Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Erdös–Mordell inequality --- Barrow’s inequality --- triangle --- interior point --- q-integral inequality --- strongly preinvex function --- Simpson inequality --- quantum integral --- statistical warped product submanifold --- statistical manifold --- B.Y.Chen inequality --- Casorati curvatures --- statistical soliton --- Wintgen inequality --- generalized complex space form --- generalized Sasakian space form --- Lagrangian submanifold --- Legendrian submanifold --- Einstein manifold --- sectional curvature --- Betti number --- Tachibana number --- spherical space form --- slant submanifolds --- generalized Sasakian space forms --- closed form --- conformal form --- Maslov form --- legendrian submanifolds --- sasakian space forms --- obata differential equation --- isometric immersion --- Casorati curvature --- statistical submanifold --- holomorphic statistical manifold --- clifford minimal hypersurfaces --- sasakian structure --- integral inequalities --- reeb function --- contact vector field --- δ(2,2)-invariant --- Chen inequalities --- Lagrangian submanifolds --- quaternionic space forms --- complex space forms --- warped product --- sphere theorem --- Laplacian --- inequalities --- diffeomorphic --- Ricci curvature --- skew CR-warped product submanifolds --- complex space form --- CR-warped product submanifolds --- semi slant warped product submanifolds --- almost Hermitian manifolds --- Kähler identities --- Lefschetz operator --- isoperimetric problem --- minimal perimeter --- log-concave functions --- isotropic measure --- extrinsic principal tangential directions --- principal first normal directions

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Intensive studies on light–matter interactions and technological breakthroughs, especially conducted in the field of dressed photon research, have led to a growing concern regarding unsettled off-shell quantum field interactions. The Special Issue, entitled “Quantum Fields and Off-Shell Sciences”, was organized to promote the progress of such research activities from a wider perspective, not limited to dressed photon studies. This book contains excellent papers that were published in this Special Issue. It will provide scientific and technical information on the quantum fields and off-shell sciences to scientists, engineers, and students who are and will be engaged in this field.

Research & information: general --- Physics --- dressed photon --- dressed photon constant --- natural units --- Heisenberg cut --- de Sitter space --- dark energy --- dark matter --- cosmological constant --- twin universes --- conformal cyclic cosmology --- quantum walk --- scattering theory --- energy --- survival probability --- attractor eigenspace --- category --- algebra --- state --- category algebra --- state on category --- noncommutative probability --- quantum probability --- GNS representation --- quantum measurement --- C*-algebra --- algebraic quantum field theory --- local net --- extension of local net --- completely positive instrument --- macroscopic distinguishability --- Grassmann manifold --- flag manifold --- pre-homogeneous vector space --- invariants --- category theory --- nonstandard analysis --- coarse geometry --- quantum field --- combinatorial optimization --- Ising spin glass --- coupled oscillator --- eigenmode --- clustering --- localization --- dissipation --- off-shell science --- non-equilibrium open system --- quantum master equation --- quantum density matrix --- projection operator --- renormalization --- discrete-time quantum walk --- scattering quantum random walk --- Grover walk --- pathfinding --- network

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In recent years, rapid development in robotics, mobile, and communication technologies has encouraged many studies in the field of localization and navigation in indoor environments. An accurate localization system that can operate in an indoor environment has considerable practical value, because it can be built into autonomous mobile systems or a personal navigation system on a smartphone for guiding people through airports, shopping malls, museums and other public institutions, etc. Such a system would be particularly useful for blind people. Modern smartphones are equipped with numerous sensors (such as inertial sensors, cameras, and barometers) and communication modules (such as WiFi, Bluetooth, NFC, LTE/5G, and UWB capabilities), which enable the implementation of various localization algorithms, namely, visual localization, inertial navigation system, and radio localization. For the mapping of indoor environments and localization of autonomous mobile sysems, LIDAR sensors are also frequently used in addition to smartphone sensors. Visual localization and inertial navigation systems are sensitive to external disturbances; therefore, sensor fusion approaches can be used for the implementation of robust localization algorithms. These have to be optimized in order to be computationally efficient, which is essential for real-time processing and low energy consumption on a smartphone or robot.

