Reconstruction of holomorphic and pluriharmonic functions in circular domains from their values on a torus

1989 ◽  
Vol 30 (1) ◽  
pp. 136-139 ◽  
Author(s):  
M. L. Agranovskii ◽  
L. A. Aizenberg
Keyword(s):  
Pluriharmonic Functions ◽  
Circular Domains

Integral Representations and Continuous Projectors in Some Spaces of Analytic and Pluriharmonic Functions

2008 ◽  
Vol 15 (4) ◽  
pp. 739-752
Author(s):  
Gigla Oniani ◽  
Lamara Tsibadze
Keyword(s):  
Integral Representations ◽  
Fractional Integrals ◽  
Boundary Values ◽  
Pluriharmonic Functions

Abstract We consider analytic and pluriharmonic functions belonging to the classes 𝐵𝑝(Ω) and 𝑏𝑝(Ω) and defined in the ball . The theorems established in the paper make it possible to obtain some integral representations of functions of the above-mentioned classes. The existence of bounded projectors from the space 𝐿(ρ, Ω) into the space 𝐵𝑝(Ω) and from the space 𝐿(ρ, Ω) into the space 𝑏𝑝(Ω) is proved. Also, consideration is given to the existence of boundary values of fractional integrals of functions of the spaces 𝐵𝑝(Ω) and 𝑏𝑝(Ω).

scholarly journals Magnetic Configurations in Modulated Cylindrical Nanowires

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 600
Author(s):  
Cristina Bran ◽  
Jose Angel Fernandez-Roldan ◽  
Rafael P. del Real ◽  
Agustina Asenjo ◽  
Oksana Chubykalo-Fesenko ◽  
...  
Keyword(s):  
Domain Walls ◽  
Magnetocrystalline Anisotropy ◽  
Logic Gates ◽  
Local Domain ◽  
Magnetic Nanowires ◽  
Precise Control ◽  
Magnetic Layers ◽  
State Present ◽  
Circular Domains ◽  
3D Applications

Cylindrical magnetic nanowires show great potential for 3D applications such as magnetic recording, shift registers, and logic gates, as well as in sensing architectures or biomedicine. Their cylindrical geometry leads to interesting properties of the local domain structure, leading to multifunctional responses to magnetic fields and electric currents, mechanical stresses, or thermal gradients. This review article is summarizing the work carried out in our group on the fabrication and magnetic characterization of cylindrical magnetic nanowires with modulated geometry and anisotropy. The nanowires are prepared by electrochemical methods allowing the fabrication of magnetic nanowires with precise control over geometry, morphology, and composition. Different routes to control the magnetization configuration and its dynamics through the geometry and magnetocrystalline anisotropy are presented. The diameter modulations change the typical single domain state present in cubic nanowires, providing the possibility to confine or pin circular domains or domain walls in each segment. The control and stabilization of domains and domain walls in cylindrical wires have been achieved in multisegmented structures by alternating magnetic segments of different magnetic properties (producing alternative anisotropy) or with non-magnetic layers. The results point out the relevance of the geometry and magnetocrystalline anisotropy to promote the occurrence of stable magnetochiral structures and provide further information for the design of cylindrical nanowires for multiple applications.

Exact Perturbation for the Vibration of Almost Annular or Circular Plates

1995 ◽  
Author(s):  
R. G. Parker ◽  
C. D. Mote
Keyword(s):  
Circular Domain ◽  
Circular Plates ◽  
Irregular Domain ◽  
Third Order ◽  
Element Analysis ◽  
Shape Deviation ◽  
Arbitrary Boundary ◽  
Boundary Shape ◽  
Circular Domains ◽  
And Control

Abstract Using perturbation analysis, the eigensolutions for plate vibration problems on nearly annular or circular domains are determined. The irregular domain eigensolutions are calculated as perturbations of the corresponding annular or circular domain eigensolutions. These perturbations are determined exactly. The simplicity of these exact solutions allows the perturbation to be carried through third order for distinct unperturbed eigenvalues and through second order for degenerate unperturbed eigenvalues. Furthermore, this simplicity allows the resulting orthonormalized eigenfunctions to be readily incorporated into response, system identification, and control analyses. The clamped, nearly circular plate is studied in detail, and the exact eigensolution perturbations are derived for an arbitrary boundary shape deviation. Rules governing the splitting of degenerate unperturbed eigenvalues at both first and second orders of perturbation are presented. These rules, which apply for arbitrary shape deviation, generalize those obtained in previous works where specific, discrete asymmetries and first order splitting are examined. The eigensolution perturbations and splitting rules reduce to simple, algebraic formulae in the Fourier coefficients of the boundary shape asymmetry. Elliptical plate eigensolutions are calculated and compared to finite element analysis and, for the fundamental eigenvalue, to the exact solution given by Shibaoka (1956).

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