scholarly journals EXTREMAL QUASIMODULAR FORMS OF LOWER DEPTH WITH INTEGRAL FOURIER COEFFICIENTS

2021 ◽  
Vol 75 (2) ◽  
pp. 351-364
Author(s):  
Tsudoi KAMINAKA ◽  
Fumiharu KATO
Keyword(s):  
Fourier Coefficients ◽  
Lower Depth

Identifikasi Potensi Air Tanah untuk Kebutuhan Penyediaan Air Bersih dengan Metode Geolistrik: Studi Kasus di Kawasan Geostech, Puspiptek Serpong

2020 ◽  
Vol 21 (2) ◽  
pp. 204-212
Author(s):  
Heru Sri Naryanto ◽  
Puspa Khaerani ◽  
Syakira Trisnafiah ◽  
Achmad Fakhrus Shomim ◽  
Wisyanto Wisyanto ◽  
...  
Keyword(s):  
Geophysical Methods ◽  
Groundwater Potential ◽  
Clean Water ◽  
Rock Types ◽  
Groundwater Aquifers ◽  
Groundwater Aquifer ◽  
Groundwater Origin ◽  
Laboratory Facility ◽  
Potential Groundwater ◽  
Lower Depth

ABSTRACTGeostech Building, as an office and laboratory facility, requires a source of clean water from groundwater related to the limited supply of clean water from the PDAM. Due to the needs of freshwater from groundwater origin, data and information are needed regarding the potential groundwater in the area, including aquifer configuration, depth, and groundwater potential. The presence of groundwater is not distributed through every area, and it's related to the geological and geohydrological conditions. One of the geophysical methods that can describe subsurface is 2D geoelectric methods. This method can distinguish and analyze rock types, geological structures, groundwater aquifers, and other important information based on the characteristics of the electricity of rocks by looking at the value of the type of resistance. In this measurement, the Wenner Alpha configuration has been used, where the arrangement of A-B current electrodes and M-N potential electrodes have constant spacing. From the measurement results, it can be interpreted that there is a low resistivity layer containing porous groundwater as an aquifer. Based on regional geological data, it has been estimated that this layer is in the form of sandy tuff (0-1.5 ohm-m). The exploitation of groundwater with drilling is expected to reach the aquifer's upper layer at depth, starting from 11.5-13 meters. The groundwater aquifer thickness cannot be ascertained because of the penetration of the lower depth of 2D geoelectric measurements truncated by the constraint of a maximum stretch of cable. The upper layer of the aquifer contains a turned layer of fine tufa and medium tuff, which is impermeable, coarse tuff, and mixed soil with varying thickness at the upper layer.Keywords: 2D geoelectric, aquifer, potential groundwater, Geostech  ABSTRAKGedung Geostech sebagai sarana perkantoran dan laboratorium memerlukan sumber air bersih dari air tanah terkait dengan terbatasnya suplai air bersih dari PDAM. Kebutuhan air bersih berasal dari air tanah, maka diperlukan data dan informasi mengenai kondisi potensi air tanah di kawasan tersebut termasuk konfigurasi akuifer, kedalaman, dan potensi air tanahnya. Keberadaan air tanah tidaklah merata untuk setiap tempat dan sangat terkait dengan kondisi geologi dan geohidrologinya. Salah satu metode geofisika yang dapat memberikan gambaran kondisi bawah permukaan adalah dengan metode geolistrik 2D. Metode ini dapat membedakan dan menganalisis jenis batuan, struktur geologi, akuifer air tanah, dan informasi penting lainnya berdasarkan sifat kelistrikan batuan dengan melihat nilai tahanan jenisnya. Dalam pengukuran ini digunakan konfigurasi Wenner Alpha, dimana susunan elektroda arus A dan B dan elektroda potensial M dan N mempunyai spasi yang konstan. Dari hasil pengukuran dapat diinterpretasikan adanya lapisan dengan resistivitas rendah yang mengandung air tanah dan bersifat porous sebagai akuifer. Berdasarkan data geologi regional diperkirakan lapisan ini berupa tuf pasiran (0-1,5 ohm-m). Pengambilan air tanah dengan pemboran diperkirakan akan mengenai batas atas lapisan akuifer pada kedalaman 11,5-13 meter. Ketebalan akuifer air tanah tidak bisa dihitung karena penetrasi kedalaman pengukuran geolistrik 2D terbatasi oleh bentangan elektroda di permukaan. Lapisan di atas akuifer merupakan lapisan selang-seling tuf halus dan tuf sedang yang kedap air, tuf kasar, dan pada bagian paling atas merupakan tanah urugan dengan ketebalan bervariasi.Kata kunci: Geolistrik 2D, akuifer, potensi air tanah, Geostech  

Image Reconstruction with the Fourier Coefficients for Magnetic Induction Tomography

2020 ◽  
Vol 16 (2) ◽  
pp. 156-163
Author(s):  
Jingwen Wang ◽  
Xu Wang ◽  
Dan Yang ◽  
Kaiyang Wang
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Magnetic Induction ◽  
Fourier Coefficients ◽  
Signal Reconstruction ◽  
Reconstruction Algorithm ◽  
Reconstruction Method ◽  
Measurement Equation ◽  
Image Reconstruction Method ◽  
Magnetic Induction Tomography

