scholarly journals A Boundary-Value-Free Reconstruction Method for Magnetic Resonance Electrical Properties Tomography Based on the Neumann-Type Integral Formula over a Circular Region

2017 ◽  
Vol 10 (6) ◽  
pp. 571-578 ◽  
Author(s):  
Motofumi FUSHIMI ◽  
Takaaki NARA
Keyword(s):  
Magnetic Resonance ◽  
Electrical Properties ◽  
Integral Formula ◽  
Boundary Value ◽  
Reconstruction Method ◽  
Circular Region ◽  
Type Integral ◽  
Neumann Type

scholarly journals On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces

2019 ◽  
Vol 27 (6) ◽  
pp. 815-834
Author(s):  
Yulia Shefer ◽  
Alexander Shlapunov
Keyword(s):  
Cauchy Problem ◽  
Sobolev Spaces ◽  
Integral Formula ◽  
Weighted Sobolev Spaces ◽  
Elliptic Systems ◽  
Fundamental Solutions ◽  
Type Integral ◽  
The Cauchy Problem ◽  
Ill Posed ◽  
Neumann Type

AbstractWe consider the ill-posed Cauchy problem in a bounded domain{\mathcal{D}}of{\mathbb{R}^{n}}for an elliptic differential operator{\mathcal{A}(x,\partial)}with data on a relatively open subsetSof the boundary{\partial\mathcal{D}}. We do it in weighted Sobolev spaces{H^{s,\gamma}(\mathcal{D})}containing the elements with prescribed smoothness{s\in\mathbb{N}}and growth near{\partial S}in{\mathcal{D}}, controlled by a real number γ. More precisely, using proper (left) fundamental solutions of{\mathcal{A}(x,\partial)}, we obtain a Green-type integral formula for functions from{H^{s,\gamma}(\mathcal{D})}. Then a Neumann-type series, constructed with the use of iterations of the (bounded) integral operators applied to the data, gives a solution to the Cauchy problem in{H^{s,\gamma}(\mathcal{D})}whenever this solution exists.

scholarly journals Polyanalytic boundary value problems for planar domains with harmonic Green function

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Heinrich Begehr ◽  
Bibinur Shupeyeva
Keyword(s):  
Green Function ◽  
Boundary Value Problems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Planar Domains ◽  
Schwarz Problem ◽  
Bianalytic Functions ◽  
Neumann Type ◽  
The Neumann Problem ◽  
Well Posed

AbstractThere are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257–1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

scholarly journals BAKER–AKHIEZER FUNCTION AS ITERATED RESIDUE AND SELBERG-TYPE INTEGRAL

2009 ◽  
Vol 51 (A) ◽  
pp. 59-73 ◽  
Author(s):  
GIOVANNI FELDER ◽  
ALEXANDER P. VESELOV
Keyword(s):  
Root System ◽  
Integral Formula ◽  
Explicit Evaluation ◽  
Type Integral

AbstractA simple integral formula as an iterated residue is presented for the Baker–Akhiezer function related toAn-type root system in both the rational and trigonometric cases. We present also a formula for the Baker–Akhiezer function as a Selberg-type integral and generalise it to the deformedAn,1-case. These formulas can be interpreted as new cases of explicit evaluation of Selberg-type integrals.

scholarly journals TWO-DIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS

2016 ◽  
Vol 56 (3) ◽  
pp. 245
Author(s):  
Marzena Szajewska ◽  
Agnieszka Tereszkiewicz
Keyword(s):  
Boundary Value Problems ◽  
Special Functions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Dirichlet Condition ◽  
Two Dimensional ◽  
Neumann Type ◽  
Neumann Boundary Value Problems ◽  
Real Euclidean Space

Boundary value problems are considered on a simplex <em>F</em> in the real Euclidean space R<sup>2</sup>. The recent discovery of new families of special functions, orthogonal on <em>F</em>, makes it possible to consider not only the Dirichlet or Neumann boundary value problems on <em>F</em>, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of <em>F</em> a Dirichlet condition is fulfilled and on the other Neumann’s works.

An m-point boundary value problem of Neumann type for a p-Laplacian like operator

2004 ◽  
Vol 56 (7) ◽  
pp. 1071-1089 ◽  
Author(s):  
M. Garcı́a-Huidobro ◽  
C.P. Gupta ◽  
R. Manásevich
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Point Boundary ◽  
Neumann Type

Diffusion tensor magnetic resonance imaging

2018 ◽  
pp. 624-628
Author(s):  
David Sosnovik
Keyword(s):  
Magnetic Resonance Imaging ◽  
Heart Failure ◽  
Magnetic Resonance ◽  
Electrical Properties ◽  
Diffusion Tensor ◽  
Resonance Imaging ◽  
Mechanical And Electrical Properties ◽  
Clinical Scenarios ◽  
Translational Studies ◽  
Whole Heart

The microstructure of the heart has a major impact on its mechanical and electrical properties. Diffusion tensor magnetic resonance imaging (DTI) exploits the anisotropic restriction of water diffusion in the myocardium to resolve its microstructure. Recent advances in the field have included the development of acceleration-compensated diffusion-encoded sequences, the investigation of sheet dynamics, and the development of highly accelerated techniques to enable whole heart coverage. Translational studies have demonstrated the utility of DTI in heart failure and other cardiomyopathies. While DTI of the heart remains investigational, ongoing advances in the field will soon allow the technique to be performed reliably and quickly in appropriate clinical scenarios.

The treatment of a Neumann boundary value problem for force-free fields by an integral equation method

1978 ◽  
Vol 82 (1-2) ◽  
pp. 71-86 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Vector Fields ◽  
Integral Formula ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Integral Equation Method ◽  
Equation Method ◽  
Fredholm Alternative ◽  
Neumann Boundary Value Problem

SynopsisA Neumann boundary value problem for the equation rot μ − λμ = u is considered. The approach is by an integral equation method based on Cauchy's integral formula for generalized harmonic vector fields. Results on existence and uniqueness are obtained in terms of the familiar Fredholm alternative.

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