Optics Express, ISSN 1094-4087, 09/2018, Volume 26, Issue 18, pp. 23844 - 23853

We propose a scheme for real-time observations of Bloch oscillations in semiconductors using time-resolved band gap emission spectroscopy. By solving the...

FIELDS | ELECTRONS | SOLIDS | DYNAMICS | OPTICS | PHOTOELECTRON HOLOGRAPHY | HIGH-HARMONIC GENERATION

FIELDS | ELECTRONS | SOLIDS | DYNAMICS | OPTICS | PHOTOELECTRON HOLOGRAPHY | HIGH-HARMONIC GENERATION

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 08/2017, Volume 62, Issue 8, pp. 1081 - 1092

Let f be a complex-valued harmonic mapping defined in the unit disk . We introduce the following notion: we say that f is a Bloch-type function if its Jacobian...

growth estimates | schlicht radius | Jacobian | univalent functions | coefficient estimates | harmonic functions | Bloch functions | MATHEMATICS | 30C50 | 30C25 | 30D45 | 30H30

growth estimates | schlicht radius | Jacobian | univalent functions | coefficient estimates | harmonic functions | Bloch functions | MATHEMATICS | 30C50 | 30C25 | 30D45 | 30H30

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 373, Issue 1, pp. 102 - 110

In this paper, our main aim is to introduce the concept of planar p-harmonic mappings and investigate the properties of these mappings. First, we discuss the...

Planar harmonic mapping | Landau's theorem and Bloch constant | Planar p-harmonic Bloch function | Planar p-harmonic mapping | MATHEMATICS | MATHEMATICS, APPLIED

Planar harmonic mapping | Landau's theorem and Bloch constant | Planar p-harmonic Bloch function | Planar p-harmonic mapping | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 6/2018, Volume 12, Issue 5, pp. 1143 - 1177

We study the family of weighted harmonic Bloch spaces $$b_\alpha , \alpha \in {\mathbb {R}}$$ bα,α∈R , on the unit ball of $${\mathbb {R}}^n$$ Rn . We provide...

Bergman space | 31B10 | Harmonic Bloch space | Mathematics | Duality | Gleason problem | Primary 31B05 | Reproducing kernel | 46E15 | Operator Theory | Analysis | Radial fractional derivative | Secondary 26A33 | Mathematics, general | Oscillatory characterization | Bergman projection | Atomic decomposition | MATHEMATICS, APPLIED | BERGMAN PROJECTIONS | REPRODUCING KERNELS | BESOV-SPACES | LIPSCHITZ | UNIT BALL | MATHEMATICS | Derivatives (Financial instruments)

Bergman space | 31B10 | Harmonic Bloch space | Mathematics | Duality | Gleason problem | Primary 31B05 | Reproducing kernel | 46E15 | Operator Theory | Analysis | Radial fractional derivative | Secondary 26A33 | Mathematics, general | Oscillatory characterization | Bergman projection | Atomic decomposition | MATHEMATICS, APPLIED | BERGMAN PROJECTIONS | REPRODUCING KERNELS | BESOV-SPACES | LIPSCHITZ | UNIT BALL | MATHEMATICS | Derivatives (Financial instruments)

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 9/2013, Volume 322, Issue 3, pp. 835 - 875

We consider a periodic Schrödinger operator and the composite Wannier functions corresponding to a relevant family of its Bloch bands, separated by a gap from...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | HARMONIC MAPS | SPACES | REGULARITY | ELECTRONS | ENERGY-BANDS | CRYSTALS | DYNAMICS | PHYSICS, MATHEMATICAL | POLARIZATION | Invisibility

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | HARMONIC MAPS | SPACES | REGULARITY | ELECTRONS | ENERGY-BANDS | CRYSTALS | DYNAMICS | PHYSICS, MATHEMATICAL | POLARIZATION | Invisibility

Journal Article

Journal of Function Spaces, ISSN 2314-8896, 11/2018, Volume 2018, pp. 1 - 6

We study Bloch-type spaces of minimal surfaces from the unit disk D into Rn and characterize them in terms of weighted Lipschitz functions. In addition, the...

MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | HARMONIC BLOCH | BESOV-SPACES | UNIT BALL | Minimal surfaces | Theorems | Mathematics

MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | HARMONIC BLOCH | BESOV-SPACES | UNIT BALL | Minimal surfaces | Theorems | Mathematics

Journal Article

New Journal of Physics, ISSN 1367-2630, 04/2019, Volume 21, Issue 4, p. 43029

Attosecond transient absorption is an ultrafast technique that has opened the possibility to study electron dynamics in condensed matter systems at its natural...

ultrafast x-ray spectroscopy | attosecond transient absorption | semiconductor and two-dimensional materials | SPECTROSCOPY | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | HIGH-HARMONIC GENERATION | Time dependence | Dynamic tests | Condensed matter | Dynamics | Spectrum analysis | Absorption spectra | Electron transport

ultrafast x-ray spectroscopy | attosecond transient absorption | semiconductor and two-dimensional materials | SPECTROSCOPY | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | HIGH-HARMONIC GENERATION | Time dependence | Dynamic tests | Condensed matter | Dynamics | Spectrum analysis | Absorption spectra | Electron transport

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 1/2016, Volume 26, Issue 1, pp. 463 - 473

Let $$M$$ M be an $$n$$ n -dimensional complex manifold. A holomorphic function $$f:M\rightarrow {\mathbb {C}}$$ f : M → C is said to be semi-Bloch if for...

Mathematics | Kobayashi–Royden pseudometric | 30D45 | 32A18 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Normal functions | Differential Geometry | Dynamical Systems and Ergodic Theory | Bloch functions | Semi-Bloch functions | MATHEMATICS | Kobayashi-Royden pseudometric | Naturvetenskap | Matematisk analys | Natural Sciences | Mathematics/Applied Mathematics | Matematik | matematik/tillämpad matematik | Mathematical Analysis

Mathematics | Kobayashi–Royden pseudometric | 30D45 | 32A18 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Normal functions | Differential Geometry | Dynamical Systems and Ergodic Theory | Bloch functions | Semi-Bloch functions | MATHEMATICS | Kobayashi-Royden pseudometric | Naturvetenskap | Matematisk analys | Natural Sciences | Mathematics/Applied Mathematics | Matematik | matematik/tillämpad matematik | Mathematical Analysis

Journal Article

IEEE Transactions on Medical Imaging, ISSN 0278-0062, 10/2015, Volume 34, Issue 10, pp. 2118 - 2130

In waveform design for magnetic resonance applications, periodic continuous-wave excitation offers potential advantages that remain largely unexplored because...

magnetic resonance | Magnetization | Harmonic analysis | Nonhomogeneous media | steady state free precession | Steady-state | harmonic balance | Convergence | continuous-wave excitation | Magnetic resonance imaging | Bloch equation | Mathematical model | convergence rate | Convergence rate | Steady state free precession | Continuous-wave excitation | Magnetic resonance | Harmonic balance | SEQUENCES | MRI | ENGINEERING, BIOMEDICAL | FIELD | NUCLEAR-MAGNETIC-RESONANCE | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ROTATING-FRAME | ENGINEERING, ELECTRICAL & ELECTRONIC | PHASE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SOLIDS | SYSTEMS | STATE FREE PRECESSION | STEADY-STATE | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Algorithms | Magnetic Resonance Imaging - instrumentation | Models, Biological | Computer Simulation | Magnetic Resonance Imaging - methods | Gray Matter - physiology | Phantoms, Imaging | Cerebrospinal Fluid - physiology | Excitation (Physiology) | Frequency modulation | Usage | Research

magnetic resonance | Magnetization | Harmonic analysis | Nonhomogeneous media | steady state free precession | Steady-state | harmonic balance | Convergence | continuous-wave excitation | Magnetic resonance imaging | Bloch equation | Mathematical model | convergence rate | Convergence rate | Steady state free precession | Continuous-wave excitation | Magnetic resonance | Harmonic balance | SEQUENCES | MRI | ENGINEERING, BIOMEDICAL | FIELD | NUCLEAR-MAGNETIC-RESONANCE | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ROTATING-FRAME | ENGINEERING, ELECTRICAL & ELECTRONIC | PHASE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SOLIDS | SYSTEMS | STATE FREE PRECESSION | STEADY-STATE | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Algorithms | Magnetic Resonance Imaging - instrumentation | Models, Biological | Computer Simulation | Magnetic Resonance Imaging - methods | Gray Matter - physiology | Phantoms, Imaging | Cerebrospinal Fluid - physiology | Excitation (Physiology) | Frequency modulation | Usage | Research

Journal Article

Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2017, Volume 54, Issue 4, pp. 1337 - 1346

We define Bloch-type spaces of C-1(H) on the upper half plane H and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness...

