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Structural analysis (Engineering). --- Matrices. --- Finite element method. --- Trapezoid.

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The book is dealing with recent progress in human–computer interaction (HCI) related to geographic information science (GIS). The Editorial starts with an overview about the evolution of the Internet and first HCI concepts and stimulates recent HCI developments using 3D and 4D apps, running on all mobile devices with OS Android, iOS, Linus, and Windows. Eight research articles present the state-of-the-art in HCI–GIS-related issues, starting with gender and age differences in using indoor maps via the estimation of building heights from space to an efficient visualization method for polygonal data with dynamic simplification. The review article deals with progress and challenges on entity alignment of geographic knowledge bases.

cyberpsychology --- n/a --- trajectory datasets --- trapezoid --- movement data --- space use intensity --- hypsography --- geospatial data --- map tasks --- knowledge integration --- immersive virtual reality --- knowledge conflation --- OLS --- multiresolution segmentation --- 3D geovisualizations --- SpatialHadoop --- contour lines --- high definition video --- immersion --- PR-Tree --- similarity metrics --- PCA --- map users --- retrospective verbal protocol --- collaborative learning --- telepresence --- 4D time density --- eye-tracking --- level-of-detail rendering --- visual data exploration --- Head-mounted display --- hedonic price model --- sense of presence --- collaborative immersive virtual environment --- gender effects --- tessellation --- spatiotemporal movement patterns --- building tracking --- indoor wayfinding --- cartographic simplification --- height estimate --- map literacy --- random forest --- 3DmoveR --- level of interactivity --- entity alignment --- 3D data cube --- human–computer interaction --- International Space Station (ISS) --- vector polygon --- cloud computing --- OSIVQ --- spatial data processing --- user study --- age effects --- geographic knowledge bases --- Ljubljana --- 3D map --- user’s performance --- similarity combination --- human-computer interaction --- user's performance

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Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950's, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical system.

Hyperbolic spaces. --- Singularities (Mathematics) --- Transformations (Mathematics) --- Geometry, Plane. --- Plane geometry --- Algorithms --- Differential invariants --- Geometry, Differential --- Geometry, Algebraic --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- Abelian group. --- Automorphism. --- Big O notation. --- Bijection. --- Binary number. --- Bisection. --- Borel set. --- C0. --- Calculation. --- Cantor set. --- Cartesian coordinate system. --- Combination. --- Compass-and-straightedge construction. --- Congruence subgroup. --- Conjecture. --- Conjugacy class. --- Continuity equation. --- Convex lattice polytope. --- Convex polytope. --- Coprime integers. --- Counterexample. --- Cyclic group. --- Diameter. --- Diophantine approximation. --- Diophantine equation. --- Disjoint sets. --- Disjoint union. --- Division by zero. --- Embedding. --- Equation. --- Equivalence class. --- Ergodic theory. --- Ergodicity. --- Factorial. --- Fiber bundle. --- Fibonacci number. --- Fundamental domain. --- Gauss map. --- Geometry. --- Half-integer. --- Homeomorphism. --- Hyperbolic geometry. --- Hyperplane. --- Ideal triangle. --- Intersection (set theory). --- Interval exchange transformation. --- Inverse function. --- Inverse limit. --- Isometry group. --- Lattice (group). --- Limit set. --- Line segment. --- Linear algebra. --- Linear function. --- Line–line intersection. --- Main diagonal. --- Modular group. --- Monotonic function. --- Multiple (mathematics). --- Orthant. --- Outer billiard. --- Parallelogram. --- Parameter. --- Partial derivative. --- Penrose tiling. --- Permutation. --- Piecewise. --- Polygon. --- Polyhedron. --- Polytope. --- Product topology. --- Projective geometry. --- Rectangle. --- Renormalization. --- Rhombus. --- Right angle. --- Rotational symmetry. --- Sanity check. --- Scientific notation. --- Semicircle. --- Sign (mathematics). --- Special case. --- Square root of 2. --- Subsequence. --- Summation. --- Symbolic dynamics. --- Symmetry group. --- Tangent. --- Tetrahedron. --- Theorem. --- Toy model. --- Translational symmetry. --- Trapezoid. --- Triangle group. --- Triangle inequality. --- Two-dimensional space. --- Upper and lower bounds. --- Upper half-plane. --- Without loss of generality. --- Yair Minsky.