dynamic objects identification and localization --- laser cluster --- radial velocity similarity --- Pearson correlation coefficient --- particle filter --- trilateral indoor positioning --- RSSI filter --- RSSI classification --- stability --- accuracy --- inertial navigation system --- artificial neural network --- motion tracking --- sensor fusion --- indoor navigation system --- indoor positioning --- indoor navigation --- radiating cable --- leaky feeder --- augmented reality --- Bluetooth --- indoor positioning system --- smart hospital --- indoor --- positioning --- visually impaired --- deep learning --- multi-layered perceptron --- inertial sensor --- smartphone --- multi-variational message passing (M-VMP) --- factor graph (FG) --- second-order Taylor expansion --- cooperative localization --- joint estimation of position and clock --- RTLS --- indoor positioning system (IPS) --- position data --- industry 4.0 --- traceability --- product tracking --- fingerprinting localization --- Bluetooth low energy --- Wi-Fi --- performance metrics --- positioning algorithms --- location source optimization --- fuzzy comprehensive evaluation --- DCPCRLB --- UAV --- unmanned aerial vehicles --- NWPS --- indoor positioning systems --- GPS denied --- GNSS denied --- autonomous vehicles --- visible light positioning --- mobile robot --- calibration --- appearance-based localization --- computer vision --- Gaussian processes --- manifold learning --- robot vision systems --- image manifold --- descriptor manifold --- indoor fingerprinting localization --- Gaussian filter --- Kalman filter --- received signal strength indicator --- channel state information --- indoor localization --- visual-inertial SLAM --- constrained optimization --- path loss model --- particle swarm optimization --- beacon --- absolute position system --- cooperative algorithm --- intercepting vehicles --- robot framework --- UWB sensors --- Internet of Things (IoT) --- wireless sensor network (WSN) --- switched-beam antenna --- electronically steerable parasitic array radiator (ESPAR) antenna --- received signal strength (RSS) --- fingerprinting --- down-conversion --- GPS --- navigation --- RF repeaters --- up-conversion --- n/a

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Third millennium engineering address new challenges in materials sciences and engineering. In particular, the advances in materials engineering combined with the advances in data acquisition, processing and mining as well as artificial intelligence allow for new ways of thinking in designing new materials and products. Additionally, this gives rise to new paradigms in bridging raw material data and processing to the induced properties and performance. This present topical issue is a compilation of contributions on novel ideas and concepts, addressing several key challenges using data and artificial intelligence, such as:- proposing new techniques for data generation and data mining;- proposing new techniques for visualizing, classifying, modeling, extracting knowledge, explaining and certifying data and data-driven models;- processing data to create data-driven models from scratch when other models are absent, too complex or too poor for making valuable predictions;- processing data to enhance existing physic-based models to improve the quality of the prediction capabilities and, at the same time, to enable data to be smarter; and- processing data to create data-driven enrichment of existing models when physics-based models exhibit limits within a hybrid paradigm.

plasticity --- machine learning --- constitutive modeling --- manifold learning --- topological data analysis --- GENERIC --- soft living tissues --- hyperelasticity --- computational modeling --- data-driven mechanics --- TDA --- Code2Vect --- nonlinear regression --- effective properties --- microstructures --- model calibration --- sensitivity analysis --- elasto-visco-plasticity --- Gaussian process --- high-throughput experimentation --- additive manufacturing --- Ti–Mn alloys --- spherical indentation --- statistical analysis --- Gaussian process regression --- nanoporous metals --- open-pore foams --- FE-beam model --- data mining --- mechanical properties --- hardness --- principal component analysis --- structure–property relationship --- microcompression --- nanoindentation --- analytical model --- finite element model --- artificial neural networks --- model correction --- feature engineering --- physics based --- data driven --- laser shock peening --- residual stresses --- data-driven --- multiscale --- nonlinear --- stochastics --- neural networks --- n/a --- Ti-Mn alloys --- structure-property relationship