THE USE OF NONLINEAR FUNCTIONAL EXPANSIONS IN CALCULATION OF THE TERRAIN EFFECT IN AIRBORNE AND MARINE GRAVIMETRY AND GRADIOMETRY

Geophysics ◽  
1974 ◽  
Vol 39 (1) ◽  
pp. 33-38 ◽  
Author(s):  
Leroy M. Dorman ◽  
Brian T. R. Lewis
Keyword(s):  
Exact Result ◽  
Expansion Method ◽  
Gravity Gradient ◽  
Nonlinear Functional ◽  
Expansion Technique ◽  
Nonlinear Functionals ◽  
Terrain Effect ◽  
Convolution Kernels ◽  
Terrain Corrections ◽  
Expansion Coefficients

The terrain corrections for gravity and gravity gradient data are nonlinear functionals of the surrounding topography. We show how to approximate these corrections by use of Volterra‐Wiener functional expansion, which is a sum of linear convolutions using the topography, the square of the topography, etc. The convolution kernels are like Taylor expansion coefficients which depend upon the distance from the source point to the field point. As an example, we compute the field [Formula: see text] for a two‐dimensional ridge by the expansion method and compare the result with the exact result. We then show how the expansion technique can be used to propagate statistical properties through nonlinear functionals. As an example of this, we compute the rms terrain correction for [Formula: see text] as a function of the flight elevation and terrain relief.

Fast Speed Expansion Technique for the Transient Analysis of Automotive Clutches

2004 ◽  
Author(s):  
Jiayin Li
Keyword(s):  
Large Scale ◽  
Expansion Method ◽  
Linear Interpolation ◽  
New Approach ◽  
Fast Speed ◽  
Transient Problem ◽  
Expansion Technique ◽  
Eigen Solutions ◽  
Modal Coordinates ◽  
Thermoelastic Contact Problem

The transient modal analysis method (TMA) has been used to solve the inhomogeneous (loaded) transient thermoelastic contact problem (ITTEC). In the TMA method, the solution of the inhomogeneous transient problem is expressed in modal coordinates, corresponding to eigenfunctions of the homogeneous (unloaded) problem. However, for the large-scale ITTEC problem, this method is found to be extremely time-consuming, because of the computation-intensive of the eigen-solutions. This paper describes a new approach to solve the large-scale ITTEC problem with a dramatic reduction in computational complexity. The method is referred to as fast speed expansion method (FSE). With the FSE method, full eigen-solutions are performed only at a limited number of sparsely located speeds. For speeds between these speeds, eigenvectors are solved by linear interpolation, while the eigenvalues are computed from Taylor series. The method is illustrated with application to an automotive clutches.

TERRAIN CORRECTIONS FOR AN INCLINED PLANE IN GRAVITY COMPUTATIONS

Geophysics ◽  
1958 ◽  
Vol 23 (4) ◽  
pp. 701-711 ◽  
Author(s):  
C. H. Sandberg
Keyword(s):  
Inclined Plane ◽  
Gravity Station ◽  
Terrain Effect ◽  
Terrain Corrections ◽  
Inclined Planes

In many instances an inclined‐plane approximation represents more accurately the terrain near a gravity station than does the conventional block‐cylinder approximation. Combinations of the terrain effect of inclined planes through various terrain zones, as represented in the accompanying tables, can be used to approximate easily and quickly such familiar land forms as valleys, ridges, and hillsides.

scholarly journals Question Expansion Technique On The Different Translations Of The Holy Quran By Using WordNet And Islamic Synonyms

2021 ◽  
Vol 10 (1) ◽  
pp. 391-396
Keyword(s):  
English Language ◽  
Expansion Method ◽  
Arabic Language ◽  
Religious Text ◽  
Expansion Technique ◽  
Holy Quran ◽  
English Translations ◽  
Islamic Religion ◽  
The Holy Quran ◽  
Search Systems

