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1

Notes on continuity result for conformable diffusion equation on the sphere: the linear case

Nguyen Van Tien

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

952--962

EN

In this article, we are interested in the linear conformable diffusion equation on the sphere. Our main goal is to establish some results on the continuity problem with respect to fractional order. The main technique is based on several evaluations on the sphere using spherical basis functions. To overcome the difficulty, we also need to use some calculations to control the generalized integrals.

2

Measures of growth and approximation of entire harmonic functions in n-dimensional space in some Banach spaces

Kumar Devendra

Journal of Mathematics and Applications

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2021

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Vol. 44

57--70

EN

The relationship between the classical order and type of an entire harmonic function in space Rn, n≥3, and the rate of its best harmonic polynomial approximation for some Banach spaces of functions harmonic in the ball of radius R has been studied.

3

Comparing variance of signal contained in the most recent GRACE solutions

Lenczuk Artur, Leszczuk Grzegorz, Klos Anna, Bogusz Janusz

Geodesy and Cartography

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2020

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Vol. 69, no. 1

19--37

EN

Gravity Recovery and Climate Experiment (GRACE) mission data is widely used in various fields of science. GRACE explored changes of the gravity field regularly from April 2002 to June 2017. In the following research, we examine variance of signal contained in two different formats of GRACE data: standard spherical harmonics and mass concentration blocks (so-called “mascons”) solutions, both provided in the most recent releases. For spherical harmonics-based solution, we use monthly gravity field solutions provided up to degree and order (d/o) 96 by three different computing centers, i.e. the NASA’s Jet Propulsion Laboratory (JPL), the German Research Center for Geosciences (GFZ) and the Center for Space Research (CSR). For the mass concentration blocks, we use values of total water storage provided by the CSR, JPL and the Goddard Space Flight Center (GSFC) computing centers, which we convert to spherical harmonic coefficients up to d/o 96. We show that using the anisotropic DDK3 filter to smooth the north-south stripes present in total wate storage obtained from standard spherical harmonics solution leaves more information than common isotropic Gaussian filter. In the case of mascons, GSFC solution contains much more information than the CSR and JPL releases, relevant for corresponding d/o. Differences in variance of signal arise from different background models as well as various shape and size of mascons used during processing of GRACE observations.

4

Local Ionospheric Modeling Using the Localized Global Ionospheric Map and Terrestrial GPS

Sharifi M. A., Farzaneh S.

Acta Geophysica

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2016

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Vol. 64, no. 1

237--252

EN

Global ionosphere maps are generated on a daily basis at CODE using data from about 200 GPS/GLONASS sites of the IGS and other institutions. The vertical total electron content is modeled in a solargeomagnetic reference frame using a spherical harmonics expansion up to degree and order 15. The spherical Slepian basis is a set of bandlimited functions which have the majority of their energy concentrated by optimization inside an arbitrarily defined region, yet remain orthogonal within the spatial region of interest. Hence, they are suitable for decomposing the spherical harmonic models into the portions that have significant strength only in the selected areas. In this study, the converted spherical harmonics to the Slepian bases were updated by the terrestrial GPS observations by use of the least-squares estimation with weighted parameters for local ionospheric modeling. Validations show that the approach adopted in this study is highly capable of yielding reliable results.

5

Features extraction of 3D objects by using Laplace series

Nowak K., Starzyński J.

Przegląd Elektrotechniczny

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2010

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R. 86, nr 1

172-174

EN

This paper deals with methods of features extraction of 3D objects focusing on their usage in a classification and recognition area. A brief review of possible approaches is given. An algorithm based on the spherical harmonics transform is presented with an appropriate theoretical background, implementation and tests results.

PL

Niniejszy artykuł dotyczy metod ekstrakcji cech obiektów trójwymiarowych w celu klasyfikacji i rozpoznawania. Po krótkiej klasyfikacji dostępnych metod skoncentrowano się na dokładnym omówieniu podejścia wykorzystującego szereg Laplace’a (harmoniki sferyczne). Przedstawiono podstawy teoretyczne, implementację i przykład zastosowania tej metody.