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This Special Issue brings together original research papers, in all areas of mathematics, that are concerned with inequalities or the role of inequalities. The research results presented in this Special Issue are related to improvements in classical inequalities, highlighting their applications and promoting an exchange of ideas between mathematicians from many parts of the world dedicated to the theory of inequalities. This volume will be of interest to mathematicians specializing in inequality theory and beyond. Many of the studies presented here can be very useful in demonstrating new results. It is our great pleasure to publish this book. All contents were peer-reviewed by multiple referees and published as papers in our Special Issue in the journal Symmetry. These studies give new and interesting results in mathematical inequalities enabling readers to obtain the latest developments in the fields of mathematical inequalities. Finally, we would like to thank all the authors who have published their valuable work in this Special Issue. We would also like to thank the editors of the journal Symmetry for their help in making this volume, especially Mrs. Teresa Yu.

Ostrowski inequality --- Hölder’s inequality --- power mean integral inequality --- n-polynomial exponentially s-convex function --- weight coefficient --- Euler–Maclaurin summation formula --- Abel’s partial summation formula --- half-discrete Hilbert-type inequality --- upper limit function --- Hermite–Hadamard inequality --- (p, q)-calculus --- convex functions --- trapezoid-type inequality --- fractional integrals --- functions of bounded variations --- (p,q)-integral --- post quantum calculus --- convex function --- a priori bounds --- 2D primitive equations --- continuous dependence --- heat source --- Jensen functional --- A-G-H inequalities --- global bounds --- power means --- Simpson-type inequalities --- thermoelastic plate --- Phragmén-Lindelöf alternative --- Saint-Venant principle --- biharmonic equation --- symmetric function --- Schur-convexity --- inequality --- special means --- Shannon entropy --- Tsallis entropy --- Fermi–Dirac entropy --- Bose–Einstein entropy --- arithmetic mean --- geometric mean --- Young’s inequality --- Simpson’s inequalities --- post-quantum calculus --- spatial decay estimates --- Brinkman equations --- midpoint and trapezoidal inequality --- Simpson’s inequality --- harmonically convex functions --- Simpson inequality --- (n,m)–generalized convexity --- n/a --- Hölder's inequality --- Euler-Maclaurin summation formula --- Abel's partial summation formula --- Hermite-Hadamard inequality --- Phragmén-Lindelöf alternative --- Fermi-Dirac entropy --- Bose-Einstein entropy --- Young's inequality --- Simpson's inequalities --- Simpson's inequality --- (n,m)-generalized convexity