The Holy Quran is the most significant religious text, which is followedby thebelievers of the Islamic religion. The translations of the Quran are the interpretation of its meaning in different languages, to assist those who are not familiar with the Arabic language.Most of the Quranic search systems that support theneeds of who are non-native speakers of the Arabic language of the contents of the Holy Quran are basedon keywords matching. Since there are several known English translations of the Holy Quran and each translation has its terminology based on the style of the translator. In addition to that, there are Islamic terms might be not used in the English language, such as "Hajj" or "Saum,"where these terms might vary from one translation to another. Therefore, these search systems do not support the needs of the user, and often there isno matching between the terms of user's questionandtheterms of the Quran.Consequently, this research has used the synonymsofWordNet to expand the user's question,and to cover all the possibilities of theterms that might be usedin the Quran translation, but there are many of Islamic terms are not available in the WordNet database. The WordNet has been enhanced with a set of Islamic synonyms that have been used in the well-known Islamic translations of the English language, which it was created by the researcher, to increase the likelihood of providing a sure matching between the question's words and the contents of the Quran translation. According to the results of this study, the evaluation of this research proved that the method of question expansion by using the both of the WordNet and the Islamic synonyms showed better accuracy and efficiency than the traditional keywords matching systems, or the system that uses only the WordNet synonyms in the question expansion method in terms of matching all user's questions words with documents and retrieve the correct answers to these questions.

scholarly journals Kriging and Prediction of Nonlinear Functionals

2016 ◽  
Vol 34 (2) ◽  
Author(s):  
Alexander Kukush ◽  
István Fazekas
Keyword(s):  
Random Field ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Nonlinear Functional ◽  
Covariance Matching ◽  
Nonlinear Functionals

The prediction of a nonlinear functional of a random field is studied. The covariance-matching constrained kriging is considered. It is proved that the optimization problem induced by it always has a solution. The proof is constructive and it provides an algorithm to find the optimal solution. Using simulation, this algorithm is compared with the method given in Aldworth and Cressie (2003).

UNIFORM Lp-STABILITY ESTIMATE FOR THE SPATIALLY INHOMOGENEOUS BOLTZMANN EQUATION NEAR VACUUM

2008 ◽  
Vol 05 (04) ◽  
pp. 713-739 ◽  
Author(s):  
SEUNG-YEAL HA ◽  
MITSURU YAMAZAKI ◽  
SEOK-BAE YUN
Keyword(s):  
Stability Analysis ◽  
Boltzmann Equation ◽  
Stability Estimate ◽  
Functional Approach ◽  
Classical Solutions ◽  
Nonlinear Functional ◽  
Spatially Inhomogeneous ◽  
Nonlinear Functionals ◽  
Spatially Inhomogeneous Boltzmann Equation

We present a new uniform Lp-stability theory for the spatially inhomogeneous Boltzmann equation near vacuum via the nonlinear functional approach proposed by the first author. Our stability analysis is based on new nonlinear functionals which are equivalent to the pth power of Lp-distance. The L1-nonlinear functionals play the key role of "modulators" which make the accumulative functional be non-increasing in time t along classical solutions.

scholarly journals SPECTROSCOPY OF Bc MESON IN A SEMI-RELATIVISTIC QUARK MODEL USING THE SHIFTED LARGE-N EXPANSION METHOD

2004 ◽  
Vol 19 (11) ◽  
pp. 1771-1791 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Bound States ◽  
Expansion Method ◽  
The Other ◽  
Minimal Subtraction ◽  
Third Order ◽  
Large N ◽  
Expansion Technique ◽  
Energy Bound ◽  
Bc Meson ◽  
Large N Expansion

We calculate the [Formula: see text] mass spectrum, the splitting values and some other properties in the framework of the semirelativistic equation by applying the shifted large-N expansion technique. We use seven different central potentials together with an improved QCD-motivated interquark potentials calculated to two loops in the modified minimal-subtraction [Formula: see text] scheme. The parameters of these potentials are fitted to generate the semirelativistic bound states of [Formula: see text] quarkonium system in close conformity with the experimental and the present available calculated center-of-gravity (c.o.g.) data. Calculations of the energy bound states are carried out up to third order. Our results are in excellent fit with the results of the other works.

