A Note on the D-trigonometry and the Relevant D-Fourier Expansions

2020 ◽  
Author(s):  
Paolo Emilio Ricci
Keyword(s):  
Fourier Expansions

scholarly journals About Liquid Filtration Under a Point Dam with a Vertical Weakly Permeable Film

2021 ◽  
Vol 16 (3) ◽  
pp. 69-74
Author(s):  
Efimova Irina A. ◽  
Keyword(s):  
Porous Medium ◽  
Half Plane ◽  
Horizontal Line ◽  
Filtration Process ◽  
Liquid Filtration ◽  
Fourier Expansions ◽  
Water Courses ◽  
Filtration Area ◽  
Homogeneous Porous Medium ◽  
Convolution Method

The problem of groundwater filtration under a point dam in a piecewise homogeneous porous medium in the presence of a weakly permeable film under the dam is considered. The filtration area is considered in the form of a vertical half-plane with a horizontal line of water courses. A weakly permeable film divides the filtration area into two quadrants with different constant permeability. By the convolution method of Fourier expansions, the solution of the problem is obtained explicitly. The influence of a weakly permeable film on the filtration process is investigated. It is shown that the presence of a weakly permeable film reduces the filtration rates in the downstream.

New solutions for periodic interfacial gravity waves

2021 ◽  
Vol 928 ◽  
Author(s):  
X. Guan ◽  
J.-M. Vanden-Broeck ◽  
Z. Wang
Keyword(s):  
Integral Equation ◽  
Excellent Agreement ◽  
Gravity Waves ◽  
Global Bifurcation ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Fourier Expansions ◽  
Wave Profiles

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673–708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

scholarly journals Fourier-Based Automatic Transformation between Mapping Shapes—Cadastral and Land Registry Applications

2020 ◽  
Vol 9 (8) ◽  
pp. 482
Author(s):  
Juan Francisco Reinoso-Gordo ◽  
Rocío Romero-Zaliz ◽  
Carlos León-Robles ◽  
Jesús Mataix-SanJuan ◽  
Marcelo Antonio Nero
Keyword(s):  
Computer Vision ◽  
Information System ◽  
Geographic Information System ◽  
Least Squares ◽  
Reference Object ◽  
Fourier Descriptors ◽  
Periodic Functions ◽  
Fourier Expansions ◽  
Elliptic Fourier Descriptors ◽  
Least Squares Approach

Sometimes it is necessary to know the transformation to apply to a mapping shape in order to locate its true place. Such an operation can be computed if a corresponding reference object exists and we can identify corresponding points in both shapes. Nevertheless our approach does not need to match any corresponding point beforehand. The method proposed defines a polygon in the frequency domain—two periodic functions are derived from a polygonal or polygon. According to the theory of elliptic Fourier descriptors those two periodic functions can be expressed by Fourier expansions. The transformation can be computed using the coefficients of the harmonics from the corresponding shapes without taking into account where each polygon vertex is placed in the spatial domain. The transformation parameters will be derived by a least squares approach. The geomatics and geosciences applications of this method go from photogrammetry, geographic information system, computer vision, to cadaster and real estates.

scholarly journals On the Fourier expansions of Jacobi forms of half-integral weight

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
B. Ramakrishnan ◽  
Brundaban Sahu
Keyword(s):  
Modular Forms ◽  
Jacobi Form ◽  
Jacobi Forms ◽  
Number Of Components ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Fourier Expansions ◽  
The Given ◽  
The Relationship ◽  
Vector Valued

Using the relationship between Jacobi forms of half-integral weight and vector valued modular forms, we obtain the number of components which determine the given Jacobi form of indexp,p2orpq, wherepandqare odd primes.

Fourier Expansions: A Collection of Formulas

1974 ◽  
Vol 25 (5) ◽  
pp. 193-193
Author(s):  
H H Hopkins
Keyword(s):  
Fourier Expansions
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