On a Local Representation of the Fine Structure in the Earth’s Gravitational Field

1970 ◽  
Vol 37 (3) ◽  
pp. 738-743 ◽  
Author(s):  
S. B. Batdorf
Keyword(s):  
Iteration Process ◽  
Effective Technique ◽  
Limited Region ◽  
Surface Data ◽  
Global Gravity ◽  
Local Gravity ◽  
The Difference ◽  
Orthogonal Set ◽  
Global Gravity Model ◽  
Complete Orthogonal Set

This paper introduces a class of nearly harmonic functions useful in analyzing gravity above a limited region of the earth’s surface. These “B functions” constitute a complete orthogonal set of functions over that portion of the surface of a sphere which lies between two latitudes and two longitudes. By an iteration process, the coefficients of a series of B functions can be determined in such a manner as to provide an optimum fit to the difference between the prediction of a global gravity model and gravity actually measured on the earth’s surface, thus bypassing the problem of reducing the data to a reference surface. Representation of local gravity as the sum of a global model in terms of spherical harmonics and a local model in terms of B functions appears to be an effective technique for handling the problem of altitude extension of surface data.

On the circle polynomials of Zernike and related orthogonal sets

1954 ◽  
Vol 50 (1) ◽  
pp. 40-48 ◽  
Author(s):  
A. B. Bhatia ◽  
E. Wolf
Keyword(s):  
Unit Circle ◽  
Generating Functions ◽  
Legendre Polynomials ◽  
Phase Contrast ◽  
Diffraction Theory ◽  
Zernike Polynomials ◽  
Optical Aberrations ◽  
Orthogonal Set ◽  
Complete Orthogonal Set ◽  
Explicit Expressions

ABSTRACTThe paper is concerned with the construction of polynomials in two variables, which form a complete orthogonal set for the interior of the unit circle and which are ‘invariant in form’ with respect to rotations of axes about the origin of coordinates. It is found that though there exist an infinity of such sets there is only one set which in addition has certain simple properties strictly analogous to that of Legendre polynomials. This set is found to be identical with the set of the circle polynomials of Zernike which play an important part in the theory of phase contrast and in the Nijboer-Zernike diffraction theory of optical aberrations.The results make it possible to derive explicit expressions for the Zernike polynomials in a simple, systematic manner. The method employed may also be used to derive other orthogonal sets. One new set is investigated, and the generating functions for this set and for the Zernike polynomials are also given.

Effects Of Gettering On Device Characteristics

1996 ◽  
Vol 442 ◽  
Author(s):  
Mitsuhiro Horikawa ◽  
Akihiko Yaoita ◽  
Tsuyoshi Nagata ◽  
Tomohisa Kitano
Keyword(s):  
Heat Treatment ◽  
State Of The Art ◽  
Annealing Process ◽  
Clean Room ◽  
Data Retention ◽  
Effective Technique ◽  
Slow Cooling ◽  
Metal Impurities ◽  
The Difference ◽  
Metallic Impurities

AbstractEffective methods of gettering metallic impurities were proposed. To achieve effective gettering, an annealing process to induce gettering was modified taking fundamental gettering steps and the difference in the gettering mechanism into account. As the concentration of heavy metal is below solubility in a state-of-the-art clean room, a combination of segregation type gettering and slow cooling heat treatment is an effective technique to remove metal impurities from the device active region. Using this technique, DRAM device characteristics such as leakage current and data retention time can be improved.

Propagator Method for Numerical Solution of Convective Fisher Equation

2011 ◽  
Vol 222 ◽  
pp. 387-390
Author(s):  
Daiga Zaime ◽  
Janis S. Rimshans ◽  
Sharif E. Guseynov
Keyword(s):  
Difference Scheme ◽  
Iteration Process ◽  
Fisher Equation ◽  
Implicit Difference Scheme ◽  
Nonlinear Convection ◽  
First Order ◽  
Truncation Errors ◽  
Propagator Method ◽  
Left And Right ◽  
The Difference

Propagator numerical method was developed as an effective tool for modeling of linear advective dispersive reactive (ADR) processes [1]. In this work implicit propagator difference scheme for Fisher equation with nonlinear convection (convective Fisher equation) is elaborated. Our difference scheme has truncation errors of the second order in space and of the first order in time. Iteration process for implicit difference scheme is proposed by introducing forcing terms in the left and right sides of the difference equation. Convergence and stability criterions for the elaborated implicit propagator difference scheme are obtained.

scholarly journals The Impact of Noise in a GRACE/GOCE Global Gravity Model on a Local Quasi‐Geoid

