ORDER RICCATI EQUATIONS

2012 ◽  
Vol 09 (02) ◽  
pp. 1260007 ◽  
Author(s):  
J. F. CARIÑENA ◽  
J. DE LUCAS ◽  
C. SARDÓN
Keyword(s):  
Systems Approach ◽  
Riccati Equations ◽  
Second Order ◽  
Point Of View ◽  
First Order ◽  
Lie Systems ◽  
Legendre Transforms

This work presents a newly renovated approach to the analysis of second-order Riccati equations from the point of view of the theory of Lie systems. We show that these equations can be mapped into Lie systems through certain Legendre transforms. This result allows us to construct new superposition rules for studying second-order Riccati equations and to reduce their integration to solving (first-order) Riccati equations.

scholarly journals A Variational Approach to an Inhomogeneous Second-Order Ordinary Differential System

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
B. Muatjetjeja ◽  
C. M. Khalique
Keyword(s):  
Positive Solutions ◽  
Differential System ◽  
Variational Approach ◽  
First Integrals ◽  
Second Order ◽  
Point Of View ◽  
Lagrangian Formulation ◽  
Multiple Positive Solutions ◽  
First Order ◽  
Ordinary Differential System

This paper studies the coupled inhomogeneous Lane-Emden system from the Lagrangian formulation point of view. The existence of multiple positive solutions has been discussed in the literature. Here we aim to classify the system with respect to a first-order Lagrangian according to the Noether point symmetries it admits. We then obtain first integrals of the various cases which admit Noether point symmetries.

scholarly journals Note About a New Evaluation of the Direct Perturbations of the Planets on the Moon’s Motion

1981 ◽  
Vol 63 ◽  
pp. 265-266
Author(s):  
D. Standaert
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Point Of View ◽  
Internal Point ◽  
First Order ◽  
Keplerian Orbits ◽  
First Order Theory ◽  
External Point ◽  
Constants Of Motion ◽  
The Mean

The aim of this paper is to present the principal features of a new evaluation of the direct perturbations of the planets on the Moon’s motion. Using the method already published in Celestial Mechanics (Standaert, 1980), we compute “a first-order theory” aiming at an accuracy of the order of the meter for all periodic terms of period less than 3 500 years.From an external point of view, we mean by that: a)keplerian orbits for the planets,b)the ELP-2000 solution of the Main Problem proposed by Mrs. Chapront (Chapront-Touzë, 1980),c)the first-order derivatives with respect to the constants of motion of the SALE theory of Henrard (Henrard, 1979).On the other hand, from an internal point of view, the computations include: d)the development in Legendre polynomials not only to the first-order in (a/a'), but also the following ones (up to the sixth-order for Venus, for example),e)the contributions of the second-order in the Lie triangle,f)second-order contributions coming from the corrections of the mean motions due to the planetary action.

scholarly journals The Effect of adding First Order Aberrations To Third Order Aberrations on Point Spread Function for Triangular Aperture

2020 ◽  
Vol 12 (01) ◽  
pp. 23-31
Author(s):  
Widad Hamza Tarkhan ◽  
◽  
Ahlam Habeeb Hussien ◽  
Areej Saeed Abdul Shaheed ◽  
◽  
...  
Keyword(s):  
Optical System ◽  
Point Spread Function ◽  
Spherical Aberration ◽  
Strehl Ratio ◽  
Third Order ◽  
First Order ◽  
Point Spread ◽  
Spread Function ◽  
Coma Aberration ◽  
Angle Of Rotation

In this work, Point Spread Function (PSF) for triangular aperture was studied, in case of ideal optical system, also in case of presence first order aberrations )focal error and tilt aberration) and third order aberrations (spherical ,coma, and astigmatism aberrations) individually, and for the same values of aberration factor )W=0.1λ …..0.5 λ ) for angle of rotation (ѱ =0). First order aberrations were added to third order aberrations, to obtain the best balance and to reduce the curve width of the (PSF), and to increase the Strehl ratio, like adding a tilt aberration to the coma aberration and adding focal error to spherical aberration and astigmatism aberration. There are some aberrations effects impact negatively on point spread function, such as focal error with coma aberration and tilt aberration with spherical aberration.

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