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Word deafness --- Auditory perception --- Auditory pathways --- Language Disorders --- Perceptual Disorders --- Biological Science Disciplines --- Auditory Diseases, Central --- Temporal Lobe --- Cognition Disorders --- Perception --- Afferent Pathways --- Communication Disorders --- Brain Diseases --- Neural Pathways --- Natural Science Disciplines --- Cerebral Cortex --- Retrocochlear Diseases --- Neurobehavioral Manifestations --- Mental Processes --- Delirium, Dementia, Amnestic, Cognitive Disorders --- Mental Disorders --- Behavior and Behavior Mechanisms --- Cerebrum --- Psychological Phenomena and Processes --- Neurologic Manifestations --- Central Nervous System Diseases --- Nervous System --- Disciplines and Occupations --- Ear Diseases --- Otorhinolaryngologic Diseases --- Signs and Symptoms --- Psychiatry and Psychology --- Nervous System Diseases --- Anatomy --- Telencephalon --- Diseases --- Prosencephalon --- Pathological Conditions, Signs and Symptoms --- Brain --- Central Nervous System --- Auditory Perception --- Auditory Perceptual Disorders --- Language Development Disorders --- Auditory Cortex --- Physiology --- Auditory Pathways --- Medicine --- Health & Biological Sciences --- Neurology --- Auditory Area --- Heschl's Convolutions --- Heschl's Gyri --- Primary Auditory Cortex --- Temporal Auditory Area --- Transverse Temporal Gyri --- Area, Auditory --- Area, Temporal Auditory --- Areas, Auditory --- Areas, Temporal Auditory --- Auditory Area, Temporal --- Auditory Areas --- Auditory Areas, Temporal --- Auditory Cortex, Primary --- Auditory Cortices, Primary --- Convolutions, Heschl's --- Cortex, Auditory --- Cortex, Primary Auditory --- Cortices, Primary Auditory --- Gyri, Heschl's --- Gyri, Transverse Temporal --- Gyrus, Transverse Temporal --- Heschl Convolutions --- Heschl Gyri --- Heschls Convolutions --- Heschls Gyri --- Primary Auditory Cortices --- Temporal Auditory Areas --- Temporal Gyri, Transverse --- Temporal Gyrus, Transverse --- Transverse Temporal Gyrus --- Auditory Processing Disorder, Central --- Central Auditory Processing Disorder --- Developmental Disorder, Speech or Language --- Developmental Language Disorders --- Language Disorders, Developmental --- Semantic-Pragmatic Disorder --- Speech or Language, Developmental Disorder --- Language Delay --- Speech Delay --- Delay, Speech --- Delays, Speech --- Development Disorder, Language --- Developmental Language Disorder --- Disorder, Language Development --- Disorders, Language Development --- Language Delays --- Language Development Disorder --- Language Disorder, Developmental --- Semantic Pragmatic Disorder --- Semantic-Pragmatic Disorders --- Speech Delays --- Specific Language Disorder --- Auditory Comprehension Disorder --- Auditory Inattention --- Auditory Processing Disorder --- Psychoacoustical Disorders --- Acoustic Perceptual Disorder --- Perceptual Disorders, Auditory --- Acoustic Perceptual Disorders --- Auditory Comprehension Disorders --- Auditory Inattentions --- Auditory Perceptual Disorder --- Auditory Processing Disorders --- Comprehension Disorder, Auditory --- Comprehension Disorders, Auditory --- Disorder, Acoustic Perceptual --- Disorder, Auditory Comprehension --- Disorder, Auditory Processing --- Disorder, Psychoacoustical --- Disorders, Acoustic Perceptual --- Disorders, Auditory Comprehension --- Disorders, Auditory Processing --- Disorders, Psychoacoustical --- Inattention, Auditory --- Inattentions, Auditory --- Perceptual Disorder, Acoustic --- Perceptual Disorder, Auditory --- Perceptual Disorders, Acoustic --- Processing Disorder, Auditory --- Processing Disorders, Auditory --- Psychoacoustical Disorder --- Auditory Processing --- Perception, Auditory --- Processing, Auditory --- Hearing --- Cerebrospinal Axis --- Axi, Cerebrospinal --- Axis, Cerebrospinal --- Central Nervous Systems --- Cerebrospinal Axi --- Nervous System, Central --- Nervous Systems, Central --- Systems, Central Nervous --- Encephalon --- Symptoms and General Pathology --- Forebrain --- Forebrains --- Endbrain --- Endbrains --- Anatomies --- Nervous System Disorders --- Neurological Disorders --- Neurologic Disorders --- Disease, Nervous