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Winding of geodesic rays chosen by a harmonic measure
We prove limit theorems for the homological winding of geodesic rays distributed via a harmonic measure on a Gromov hyperbolic space. We obtain...
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Linear measure of non-iterative dynamic system of harmonic functions
The main purpose of this paper is to determine the linear measure of non-iterative dynamic system of some classes of harmonic functions.
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Absolute Continuity of the Harmonic Measure on Low Dimensional Rectifiable Sets
In the past decades, we learnt that uniform rectifiability is often a right candidate to go past Lipschitz boundaries in boundary value problems. If
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Boundary behavior of harmonic functions on metric measure spaces with non-negative Ricci curvature
Let ( X, d, μ ) be a metric measure space with non-negative Ricci curvature. This paper is concerned with the boundary behavior of harmonic function on...
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Harmonic Measure of Arcs of Fixed Length
We consider Jordan domains Ω with piece-wise smooth boundaries such that all arcs α ⊂ ∂Ω having fixed length l, 0 < l < length(∂Ω), have equal...
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Coherent Harmonic Radiation
The electron beam energy required for operation at a given frequency varies inversely as the square root of the harmonic number. For this reason, the...
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Geometric Harmonic Analysis III Integral Representations, Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate...
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Geometric Harmonic Analysis IV Boundary Layer Potentials in Uniformly Rectifiable Domains, and Applications to Complex Analysis
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate...
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Geometric Harmonic Analysis V Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate...
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Higher Harmonic Generation Microscopy
Higher harmonic-generation, including second harmonic generation and third harmonic generation, leaves no energy deposition to the interacted matters...
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Generating chord progression from melody with flexible harmonic rhythm and controllable harmonic density
Melody harmonization, which involves generating a chord progression that complements a user-provided melody, continues to pose a significant...
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A harmonic property of right invariant priors
It is shown that, on any Lie group, the density ratio of the right invariant measure to the left invariant measure is harmonic with respect to the...
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A Harmonic Impact Assessment Method for Multiple Harmonic Sources Connected to Distribution Network
The pollution of the common connection point (CCP) in the power grid is the result of the interaction of multiple harmonic sources. In order to more...
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Orbital perspective on high-harmonic generation from solids
High-harmonic generation in solids allows probing and controlling electron dynamics in crystals on few femtosecond timescales, paving the way to...
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Subclasses of Harmonic Functions with Nonnegative Harmonic Majorants in the Halfplane
In this chapter, we consider some \(\omega \)...
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Groups, Drift and Harmonic Measures
In this short note we will describe an old problem and a new approach which casts light upon it. The old problem is to understand the nature of...
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A New Compatibility Measure for Harmonic EDM Mixing
DJ track selection can benefit from software-generated recommendations that optimise harmonic transitions. Emerging techniques (such as Tonal...
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Bounded harmonic maps
The classical Fatou theorem identifies bounded harmonic functions on the unit disk with bounded measurable functions on the boundary circle. We...