Majorant | Bloch space | Composition operator | MATHEMATICS | majorant | composition operator | COMPOSITION OPERATORS | HARMONIC BLOCH | C-N | BESOV-SPACES | LIPSCHITZ-TYPE SPACES | UNIT BALL

Majorant | Bloch space | Composition operator | MATHEMATICS | majorant | composition operator | COMPOSITION OPERATORS | HARMONIC BLOCH | C-N | BESOV-SPACES | LIPSCHITZ-TYPE SPACES | UNIT BALL

Journal Article

Filomat, ISSN 0354-5180, 1/2017, Volume 31, Issue 1, pp. 97 - 102

We decompose the invariant Laplacian of the deleted unit complex ball by two directional Laplacians, tangential one and radial one. We give a characterization...

Potential theory | Laplacians | Mathematical functions | Operator theory | Bloch function | Invariant laplacian | Pluriharmonic | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | Laplacian | pluriharmonic | M-HARMONIC FUNCTIONS | UNIT BALL

Potential theory | Laplacians | Mathematical functions | Operator theory | Bloch function | Invariant laplacian | Pluriharmonic | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | Laplacian | pluriharmonic | M-HARMONIC FUNCTIONS | UNIT BALL

Journal Article

Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 10/2015, Volume 145, Issue 6, pp. 1283 - 1311

When an incident Herglotz wave function scatters from a periodic Lipschitz continuous surface with a Dirichlet boundary condition, the classical (quasi-)...

Herglotz wave function | Floquet transform | scattering | Bloch transform | periodic surface | GRATINGS | MATHEMATICS | MATHEMATICS, APPLIED | HARMONIC MAXWELL EQUATIONS | INVERSE SCATTERING | DIFFRACTION PROBLEM | UNIQUENESS THEOREMS | Boundary conditions | Mathematics | Maps | Wave propagation | Equivalence | Scattering | Transforms | Dirichlet problem | Wave functions | Periodic structures

Herglotz wave function | Floquet transform | scattering | Bloch transform | periodic surface | GRATINGS | MATHEMATICS | MATHEMATICS, APPLIED | HARMONIC MAXWELL EQUATIONS | INVERSE SCATTERING | DIFFRACTION PROBLEM | UNIQUENESS THEOREMS | Boundary conditions | Mathematics | Maps | Wave propagation | Equivalence | Scattering | Transforms | Dirichlet problem | Wave functions | Periodic structures

Journal Article

Journal of scientific computing, ISSN 0885-7474, 02/2017, Volume 70, Issue 2, pp. 922 - 964

We analyze discontinuous Galerkin finite element discretizations of the Maxwell equations with periodic coefficients. These equations are used to model the...

Band structure | Mixed finite element methods | Discrete compactness property | EWI-27715 | Discontinuous Galerkin methods | Eigenvalue problems | Photonic crystals | IR-103360 | Maxwell equations | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | EIGENVALUE PROBLEM | EDGE-ELEMENTS | MATHEMATICS, APPLIED | HARMONIC MAXWELL EQUATIONS | FINITE-ELEMENTS | SPURIOUS MODES | SPECTRAL APPROXIMATION | INTERIOR PENALTY METHOD | EFFICIENT METHOD | DISCRETE COMPACTNESS | BAND-STRUCTURE CALCULATIONS

Band structure | Mixed finite element methods | Discrete compactness property | EWI-27715 | Discontinuous Galerkin methods | Eigenvalue problems | Photonic crystals | IR-103360 | Maxwell equations | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | EIGENVALUE PROBLEM | EDGE-ELEMENTS | MATHEMATICS, APPLIED | HARMONIC MAXWELL EQUATIONS | FINITE-ELEMENTS | SPURIOUS MODES | SPECTRAL APPROXIMATION | INTERIOR PENALTY METHOD | EFFICIENT METHOD | DISCRETE COMPACTNESS | BAND-STRUCTURE CALCULATIONS

Journal Article

Journal d'Analyse Mathématique, ISSN 0021-7670, 3/2019, Volume 137, Issue 2, pp. 663 - 677

Let B X be a homogeneous unit ball in X = ℂ n . In this paper, we generalize Bonk’s distortion theorem to Bloch mappings on B X . As an application, we give a...

Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS

Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 337, Issue 2, pp. 880 - 887

The Schwarz lemma and Bloch constants for planar bounded harmonic mappings are considered. Sharper form and better estimates are obtained. Our results improve...

