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Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks

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ISBN: 9783039217205 9783039217212 Year: Pages: 144 DOI: 10.3390/books978-3-03921-721-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems.

Liquid Crystal on Silicon Devices: Modeling and Advanced Spatial Light Modulation Applications

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ISBN: 9783039218288 9783039218295 Year: Pages: 172 DOI: 10.3390/books978-3-03921-829-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Liquid Crystal on Silicon (LCoS) has become one of the most widespread technologies for spatial light modulation in optics and photonics applications. These reflective microdisplays are composed of a high-performance silicon complementary metal oxide semiconductor (CMOS) backplane, which controls the light-modulating properties of the liquid crystal layer. State-of-the-art LCoS microdisplays may exhibit a very small pixel pitch (below 4 ?m), a very large number of pixels (resolutions larger than 4K), and high fill factors (larger than 90%). They modulate illumination sources covering the UV, visible, and far IR. LCoS are used not only as displays but also as polarization, amplitude, and phase-only spatial light modulators, where they achieve full phase modulation. Due to their excellent modulating properties and high degree of flexibility, they are found in all sorts of spatial light modulation applications, such as in LCOS-based display systems for augmented and virtual reality, true holographic displays, digital holography, diffractive optical elements, superresolution optical systems, beam-steering devices, holographic optical traps, and quantum optical computing. In order to fulfil the requirements in this extensive range of applications, specific models and characterization techniques are proposed. These devices may exhibit a number of degradation effects such as interpixel cross-talk and fringing field, and time flicker, which may also depend on the analog or digital backplane of the corresponding LCoS device. The use of appropriate characterization and compensation techniques is then necessary.

Differential Geometry

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ISBN: 9783039218004 9783039218011 Year: Pages: 166 DOI: 10.3390/books978-3-03921-801-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions. This book covers a variety of both classical and modern topics in differential geometry. We mention properties of both rectifying and affine curves, the geometry of hypersurfaces, angles in Minkowski planes, Euclidean submanifolds, differential operators and harmonic forms on Riemannian manifolds, complex manifolds, contact manifolds (in particular, Sasakian and trans-Sasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds). We wish to mention that among the authors, there are both well-known geometers and young researchers. The authors are from countries with a tradition in differential geometry: Belgium, China, Greece, Japan, Korea, Poland, Romania, Spain, Turkey, and United States of America. Many of these papers were already cited by other researchers in their articles. This book is useful for specialists in differential geometry, operator theory, physics, and information geometry as well as graduate students in mathematics.

Keywords

Euclidean submanifold --- position vector field --- concurrent vector field --- concircular vector field --- rectifying submanifold --- T-submanifolds --- constant ratio submanifolds --- Ricci soliton --- Kähler–Einstein metrics --- compact complex surfaces --- pinching of the curvatures --- statistical manifolds --- Hessian manifolds --- Hessian sectional curvature --- scalar curvature --- Ricci curvature --- Minkowski plane --- Minkowskian length --- Minkowskian angle --- Minkowskian pseudo-angle --- L2-harmonic forms --- Hodge–Laplacian --- manifold with singularity --- L2-Stokes theorem --- capacity --- k-th generalized Tanaka–Webster connection --- non-flat complex space form --- real hypersurface --- lie derivative --- shape operator --- conical surface --- developable surface --- generalized 1-type Gauss map --- cylindrical hypersurface --- inextensible flow --- lightlike surface --- ruled surface --- Darboux frame --- C-Bochner tensor --- generalized normalized ?-Casorati curvature --- Sasakian manifold --- slant --- invariant --- anti-invariant --- trans-Sasakian 3-manifold --- Reeb flow symmetry --- Ricci operator --- Sasakian statistical manifold --- conjugate connection --- Casorati curvature --- framed rectifying curves --- singular points --- framed helices --- centrodes --- circular rectifying curves --- statistical structure --- affine hypersurface --- affine sphere --- conjugate symmetric statistical structure --- sectional ?-curvature --- complete connection --- symplectic curves --- circular helices --- symplectic curvatures --- Frenet frame

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