Local determination of the components of the deflection of the vertical using gravitational potential parameters at a neighboring point

2020 ◽  
Author(s):  
Gerassimos Manoussakis ◽  
Romylos Korakitis
Keyword(s):  
Gravitational Potential ◽  
Simulated Data ◽  
Deflection Of The Vertical ◽  
Neighboring Point ◽  
Geodetic Coordinates ◽  
S Matrix ◽  
Local Determination ◽  
Derivatives Of ◽  
Potential Parameters

<p>We present a method for the estimation of the components ξ and η of the deflection of the vertical using several parameters of the gravitational potential. Specifically, we assume that we know the geodetic coordinates (φ, λ, h), the magnitude of gravity g, the components ξ, η and the second partial derivatives of the gravitational potential (elements of the Eötvös matrix) at a point P. Knowing only the geodetic coordinates of a neighboring point A (at a distance up to several kilometers from P), we estimate the components ξ and η at A. The proposed method is evaluated with simulated data at several points in Greece. The results show that it may be used for the densification of a given astrogeodetic net.</p>

scholarly journals ВЫЧИСЛЕНИЕ ВЫСШИХ ПРОИЗВОДНЫХ ГРАВИТАЦИОННОГО ПОТЕНЦИАЛА НА ОСНОВЕ F-АППРОКСИМАЦИИ

2016 ◽  
Author(s):  
И.А. Керимов
Keyword(s):  
Gravitational Field ◽  
Approximate Method ◽  
Gravitational Potential ◽  
Basic Data ◽  
Gravity Potential ◽  
Irregular Grid ◽  
Field Transformation ◽  
Gravimetric Data ◽  
Derivatives Of

В статье рассмотрен метод трансформации гравитационного поля (определение различных компонент потенциала силы тяжести) на аппроксимационной основе. Разработанный автором метод и компьютерные технологии F-аппроксимации позволяют вычислять горизонтальные и вертикальные  производные гравитационного потенциала для исходных данных, заданных как на регулярной, так и на нерегулярной сети. Метод апробирован на модельных и фактических гравиметрических данных This article considers an approximate method of the gravitational field transformation (the determination of different components of the gravity potential). The method developed by the author and computer technologies of the F-approximation permit the calculation of horizontal and vertical derivatives of the gravitational potential for basic data defined both on a regular and on an irregular grid. The method is tested on model and actual gravimetric data.

Retrieval of the projected potential by inversion from the scattering matrix in electron–crystal scattering

1999 ◽  
Vol 55 (2) ◽  
pp. 105-111 ◽  
Author(s):  
L. J. Allen ◽  
H. Leeb ◽  
A. E. C. Spargo
Keyword(s):  
Simulated Data ◽  
Incident Beam ◽  
Scattering Matrix ◽  
High Energy ◽  
Crystal Potential ◽  
Transmission Electron ◽  
S Matrix ◽  
General Data ◽  
Limiting Case

The retrieval of a unique crystal potential from the scattering matrix {\cal S} in high-energy transmission electron diffraction is discussed. It is shown that, in general, data taken at a single orientation are not sufficient to determine all the elements of {\cal S}. Additional measurements with tilted incident beam are required for the determination of the whole {\cal S} matrix. An algorithm for the extraction of the crystal potential from the {\cal S} matrix measured at a single energy and thickness is presented. The limiting case of thin crystals is discussed. Several examples with simulated data are considered.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

Spectrophotometric study of the complexation equilibria of cadmium ions with 5-bromo and 5-chloro derivatives of 2-(2-pyridylazo)-5-diethylaminophenol (BrPADAP, ClPADAP)

1983 ◽  
Vol 48 (1) ◽  
pp. 52-59 ◽  
Author(s):  
Vlastimil Kubáň ◽  
Miroslav Macka
Keyword(s):  
Equilibrium Constants ◽  
Spectrophotometric Study ◽  
Graphical Analysis ◽  
Optimal Conditions ◽  
Cadmium Ions ◽  
Brij 35 ◽  
Ethanol Medium ◽  
Triton X ◽  
Derivatives Of

The composition, optical characteristics, molar absorption coefficients and equilibrium constants of the reactions of formation of the ML and ML2 complexes of both reagents with cadmium(II) ions were determined by graphical analysis and numerical interpretation of the absorbance-pH curves by the modified SQUAD-G program. Optimal conditions were proposed for the spectrophotometric determination of Cd in 10% v/v ethanol medium in the presence of 0.1% w/v Triton X-100 or 1% w/v Brij 35. BrPADAP and ClPADAP are the most sensitive spectrophotometric reagents for the determination of cadmium(II) ions (ε = 1.28-1.44 . 105 mmol-1 cm2 at 560 nm and pH 8.0-9.5) with a high colour contrast in the reaction (Δλmax ~117 nm) and a selectivity similar to that of other N-heterocyclic azodyes (PAR, PAN, etc.).

Spectrophotometric study of the acid-base and optical properties of the 5-bromo and 5-chloro derivatives of 2-(2-pyridylazo)-5-(diethylamino)phenol (BrPADAP, ClPADAP) and their complexation equilibria with zinc(II) ions

1982 ◽  
Vol 47 (10) ◽  
pp. 2676-2691 ◽  
Author(s):  
Miroslav Macka ◽  
Vlastimil Kubáň
Keyword(s):  
Equilibrium Constants ◽  
Spectrophotometric Study ◽  
Graphical Analysis ◽  
Alkaline Media ◽  
Acid Base ◽  
Ethanol Medium ◽  
Triton X ◽  
Mixed Water ◽  
Derivatives Of

The optical and acid-base characteristics of BrPADAP and ClPADAP were studied in mixed water-ethanol and water-DMF media and in 10% ethanol medium in the presence of cationic, anionic and nonionic tensides. The composition, optical characteristics, molar absorption coefficients and equilibrium constants of the ML and ML2 complexes with zinc(II) ions were found by graphical analysis and numerical interpretation of the absorbance curves by the modified SQUAD-G program. Optimal conditions were found for the spectrophotometric determination of Zn(II) in the presence of 0.1% Triton X-100 or 1% Brij 35 in alkaline media with pH = 6.5-10. BrPADAP and ClPADAP are the most sensitive reagents (ε = 1.3-1.6 . 105 mmol-1 cm2 at 557 and 560 nm, respectively) for the determination of zinc with high colour contrast of the reaction (Δλ = 104 nm) and selectivity similar to that for the other N-heterocyclic azodyes (PAN, PAR, etc.).

scholarly journals Simultaneous determination of ibuprofen and paracetamol using derivatives of the ratio spectra method

2011 ◽  
Vol 4 (3) ◽  
pp. 259-263 ◽  
Author(s):  
Yousry M. Issa ◽  
Sayed I.M. Zayed ◽  
Ibrahim H.I. Habib
Keyword(s):  
Simultaneous Determination ◽  
Derivatives Of
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