Harmonic Schwarz lemma | Harmonic mappings | Bloch constant | MATHEMATICS | harmonic mappings | harmonic Schwarz lemma | MATHEMATICS, APPLIED

Harmonic Schwarz lemma | Harmonic mappings | Bloch constant | MATHEMATICS | harmonic mappings | harmonic Schwarz lemma | MATHEMATICS, APPLIED

Journal Article

Physical Review A - Atomic, Molecular, and Optical Physics, ISSN 1050-2947, 01/2010, Volume 81, Issue 1

We have investigated and experimentally demonstrated the applicability of the Bloch vector for one-dimensional, nonlinear, finite, dissipative systems. The...

REFLECTION | GENERATION | OPTICS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | TENSORS | THIN FILMS | FILTERS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | NANOSTRUCTURES | ONE-DIMENSIONAL CALCULATIONS | LAYERS | ELEMENTS | FILMS | METALS | NONLINEAR PROBLEMS | HARMONIC GENERATION | FREQUENCY MIXING | VECTORS

REFLECTION | GENERATION | OPTICS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | TENSORS | THIN FILMS | FILTERS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | NANOSTRUCTURES | ONE-DIMENSIONAL CALCULATIONS | LAYERS | ELEMENTS | FILMS | METALS | NONLINEAR PROBLEMS | HARMONIC GENERATION | FREQUENCY MIXING | VECTORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2018, Volume 468, Issue 2, pp. 1066 - 1081

In this paper, we first establish the sharp version of Landau–Bloch type theorem for holomorphic functions with bounded derivative by applying Schwarz–Pick...

Landau–Bloch type theorem | The extremal function | Harmonic mappings | Univalent | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | LEMMA | Landau-Bloch type theorem

Landau–Bloch type theorem | The extremal function | Harmonic mappings | Univalent | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | LEMMA | Landau-Bloch type theorem

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 8/2011, Volume 84, Issue 1, pp. 67 - 78

AbstractIn this paper, our main aim is to discuss the properties of harmonic mappings in the unit ball n. First, we characterize the harmonic Bloch spaces and...

harmonic Bloch space | weighted Lipschitz function | characterization | little harmonic Bloch space

harmonic Bloch space | weighted Lipschitz function | characterization | little harmonic Bloch space

Journal Article

19.
Full Text
Coefficients Estimate for Harmonic v-Bloch Mappings and Harmonic K-Quasiconformal Mappings

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 1/2016, Volume 39, Issue 1, pp. 349 - 358

Let $$f(z)=h(z)+\overline{g(z)}$$ f ( z ) = h ( z ) + g ( z ) ¯ be a harmonic v-Bloch mapping defined in the unit disk $${\mathbb {D}}$$ D with $$\Vert f\Vert...

Bloch constant | Primary 30C62 | Harmonic quasiconformal mappings | Harmonic v -Bloch mappings | 30F15 | Mathematics, general | Secondary 30C20 | Mathematics | Applications of Mathematics | Coefficient estimates | Harmonic v-Bloch mappings | MATHEMATICS | BOUNDARY CORRESPONDENCE | CONSTANT | Theorems | Mapping

Bloch constant | Primary 30C62 | Harmonic quasiconformal mappings | Harmonic v -Bloch mappings | 30F15 | Mathematics, general | Secondary 30C20 | Mathematics | Applications of Mathematics | Coefficient estimates | Harmonic v-Bloch mappings | MATHEMATICS | BOUNDARY CORRESPONDENCE | CONSTANT | Theorems | Mapping

Journal Article

Journal of Function Spaces, ISSN 2314-8896, 8/2017, Volume 2017, pp. 1 - 6

We investigate some properties of pluriharmonic mappings in an infinite dimensional complex Hilbert space. Several characterizations for pluriharmonic mappings...

MATHEMATICS | MATHEMATICS, APPLIED | HARMONIC BLOCH | C-N | BESOV-SPACES | HOLOMORPHIC-FUNCTIONS | EQUIVALENT NORMS | UNIT BALL | Hilbert space | Functions of complex variables | Research | Mathematical research | Mappings (Mathematics) | Complex variables | Remakes & sequels | Mathematical analysis

MATHEMATICS | MATHEMATICS, APPLIED | HARMONIC BLOCH | C-N | BESOV-SPACES | HOLOMORPHIC-FUNCTIONS | EQUIVALENT NORMS | UNIT BALL | Hilbert space | Functions of complex variables | Research | Mathematical research | Mappings (Mathematics) | Complex variables | Remakes & sequels | Mathematical analysis

Journal Article

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