Background: Image reconstruction of magnetic induction tomography (MIT) is a typical ill-posed inverse problem, which means that the measurements are always far from enough. Thus, MIT image reconstruction results using conventional algorithms such as linear back projection and Landweber often suffer from limitations such as low resolution and blurred edges. Methods: In this paper, based on the recent finite rate of innovation (FRI) framework, a novel image reconstruction method with MIT system is presented. Results: This is achieved through modeling and sampling the MIT signals in FRI framework, resulting in a few new measurements, namely, fourier coefficients. Because each new measurement contains all the pixel position and conductivity information of the dense phase medium, the illposed inverse problem can be improved, by rebuilding the MIT measurement equation with the measurement voltage and the new measurements. Finally, a sparsity-based signal reconstruction algorithm is presented to reconstruct the original MIT image signal, by solving this new measurement equation. Conclusion: Experiments show that the proposed method has better indicators such as image error and correlation coefficient. Therefore, it is a kind of MIT image reconstruction method with high accuracy.

ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS

2010 ◽  
Vol 06 (01) ◽  
pp. 69-87 ◽  
Author(s):  
ALISON MILLER ◽  
AARON PIXTON
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Algebraic Numbers ◽  
Heegner Points ◽  
Positive Weight ◽  
Poincare Series ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Modular Invariants

We extend results of Bringmann and Ono that relate certain generalized traces of Maass–Poincaré series to Fourier coefficients of modular forms of half-integral weight. By specializing to cases in which these traces are usual traces of algebraic numbers, we generalize results of Zagier describing arithmetic traces associated to modular forms. We define correspondences [Formula: see text] and [Formula: see text]. We show that if f is a modular form of non-positive weight 2 - 2 λ and odd level N, holomorphic away from the cusp at infinity, then the traces of values at Heegner points of a certain iterated non-holomorphic derivative of f are equal to Fourier coefficients of the half-integral weight modular forms [Formula: see text].

scholarly journals The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 389
Author(s):  
Jeong-Gyoo Kim
Keyword(s):  
Hilbert Space ◽  
Fourier Series ◽  
Fourier Coefficients ◽  
Double Sequence ◽  
Intermediate Stage ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Abstract Space ◽  
Double Sequences ◽  
Two Parameter

Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences. We understand the space of double Fourier coefficients as an abstract space of sequences and examine relationships to spaces of general double sequences: p-power summable sequences for p = 1, 2, and the Hilbert space of double sequences. Using uniform convergence in the sense of a Cesàro mean, we verify the inclusion relationships between the four spaces of double sequences; they are nested as proper subsets. The completions of two spaces of them are found to be identical and equal to the largest one. We prove that the two-parameter Wiener space is isomorphic to the space of Cesàro means associated with double Fourier coefficients. Furthermore, we establish that the Hilbert space of double sequence is an abstract Wiener space. We think that the relationships of sequence spaces verified at an intermediate stage in this paper will provide a basis for the structures of those spaces and expect to be developed further as in the spaces of single-indexed sequences.

On Estimating Integral Moduli of Continuity of Functions of Several Variables in Terms of Fourier Coefficients

1999 ◽  
Vol 6 (4) ◽  
pp. 307-322
Author(s):  
L. Gogoladze
Keyword(s):  
Fourier Coefficients ◽  
Moduli Of Continuity ◽  
Several Variables

Abstract Inequalities are derived which enable one to estimate integral moduli of continuity of functions of several variables in terms of Fourier coefficients.

scholarly journals On triple correlations of Fourier coefficients of cusp forms

2018 ◽  
Vol 183 ◽  
pp. 485-492 ◽  
Author(s):  
Guangshi Lü ◽  
Ping Xi
Keyword(s):  
Fourier Coefficients ◽  
Cusp Forms

scholarly journals On the growth and zeros of polynomials attached to arithmetic functions

2021 ◽  
Author(s):  
Bernhard Heim ◽  
Markus Neuhauser
Keyword(s):  
Lie Algebras ◽  
Chebyshev Polynomials ◽  
Fourier Coefficients ◽  
Arithmetic Functions ◽  
Zeros Of Polynomials ◽  
Simple Complex ◽  
Hook Length ◽  
Moderate Growth ◽  
Growth Properties ◽  
Sum Of Divisors

AbstractIn this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions g and h, where g is normalized, of moderate growth, and $$0<h(n) \le h(n+1)$$ 0 < h ( n ) ≤ h ( n + 1 ) . We put $$P_0^{g,h}(x)=1$$ P 0 g , h ( x ) = 1 and $$\begin{aligned} P_n^{g,h}(x) := \frac{x}{h(n)} \sum _{k=1}^{n} g(k) \, P_{n-k}^{g,h}(x). \end{aligned}$$ P n g , h ( x ) : = x h ( n ) ∑ k = 1 n g ( k ) P n - k g , h ( x ) . As an application we obtain the best known result on the domain of the non-vanishing of the Fourier coefficients of powers of the Dedekind $$\eta $$ η -function. Here, g is the sum of divisors and h the identity function. Kostant’s result on the representation of simple complex Lie algebras and Han’s results on the Nekrasov–Okounkov hook length formula are extended. The polynomials are related to reciprocals of Eisenstein series, Klein’s j-invariant, and Chebyshev polynomials of the second kind.

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