Development of mathematical model Gauss – Kruger coordinate system for calculating planimetric rectangular coordinates using geodesic coordinates

Algorithms with improved convergence for the calculation of rectangular coordinates in the Gauss – Kruger coordinate system according to the parameters of any ellipsoid were designed. The approach of definition the spherical components in the classic series defined variables x, y, represented by the difference between the degrees of longitude l, followed by the replacement of their sums by formulas of spherical trigonometry. For definition of the amounts of spherical components of the relevant decompositions patterns of transverse-cylindrical sphere plane projection in the condition of the initial data equality on the ellipsoid and sphere radius N were used. Analysis of othertransformation methods of classical expansions in series, used in derivation of both logarithmical and non-logarithmical working formulas is carried outfor comparison with developed algorithms. The technique of algorithms development with usage of hyperbolic tangent function, applied by L. Kruger, Yu. Karelin, A. Schödlbauer is considered and their analysis is carried out. Advantages of Krasovskii – Isotov formulas for six-degree strips are pointed out. The usage of the spherical function sin τ in the expansion made it possible not only to obtain a rapidly convergent series, but also to represent the spherical part of the solution of the problem with the help of trigonometric identities in different types. It is proved that derived for the calculation algorithms with the proposed estimates of their accuracy, are optimal in removing points from the central meridian to l ≤ 6°. For the difference of longitudes l > 6°, the expansions of the unknown quantities into Fourier series should be applied. An example of the calculation of coordinates in the system SK-2011 is given. Theoretical studies have been carried out and shortened formulas with a reliability estimate for the determination of coordinates in the area l ≤ 3° have been proposed.

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Mathematical models of Gauss – Kruger projection for calculation of meridians conversion on the plane and scale of the image

Geodesy and Cartography ◽

10.22389/0016-7126-2018-934-4-2-7 ◽

2018 ◽

Vol 934 (4) ◽

pp. 2-7

Author(s):

P.A. Medvedev ◽

M.V. Novgorodskaya

Keyword(s):

Mathematical Models ◽

Analytical Methods ◽

Theoretical Studies ◽

Spherical Trigonometry ◽

Cylindrical Projection ◽

Rectangular Coordinates ◽

In Series ◽

Observational Errors ◽

The Difference

This work contains continued research carried out on improving mathematical models of the Gauss-Krueger projection in accordance with the parameters of any ellipsoid with the removal of points from the axial meridian to l ≤ 6° . In terms of formulae earlier derived by the authors with improved convergence for the calculation of planar rectangular coordinates by geodesic coordinates, the algorithms for determining the convergence of meridians on the plane and the scale of the image are obtained. The improvement of the formulae represented in the form of series in powers of the difference in longitudes was accomplished by separating spherical terms in series and then replacing their approximate sums by exact expressions using the formulae of spherical trigonometry. As in previous works published in this journal [7, 8], determining the sums of the spherical terms was carried out according to the laws of the transverse-cylindrical projection of the sphere on the plane. Theoretical studies are given and formulae are proposed for estimating the observational errors in the results of the derived algorithms. The maximum of observational errors of convergence of meridians and scale, proceeding from the specified accuracy of the determined quantities was established through analytical methods.

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Determining the parameters of a local coordinate system with a non-standard longitude of the central meridian. Ways to improve the accuracy of determining parameters

Geodesy and Cartography ◽

10.22389/0016-7126-2021-972-6-2-9 ◽

2021 ◽

Vol 972 (6) ◽

pp. 2-9

Author(s):

A.V. Vinogradov

Keyword(s):

Coordinate System ◽

Local Coordinate System ◽

The State ◽

State System ◽

Central Meridian ◽

Mathematical Apparatus ◽

Coordinate Systems ◽

Starting Point ◽

The Difference ◽

Residual Errors

Improving the accuracy of calculating the longitude of the axial meridian, the coordinates of the starting point and the height of the local coordinate system is achieved through introducing an intermediate coordinate system. The longitude of the axial meridian of the intermediate coordinate system is chosen equal to the approximate value of the longitude of the axial meridian of the local coordinate system. The difference in longitudes of the axial meridians of the state coordinate system and the intermediate coordinate system is known. The final value of the axial meridian`s longitude of the local coordinate system relative to the longitude of the axial meridian of the state coordinate system is calculated as the sum of two longitude differences. The first is the difference between the axial meridians of the local and the intermediate coordinate systems; the second is the difference in longitudes between the axial meridians of the intermediate and the state system. The residual errors of the mathematical apparatus for calculating the longitude of the axial meridian are less than 0.005 arc seconds. The proposed technology has been tested at real works.

