DETERMINING PARAMETERS OF CONFORMAL MAPPINGS FROM THE UPPER HALF-PLANE ONTO STRAIGHT-LINE PERIODIC POLYGONS WITH DOUBLE SYMMETRY AND ONTO CIRCULAR PERIODIC POLYGONS

2019 ◽  
pp. 42-60
Author(s):  
Kolesnikov I. A. ◽  
Keyword(s):  
Half Plane ◽  
Conformal Mappings ◽  
Straight Line ◽  
Upper Half Plane ◽  
Double Symmetry

scholarly journals OVERVIEW OF VNC PUBLICATIONS 

2018 ◽  
Author(s):  
Г.П. Селиверстова
Keyword(s):  
Fourier Transform ◽  
Dirichlet Problem ◽  
Half Plane ◽  
Boundary Function ◽  
Optimal Recovery ◽  
Recovery Method ◽  
Finite Segment ◽  
Plane Parallel ◽  
Straight Line ◽  
Upper Half Plane

Работа посвящена задаче наилучшего восстановления реше- ния задачи Дирихле в пространстве квадратично суммируемых функций на прямой в верхней полуплоскости, параллельной оси абсцисс, по следующей информации о граничной функции: гра- ничная функция принадлежит некоторому соболевскому про- странству функций, а ее преобразование Фурье известно при- ближенное на конечном отрезке, симметричном относительно нуля. Построен оптимальный метод восстановления и найдено точное значение погрешности оптимального восстановления. The work is devoted to the problem of the best recovery solution- the Dirichlet problem in the space of quadratically summable functions on a straight line in the upper half plane parallel to the axis abscissa, on the following information on the boundary function: gra- personal function belongs to some Sobolev Pro- the wandering of functions, and its Fourier transform is known in- near on a finite segment, symmetric with respect to zero's. The optimal recovery method was constructed and found the exact error value of the optimal recovery.

scholarly journals On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve

2014 ◽  
Vol 57 (2) ◽  
pp. 381-389
Author(s):  
Adrian Łydka
Keyword(s):  
Functional Equation ◽  
Meromorphic Function ◽  
Elliptic Curve ◽  
Explicit Formula ◽  
Half Plane ◽  
Complex Plane ◽  
Möbius Function ◽  
Mobius Function ◽  
Upper Half Plane ◽  
Explicit Formulae

AbstractWe study analytic properties function m(z, E), which is defined on the upper half-plane as an integral from the shifted L-function of an elliptic curve. We show that m(z, E) analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for m(z, E) in the strip |ℑz| < 2π.

Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

1983 ◽  
Vol 20 (1) ◽  
pp. 47-54 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib
Keyword(s):  
Plane Strain ◽  
Half Plane ◽  
Inclination Angle ◽  
Complex Variable ◽  
Earth Pressure ◽  
Exact Distributions ◽  
Exact Determination ◽  
Upper Half Plane ◽  
Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

scholarly journals Revisiting the Siegel upper half plane II

2004 ◽  
Vol 376 ◽  
pp. 45-67 ◽  
Author(s):  
Pedro J. Freitas ◽  
Shmuel Friedland
Keyword(s):  
Half Plane ◽  
Upper Half Plane

An AF Algebra Associated with the Farey Tessellation

2008 ◽  
Vol 60 (5) ◽  
pp. 975-1000 ◽  
Author(s):  
Florin P. Boca
Keyword(s):  
Half Plane ◽  
Path Algebra ◽  
Cutting Sequences ◽  
Upper Half Plane ◽  
Af Algebras ◽  
Algebra Model

AbstractWe associate with the Farey tessellation of the upper half-plane an AF algebra encoding the “cutting sequences” that define vertical geodesics. The Effros–Shen AF algebras arise as quotients of . Using the path algebra model for AF algebras we construct, for each τ ∈ ( 0, ¼], projections (En) in such that EnEn±1En ≤ τ En.

Sign in / Sign up

Export Citation Format

Share Document