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Showing 1 to 20 of 31 for “"Harmonic functions"”.
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EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS
This thesis mainly studies harmonic functions on exterior regions, having compact, Lipschitz boundaries, in our new finite energy function space, via the sequence of exterior harmonic Steklov eigenvalues and associated eigenfunctions. The new space is strictly larger than the standard …
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An Integral Problem for Positive Harmonic Functions
Made available in DSpace on 2014-12-11T18:24:16Z (GMT). No. of bitstreams: 1 7511761.pdf: 2078928 bytes, checksum: 48fe58fab6babee10ac246329d817b07 (MD5) Previous issue date: 1974
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Integrals of harmonic functions over curves and surfaces
… of integrals over this family is estimated for harmonic functions given by the Cantors measures on the unit circle in terms of the porosity of the Cantor set. The exact lower bound of it for all normalized positive harmonic functions in the unit ball of $R\sp{n}$ is established. Also, its value …
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Coefficient Problem for Positive Harmonic Functions on an Annulus
Made available in DSpace on 2014-12-11T18:23:41Z (GMT). No. of bitstreams: 1 7114944.pdf: 1498294 bytes, checksum: 02a322f47da801dbfe91c98ad7b7139f (MD5) Previous issue date: 1970
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The Lie Symmetries of a Few Classes of Harmonic Functions
… system of equations, applying this theory to harmonic functions in the complex plane. We will consider harmonic functions in general, harmonic functions with constant Jacobian, harmonic functions with fixed convexity and a few other subclasses of harmonic functions.
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On Connections Between Univalent Harmonic Functions, Symmetry Groups, and Minimal Surfaces
… theory for studying applications of univalent harmonic function theory to minimal surfaces. We then proceed to consider convex combination harmonic mappings of the form f=sf_1+(1-s) f_2 and give conditions on when f lifts to a one-parameter family of minimal surfaces via the …
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Inequalities for the differential subordinates of Martingales, harmonic functions and Ito processes
… v\vert\geq1)\leq2\Vert u\Vert\sb1$ for two harmonic functions u and v by adjoining an extra assumption. That is, we prove the weak-type inequality $\mu(\vert v\vert\geq1)\leq K\Vert u\Vert\sb1$ under the assumptions that $\vert v(\xi)\vert\leq\vert u(\xi)\vert, \vert\nabla …
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Potential Theory for Subordinate Killed Brownian Motion in Some Unbounded Domains
… the canonical representation of the positive harmonic functions in terms of the Martin boundary and the Martin kernel. Moreover, each positive harmonic function consists of two nonnegative harmonic functions: one is purely excessive and the other is invariant under the semigroup of the …
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A New Approach to Lie Symmetry Groups of Minimal Surfaces
… groups of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the associated family …
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Steklov Eigenvalue Problems on Nearly Spherical and Annular Domains
… using the Green-Beltrami identity for spherical harmonic functions, the derivatives of Steklov eigenvalues with respect to the domain perturbation parameter can be determined by the eigenvalues of a matrix involving the integral of the product of three spherical harmonic functions. By using the …
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A Numerical Scheme for Mullins-Sekerka Flow in Three Space Dimensions
… spherical. This process is described by evolving harmonic functions within the two phases with the moving interface driven by the jump in the normal derivatives of the harmonic functions at the interface. The harmonic functions are continuous across the interface, taking on values equal to the …
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Potential Theory on Compact Sets
… are several equivalent ways to define continuous harmonic functions <em>H</em>(<em>K</em>) on a compact set <em>K</em> in [the set of real numbers]<sup>n</sup>. One may let <em>H</em>(<em>K</em>) be the uniform closure of all functions in <em>C</em>(<em>K</em>) which are restrictions of harmonic …
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MODES IN HEAVY METAL MUSIC
… metal genres. The study also explores how the harmonic functions of modes differ from harmonic functions found throughout the Common Practice Period and argues how uncommon modes such as Locrian have legitimate functionality within a heavy metal setting.</p>
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Multi-dimensional continuous wavelet transforms and generalized fourier transforms in Clifford analysis
… to higher dimension of the theory of holomorphic functions in the complex plane. The generalized holomorphic functions, known as monogenic functions, are null-solutions of the so-called Dirac operator, a first order rotationally invariant differential operator factorizing the Laplacian in higher …
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Potential Theory for Subordinate Brownian Motion by Tempered Stable Subordinator
… bounded open set D with C1,1 boundary, the Green functions of the killed symmetric alpha-stable processes and relativistic alpha-stable processes upon leaving D were studied and sharp estimates were established. Under some assumptions on the Levy measure of the subordinator {Zt : t ≥ 0}, we can …
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A Weak Type Inequality for Martingale Transforms and Other Subordinate Martingales
… continuous-time case and give an application to harmonic functions.
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Regularity of Neumann solutions to an elliptic free boundary problem
… a bounded, convex domain ... This function u is harmonic in its positive phase and satisfies ... along the free boundary ... , in a weak sense. We prove various basic properties of such a minimizer near the portion of the boundary ... on which ... weakly. These results include up-to-the boundary …
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Self-adjoint Laplacians and Symmetric Diffusions on Hyperbolic Attractors
… case and the existence of nonconstant harmonic functions of zero energy in the ergodic case. In the special case of partially hyperbolic diffeomorphisms induced by geodesic flows on manifolds of negative sectional curvature the Laplacians we consider are self-adjoint extensions of …
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Sequential test for homogeneity of Poisson populations
Not available
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