2019 ◽  
Vol 124 (3) ◽  
pp. 3219-3237 ◽  
Author(s):  
Cornelis Slobbe ◽  
Roland Klees ◽  
Hassan H. Farahani ◽  
Lennard Huisman ◽  
Bas Alberts ◽  
...  
Keyword(s):  
Gravity Model ◽  
Global Gravity ◽  
The Impact ◽  
Global Gravity Model

Gravity Requirements for Compensation of Ultra-Precise Inertial Navigation

2005 ◽  
Vol 58 (3) ◽  
pp. 479-492 ◽  
Author(s):  
Jay Hyoun Kwon ◽  
Christopher Jekeli
Keyword(s):  
Inertial Sensors ◽  
Interpolation Method ◽  
Gravity Data ◽  
Inertial Navigation ◽  
Navigation Systems ◽  
Gravity Compensation ◽  
Global Gravity ◽  
Navigation Error ◽  
Global Gravity Model

Precision inertial navigation depends not only on the quality of the inertial sensors (accelerometers and gyros), but also on the accuracy of the gravity compensation. With a view toward the next-generation inertial navigation systems, based on sensors whose errors contribute as little as a few metres per hour to the navigation error budget, we have analyzed the required quality of gravity compensation to the navigation solution. The investigation considered a standard compensation method using ground data to predict the gravity vector at altitude for aircraft free-inertial navigation. The navigation effects of the compensation errors were examined using gravity data in two gravimetrically distinct areas and a navigation simulator with parameters such as data noise and resolution, supplemental global gravity model noise, and on-track interpolation method. For a typical flight trajectory at 5 km altitude and 300 km/hr aircraft speed, the error in gravity compensation contributes less than 5 m to the position error after one hour of free-inertial navigation if the ground data are gridded with 2 arcmin resolution and are accurate to better than 5 mGal.

Teaching Inventory Accounting: A Simple Learning Strategy to Achieve Student Understanding

2011 ◽  
Vol 26 (4) ◽  
pp. 835-844 ◽  
Author(s):  
Rochelle K. Greenberg ◽  
Neil A. Wilner
Keyword(s):  
Cash Flow ◽  
Learning Strategy ◽  
Weighted Average ◽  
Financial Accounting ◽  
Effective Technique ◽  
The Subject ◽  
Cost Flow ◽  
The Difference ◽  
The Cost ◽  
First In First Out

ABSTRACT This learning strategy offers an efficient and effective technique for teaching inventory in the introductory financial accounting course. It is motivated by the belief that many students memorize how to calculate the cost of goods sold and ending inventory under different cost flow assumptions, but that few understand the subject. This fundamental lack of understanding prohibits them from fully appreciating other issues, such as the difference between the physical flow and the cost flow assumption, the relevance of the cost flow assumption when computing cost of goods sold and income, and the irrelevance of the cost flow assumption when computing cash flow unless taxes are considered. Our learning strategy involves a convenience store selling three bottles of water. Inventory flow, cash flow, and the calculations of cost of goods sold, income, and ending inventory are illustrated under the first-in, first-out method; the last-in, first-out method; the weighted-average method; and specific identification.

scholarly journals Testing for the Equality of Variance for the Four-parameter Logistic (4PL) Model for the Detection of Vibrio cholerae DNA with Polystyrene-coacrylic Acid Composite Nanospheres

2021 ◽  
Vol 5 (2) ◽  
pp. 5-7
Author(s):  
Mohd Yunus Shukor
Keyword(s):  
Vibrio Cholerae ◽  
Statistical Tests ◽  
Critical Value ◽  
P Value ◽  
Effective Technique ◽  
Bartlett’S Test ◽  
Homogeneity Of Variance ◽  
The Difference ◽  
Residual Variances ◽  
Best Fit

When it comes to finding the best fit of nonlinear curves to acceptable models, linear regression with least squares is the most effective technique. Because residuals (the difference between observed and predicted data) must follow a normal distribution and the data must be free of outliers and uniform variance, statistical tests are used to identify the most appropriate model for a given situation (homoscedasticity). If all of these characteristics are satisfied, the system is said to be robust. In parametric nonlinear regression, one of the numerous assumptions is that the within-group variances of the groups are all the same, which is one of several assumptions (exhibit homoscedasticity). If the variances vary from one another (show heteroscedasticity), then the model is not statistically competent to describe the data as a whole. Data on the detection of Vibrio cholerae DNA with polystyrene-coacrylic acid composite nanospheres as modelled using the nonlinear four-parameter logistic (4PL) regression was preliminary check for homogeneity of variance using the Bartlett’s and Levene’s tests. It was found that the critical value of 2 was 28.869, according to Bartlett's test findings. Excel's CHIDIST function yielded a probability of 0.389 (not significant), suggesting that the variances of the residuals did not change significantly. The p-value for Levenes's test was 0.917, indicating that there were no distinct changes between the residual variances meaning that the use of the 4-PL model in fitting the data was adequate statistically.

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