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Harmonization of different type of coordinate systems used for North Macedonian official spatial data

Proceedings of the ICA ◽

10.5194/ica-proc-2-46-2019 ◽

2019 ◽

Vol 2 ◽

pp. 1-6

Author(s):

Bashkim Idrizi

Keyword(s):

Coordinate System ◽

Spatial Data ◽

Data Sets ◽

Central Meridian ◽

Vector Data ◽

Coordinate Systems ◽

Data Harmonization ◽

Legal Documents ◽

Spatial Data Sets ◽

Definition Of

Abstract. From the beginning of developing vector data sets in Macedonia, till now, three type of coordinate values for North Macedonian spatial data have been used.Law for real estate cadaster and Regulation for basic geodetic works are the official legal bases for definition of official state coordinate system. In both legal documents, state coordinate system is defined by Ellipsoid of Bessel 1841, Datum of Hermannskogel, and Gauss-Kruger projection with central meridian 21&deg;&thinsp;E, scale factor 0.9999, false easting 500000&thinsp;m, false northing 0&thinsp;m and 7th projecting zone per 3&deg;. Based on mentioned parameters, the coordinate systems EPSG 6204 and EPSG 6316 are defined and internationally recognized. The core deferens between them is false easting value. As a result of both coordinate systems parameters, the values of easting coordinates are far from each other for 7000&thinsp;km!Beside EPSG 6204 and 6316, official spatial data sets defined in CAD software were digitized by excluding first digits of easting and northing coordinates, by excluding digits 7 for easting and 4 for northing coordinates of spatial data.Using three types of coordinate values, requires process of data harmonization before their usage in same project, in order to reach the spatial data overlapping. Third type of coordinate system, due to the lack of coordinate system parameters, can not be automatically overlapped with data defined in EPSG6204 and EPSG6316, which requires defining of intermediate coordinate system for third type of data in order to establish the mathematical base for data harmonization/overlapping by transformation of coordinates between three systems.

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2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

International Astronomical Union Colloquium ◽

10.1017/s0252921100050867 ◽

1975 ◽

Vol 26 ◽

pp. 21-26

Keyword(s):

Coordinate System ◽

Working Group ◽

General Character ◽

Coordinate Systems ◽

Reference Coordinate System ◽

Group 2 ◽

Definition Of ◽

Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

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The Shikani HME: A New Tracheostomy Heat and Moisture Exchanger

Journal of Speech Language and Hearing Research ◽

10.1044/2020_jslhr-19-00107 ◽

2020 ◽

Vol 63 (9) ◽

pp. 2921-2929

Author(s):

Alan H. Shikani ◽

Elamin M. Elamin ◽

Andrew C. Miller

Keyword(s):

Ex Vivo ◽

Moisture Loss ◽

Speaking Valve ◽

Time Zero ◽

In Series ◽

Turbulent Airflow ◽

The Difference ◽

Loss Efficiency ◽

Heat And Moisture ◽

Lung Simulation

Purpose Tracheostomy patients face many adversities including loss of phonation and essential airway functions including air filtering, warming, and humidification. Heat and moisture exchangers (HMEs) facilitate humidification and filtering of inspired air. The Shikani HME (S-HME) is a novel turbulent airflow HME that may be used in-line with the Shikani Speaking Valve (SSV), allowing for uniquely preserved phonation during humidification. The aims of this study were to (a) compare the airflow resistance ( R airflow ) and humidification efficiency of the S-HME and the Mallinckrodt Tracheolife II tracheostomy HME (M-HME) when dry (time zero) and wet (after 24 hr) and (b) determine if in-line application of the S-HME with a tracheostomy speaking valve significantly increases R airflow over a tracheostomy speaking valve alone (whether SSV or Passy Muir Valve [PMV]). Method A prospective observational ex vivo study was conducted using a pneumotachometer lung simulation unit to measure airflow ( Q ) amplitude and R airflow , as indicated by a pressure drop ( P Drop ) across the device (S-HME, M-HME, SSV + S-HME, and PMV). Additionally, P Drop was studied for the S-HME and M-HME when dry at time zero (T 0 ) and after 24 hr of moisture testing (T 24 ) at Q of 0.5, 1, and 1.5 L/s. Results R airflow was significantly less for the S-HME than M-HME (T 0 and T 24 ). R airflow of the SSV + S-HME in series did not significant increase R airflow over the SSV or PMV alone. Moisture loss efficiency trended toward greater efficiency for the S-HME; however, the difference was not statistically significant. Conclusions The turbulent flow S-HME provides heat and moisture exchange with similar or greater efficacy than the widely used laminar airflow M-HME, but with significantly lower resistance. The S-HME also allows the innovative advantage of in-line use with the SSV, hence allowing concurrent humidification and phonation during application, without having to manipulate either device.

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The Distinction between [P] and [S]

10.23943/princeton/9780691161006.003.0018 ◽

2017 ◽

Author(s):

Galen Strawson

Keyword(s):

Personal Identity ◽

Radical Change ◽

Legal Responsibility ◽

The Difference ◽

Definition Of ◽

Over Time

This chapter examines the difference between John Locke's definition of a person [P], considered as a kind of thing, and his definition of a subject of experience of a certain sophisticated sort [S]. It first discusses the equation [P] = [S], where [S] is assumed to be a continuing thing that is able to survive radical change of substantial realization, as well as Locke's position about consciousness in relation to [P]'s identity or existence over time as [S]. It argues that Locke is not guilty of circularity because he is not proposing consciousness as the determinant of [S]'s identity over time, but only of [S]'s moral and legal responsibility over time. Finally, it suggests that the terms “Person” and “Personal identity” pull apart, in Locke's scheme of things, but in a perfectly coherent way.

