Boundary Properties of First-Order Partial Derivatives of the Poisson Integral for the Half-Space

1997 ◽  
Vol 4 (6) ◽  
pp. 585-600
Author(s):  
S. Topuria
Keyword(s):  
Half Space ◽  
Poisson Integral ◽  
Partial Derivatives ◽  
First Order ◽  
Boundary Properties ◽  
Derivatives Of

Abstract Boundary properties of first-order partial derivatives of the Poisson integral are studied in the half-space .

Boundary Properties of Second-Order Partial Derivatives of the Poisson Integral for a Half-Space

1998 ◽  
Vol 5 (4) ◽  
pp. 385-400
Author(s):  
S. Topuria
Keyword(s):  
Half Space ◽  
Second Order ◽  
Poisson Integral ◽  
Partial Derivatives ◽  
Boundary Properties ◽  
Derivatives Of

Abstract The boundary properties of second-order partial derivatives of the Poisson integral are studied for a half-space .

scholarly journals A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function

2002 ◽  
Vol 65 (2) ◽  
pp. 253-258 ◽  
Author(s):  
Hitoshi Tanaka
Keyword(s):  
Sobolev Space ◽  
Maximal Function ◽  
60Th Birthday ◽  
One Dimensional ◽  
Partial Derivatives ◽  
First Order ◽  
Littlewood Maximal Function ◽  
The One ◽  
Derivatives Of

Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthdayJ. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W1,P(Rd), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to LP(Rd). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

Potential fields and their partial derivatives produced by a 2D homogeneous polygonal source: A summary with some revisions

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. L29-L34 ◽  
Author(s):  
Zhen Jia ◽  
Shiguo Wu
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Observation Point ◽  
Potential Fields ◽  
Data Sets ◽  
Partial Derivatives ◽  
First Order ◽  
Gravity And Magnetic ◽  
Derivatives Of ◽  
The Magnetic Field

We summarized and revised the present forward modeling methods for calculating the gravity- and magnetic-field components and their partial derivatives of a 2D homogeneous source with a polygonal cross section. The responses of interest include the gravity-field components and their first- and second-order partial derivatives and the magnetic-field components and their first-order partial derivatives. The revised formulas consist of several basic quantities that are common in all the formulations. A singularity appears when the observation point coincides with a polygon vertex. This singularity is removable for the gravity formulas but not for the others. The compact forms of the revised formulas make them easy to implement. We compare the gravity- and magnetic-field components and their partial derivatives produced by a 2D prism whose polygonal cross section approximates a cylinder with the corresponding analytical fields and partial derivatives of the cylinder. The perfect fittings presented by both data sets confirm the reliability of the updated formulas.

On the Regularity of the Multisublinear Maximal Functions

2015 ◽  
Vol 58 (4) ◽  
pp. 808-817 ◽  
Author(s):  
Feng Liu ◽  
Huoxiong Wu
Keyword(s):  
Sobolev Spaces ◽  
Maximal Function ◽  
Maximal Operator ◽  
Maximal Functions ◽  
Partial Derivatives ◽  
First Order ◽  
Derivatives Of

AbstractThis paper is concerned with the study of the regularity for the multisublinear maximal operator. It is proved that the multisublinear maximal operator is bounded on first-order Sobolev spaces. Moreover, two key point-wise inequalities for the partial derivatives of the multisublinear maximal functions are established. As an application, the quasi-continuity on the multisublinear maximal function is also obtained.

Generalized Derivatives of an Arbitrary Order and the Boundary Properties of Differentiated Poisson Integrals for the Half-Space

2000 ◽  
Vol 7 (2) ◽  
pp. 387-400
Author(s):  
S. Topuria
Keyword(s):  
Half Space ◽  
Arbitrary Order ◽  
Generalized Derivatives ◽  
Spherical Derivative ◽  
Poisson Integrals ◽  
Several Variables ◽  
Integral Density ◽  
Boundary Properties ◽  
Generalized Differential ◽  
Derivatives Of

Abstract The notions of a generalized differential and a generalized spherical derivative of an arbitrary order are introduced for a function of several variables and Fatou type theorems are proved on the boundary properties of partial derivatives of an arbitrary order of the Poisson integral for the half-space, when the integral density has a generalized differential or a generalized spherical derivative.

scholarly journals Detection of degenerate points on the surface

2018 ◽  
Author(s):  
Marián Jenčo
Keyword(s):  
Automatic Recognition ◽  
Second Order ◽  
Ridge Line ◽  
Partial Derivatives ◽  
First Order ◽  
Convex Section ◽  
Pass Through ◽  
Derivatives Of

Landslides, bifurcations, multi-saddles and remnants of terraces are distinctive landforms. Some points on the surfaces of these objects are degenerate points. This may help us with their automatic recognition and identification. All first-order and second-order partial derivatives of analyzed function are necessary for detection of degenerate points. Terrain slope, curvatures and Hessian are required for classification of degenerate points. The paper is aimed at detection of fossil landslides. A point of landslide surface where the concave section of thalweg is turning into convex section of ridge line is a degenerate point. Two zero isolines of Hessian and zero isoline of profile, streamline and plan or tangential curvatures pass through this point. Final result of the detection procedure depends to a great extent on the quality of DEM and accuracy of derivatives.

scholarly journals Detection of degenerate points on the surface

2018 ◽  
Author(s):  
Marián Jenčo
Keyword(s):  
Automatic Recognition ◽  
Second Order ◽  
Ridge Line ◽  
Partial Derivatives ◽  
First Order ◽  
Convex Section ◽  
Pass Through ◽  
Derivatives Of

Landslides, bifurcations, multi-saddles and remnants of terraces are distinctive landforms. Some points on the surfaces of these objects are degenerate points. This may help us with their automatic recognition and identification. All first-order and second-order partial derivatives of analyzed function are necessary for detection of degenerate points. Terrain slope, curvatures and Hessian are required for classification of degenerate points. The paper is aimed at detection of fossil landslides. A point of landslide surface where the concave section of thalweg is turning into convex section of ridge line is a degenerate point. Two zero isolines of Hessian and zero isoline of profile, streamline and plan or tangential curvatures pass through this point. Final result of the detection procedure depends to a great extent on the quality of DEM and accuracy of derivatives.

Assessment of the Truth Foreseen in the Intuition

2009 ◽  
pp. 47-51
Author(s):  
Carlo Ciulla
Keyword(s):  
Energy Level ◽  
Polynomial System ◽  
Interpolation Function ◽  
Partial Derivatives ◽  
First Order ◽  
Signal Image ◽  
Set Of Points ◽  
Derivatives Of

This chapter continues the investigation conducted through deduction from the previous three chapters. Chapter II of the book has brought to light an intuition that has allowed the conception of the Sub- Pixel Efficacy Region and its definition. Chapter III outlines the conception of the Intensity-Curvature functional as a measure of the change in energy level of the signal because of the effect of the model interpolation function on the signal (image). Chapter IV studies the Intensity-Curvature Functional (?E) and through the solution of the polynomial system obtained from the first order partial derivatives of ?E, elucidates that a spatial set of points within the voxel is calculated from the Intensity-Curvature Functional and is assigned the name of Sub-pixel Efficacy Region (SRE).

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