A comparison of approximations for the elastic electron–electron scattering amplitude in jellium

1982 ◽  
Vol 60 (7) ◽  
pp. 1016-1028 ◽  
Author(s):  
A. H. MacDonald ◽  
D. J. W. Geldart
Keyword(s):  
Electron Scattering ◽  
Density Functional ◽  
Scattering Amplitude ◽  
Magnetic Interaction ◽  
Exact Result ◽  
Many Body ◽  
Many Body Theory ◽  
Expansion Technique ◽  
Low Energy Electrons ◽  
Body Theory

An approximation for the electron–electron scattering amplitude, Γ, in jellium, motivated by comparing formal many-body theory and density-functional theory expressions for the jellium response function, is suggested. The approximation is compared with previously suggested approximations for Γ, using an exact result for the forward scattering limit to assess the reliability of each approximation. It is pointed out that the magnetic interaction contribution to Γ becomes dominant at low density in jellium and that this contribution is absent in most commonly adopted approximations. Mean free paths for low energy electrons in jellium-like metals have been calculated for various approximations to Γ and the magnetic-interaction effect is identified as being responsible for a previously noted discrepancy between Thomas–Fermi-like and more sophisticated approximations to Γ. A systematic method, using the parquet expansion technique, has been proposed for antisymmetrizing the density-functional based approximation to Γ when necessary.

Application of an Eigenfunction Expansion Method in Plasticity

1974 ◽  
Vol 41 (2) ◽  
pp. 448-452 ◽  
Author(s):  
T. Wierzbicki
Keyword(s):  
Plastic Material ◽  
Expansion Method ◽  
Plastic Behavior ◽  
Sensitive Material ◽  
Rigid Plastic ◽  
Simple Method ◽  
Elastic Mode ◽  
Perfectly Plastic ◽  
Eigenfunction Expansion Method ◽  
Expansion Technique

Possibilities of extending the eigenvalue expansion method to dynamic problems for plastic continua and structures are examined. A model of a pseudo strain rate sensitive material is introduced as an approximation to the concept of rigid-perfectly plastic material. A simple method is then developed which parallels the familiar elastic mode expansion technique but yet retains the main features of rigid-plastic behavior. The accuracy of the method is discussed and comparison with previous theories is made. An illustrative example is presented.

scholarly journals Gravity terrain correction for mainland territory of Vietnam

2017 ◽  
Vol 17 (4B) ◽  
pp. 145-150
Author(s):  
Pham Nam Hung ◽  
Cao Dinh Trieu ◽  
Le Van Dung ◽  
Phan Thanh Quang ◽  
Nguyen Dac Cuong
Keyword(s):  
Gravity Data ◽  
Computing Time ◽  
Terrain Correction ◽  
Bouguer Gravity ◽  
Mountainous Region ◽  
Terrain Effect ◽  
Rugged Topography ◽  
Terrain Corrections ◽  
Gravity Map

Terrain corrections for gravity data are a critical concern in rugged topography, because the magnitude of the corrections may be largely relative to the anomalies of interest. That is also important to determine the inner and outer radii beyond which the terrain effect can be neglected. Classical methods such as Lucaptrenco, Beriozkin and Prisivanco are indeed too slow with radius correction and are not extended while methods based on the Nagy’s and Kane’s are usually too approximate for the required accuracy. In order to achieve 0.1 mGal accuracy in terrain correction for mainland territory of Vietnam and reduce the computing time, the best inner and outer radii for terrain correction computation are 2 km and 70 km respectively. The results show that in nearly a half of the Vietnam territory, the terrain correction values ≥ 10 mGal, the corrections are smaller in the plain areas (less than 2 mGal) and higher in the mountainous region, in particular the correction reaches approximately 21 mGal in some locations of northern mountainous region. The complete Bouguer gravity map of mainland territory of Vietnam is reproduced based on the full terrain correction introduced in this paper.

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