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L'anglicisme dans la langue française

Digital Press Social Sciences and Humanities ◽

10.29037/digitalpress.43286 ◽

2019 ◽

Vol 3 ◽

pp. 00013

Author(s):

Danny Susanto

Keyword(s):

English Language ◽

Oil Industry ◽

English Word ◽

Public Institutions ◽

Font Size ◽

The World ◽

French Speaking ◽

The Difference ◽

Definition Of ◽

Bibliographic Study

The purpose of this study is to analyze the phenomenon known as “anglicism”: a loan made to the English language by another language. Anglicism arose either from the adoption of an English word as a result of a translation defect despite the existence of an equivalent term in the language of the speaker, or from a wrong translation, as a word-by-word translation. Said phenomenon is very common nowadays and most languages of the world including making use of some linguistic concepts such as anglicism, neologism, syntax, morphology etc, this article addresses various aspects related to Anglicisms in French through a bibliographic study: the definition of Anglicism, the origin of Anglicisms in French and the current situation, the areas most affected by Anglicism, the different categories of Anglicism, the difference between French Anglicism in France and French-speaking Canada, the attitude of French-speaking society towards to the Anglicisms and their efforts to stop this phenomenon. The study shows that the areas affected are, among others, trade, travel, parliamentary and judicial institutions, sports, rail, industrial production and most recently film, industrial production, sport, oil industry, information technology, science and technology. Various initiatives have been implemented either by public institutions or by individuals who share concerns about the increasingly felt threat of the omnipresence of Anglicism in everyday life.

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

Geodesy and Cartography ◽

10.22389/0016-7126-2017-919-1-7-12 ◽

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.

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The characteristics of transforming coordinates from the geocentric system WGS-84 for the Mercator projection under low latitudes conditions

Geodesy and Cartography ◽

10.22389/0016-7126-2018-940-10-2-6 ◽

2018 ◽

Vol 940 (10) ◽

pp. 2-6

Author(s):

J.A. Younes ◽

M.G. Mustafin

Keyword(s):

Coordinate System ◽

Satellite System ◽

Programming Algorithm ◽

Low Latitude ◽

Model Calculations ◽

Mercator Projection ◽

Low Latitudes ◽

Rectangular Coordinates ◽

Global Navigation Satellite ◽

Coordination Methods

The issue of calculating the plane rectangular coordinates using the data obtained by the satellite observations during the creation of the geodetic networks is discussed in the article. The peculiarity of these works is in conversion of the coordinates into the Mercator projection, while the plane coordinate system on the base of Gauss-Kruger projection is used in Russia. When using the technology of global navigation satellite system, this task is relevant for any point (area) of the Earth due to a fundamentally different approach in determining the coordinates. The fact is that satellite determinations are much more precise than the ground coordination methods (triangulation and others). In addition, the conversion to the zonal coordinate system is associated with errors; the value at present can prove to be completely critical. The expediency of using the Mercator projection in the topographic and geodetic works production at low latitudes is shown numerically on the basis of model calculations. To convert the coordinates from the geocentric system with the Mercator projection, a programming algorithm which is widely used in Russia was chosen. For its application under low-latitude conditions, the modification of known formulas to be used in Saudi Arabia is implemented.

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Establishment of local coordinate systems in the transition to the geodetic system of coordinates of GSK-2011

Geodesy and Cartography ◽

10.22389/0016-7126-2017-929-11-2-10 ◽

2017 ◽

Vol 929 (11) ◽

pp. 2-10

Author(s):

A.V. Vinogradov

Keyword(s):

Coordinate System ◽

Small Businesses ◽

Transition Period ◽

Local Coordinate System ◽

Initial Point ◽

Central Meridian ◽

Administrative District ◽

Local Networks ◽

Small Areas ◽

Geodetic System

Pretty before long there will be transition to the geodetic system of coordinates of GSK-2011. For the transition period it is necessary to develop a method of recalculating coordinates from one system to another. The existing methods of recalculating coordinates are designed for recalculating coordinate points of state geodetic networks (GGS) and geodetic local networks (GSS). For small areas (administrative districts, populated areas) simplified methods are more acceptable. You need to choose the resampling methods that can be applied in small businesses, performing surveying works. The article presents the the results of calculations of changes of coordinates of the same point in GSK-2011 and SC-95 in six-degree zones of Gauss projection. It was found that in each region values of the shifts changed to small ones. Therefore, it is possible to convert the coordinates of the points by the simplified formulae. For recalculation from the coordinates of GSK-2011 in SK-95 or local coordinate system (WCS) of the administrative district it is necessary to find the origin of coordinates, scale value and rotation of the coordinate axes. The error of the conversion shall not exceed 0,001 m. The coordinates of the initial point of the local coordinate system relative to the central meridian of the local coordinate system shall be added in the list of parameters of the transition from local coordinate system to the state one.

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