System --- Diseases, Nervous System --- Disorder, Nervous System --- Disorder, Neurologic --- Disorder, Neurological --- Disorders, Nervous System --- Disorders, Neurologic --- Disorders, Neurological --- Nervous System Disease --- Nervous System Disorder --- Neurologic Disorder --- Neurological Disorder --- Symptoms and Signs --- Auditory system --- Afferent pathways --- Sound perception --- Acoustic aphasia --- Amnesia, Auditory --- Aphememesthesia --- Auditory amnesia --- Auditory aphasia --- Auditory perceptual disorders --- Auditory processing disorder --- Auditory sensory deficit --- Auditory sequencing problems --- Central auditory dysfunction --- Central auditory processing disorder --- Central deafness --- Central hearing loss --- Deafness, Central --- Hearing loss, Central --- Logokophosis --- Receptive aphasia --- Aphasia --- Hearing disorders --- Perceptual disorders --- ENT Diseases --- Otolaryngological Diseases --- Otorhinolaryngologic Disease --- Otorhinolaryngological Disease --- Otolaryngologic Diseases --- Disease, ENT --- Disease, Otolaryngologic --- Disease, Otolaryngological --- Disease, Otorhinolaryngologic --- Disease, Otorhinolaryngological --- Diseases, ENT --- Diseases, Otolaryngologic --- Diseases, Otolaryngological --- Diseases, Otorhinolaryngologic --- Diseases, Otorhinolaryngological --- ENT Disease --- Otolaryngologic Disease --- Otolaryngological Disease --- Otorhinolaryngological Diseases --- Otolaryngology --- Otological Diseases --- Otologic Diseases --- Disease, Ear --- Disease, Otologic --- Disease, Otological --- Ear Disease --- Otologic Disease --- Otological Disease --- Nervous Systems --- System, Nervous --- Systems, Nervous --- CNS Diseases --- Central Nervous System Disorders --- CNS Disease --- Central Nervous System Disease --- Central Nervous System Disorder --- Focal Neurologic Deficits --- Manifestations, Neurologic --- Manifestations, Neurological --- Neurologic Dysfunction --- Neurologic Findings --- Neurologic Manifestation --- Neurologic Signs --- Neurologic Symptoms --- Neurological Manifestations --- Neurologic Deficits --- Neurologic Signs and Symptoms --- Deficit, Focal Neurologic --- Deficit, Neurologic --- Deficits, Focal Neurologic --- Deficits, Neurologic --- Dysfunction, Neurologic --- Dysfunctions, Neurologic --- Finding, Neurologic --- Findings, Neurologic --- Focal Neurologic Deficit --- Manifestation, Neurologic --- Manifestation, Neurological --- Neurologic Deficit --- Neurologic Deficit, Focal --- Neurologic Deficits, Focal --- Neurologic Dysfunctions --- Neurologic Finding --- Neurologic Sign --- Neurologic Symptom --- Neurological Manifestation --- Sign, Neurologic --- Signs, Neurologic --- Symptom, Neurologic --- Symptoms, Neurologic --- Psychologic Processes --- Psychologic Processes and Principles --- Psychological Processes --- Phenomena, Psychological --- Processes, Psychologic --- Processes, Psychological --- Psychological Phenomenas --- Psychological Processe --- Cerebral Hemispheres --- Left Cerebral Hemisphere --- Right Cerebral Hemisphere --- Cerebral Hemisphere --- Cerebral Hemisphere, Left --- Cerebral Hemisphere, Right --- Behavior And Behavior Mechanism --- Behavior Disorders --- Diagnosis, Psychiatric --- Mental Disorders, Severe --- Psychiatric Diagnosis --- Mental Illness --- Psychiatric Diseases --- Psychiatric Disorders --- Psychiatric Illness --- Illness, Mental --- Mental Disorder --- Mental Disorder, Severe --- Mental Illnesses --- Psychiatric Disease --- Psychiatric Disorder --- Psychiatric Illnesses --- Severe Mental Disorder --- Severe Mental Disorders --- Mentally Ill Persons --- Nonpsychotic Organic Brain Syndrome --- Clerambault Syndrome --- Kandinsky Syndrome --- Mental Disorders, Organic --- Organic Brain Syndrome, Nonpsychotic --- Organic Mental Disorders --- Organic Mental Disorders, Psychotic --- Psychoses, Traumatic --- Disorder, Neurocognitive --- Disorders, Neurocognitive --- Disorders, Organic Mental --- Mental Disorder, Organic --- Neurocognitive Disorder --- Organic Mental Disorder --- Traumatic Psychoses --- Human Information Processing --- Information Processing, Human --- Cognitive Manifestations --- Neurobehavioral Signs and Symptoms --- Cognitive Symptoms --- Signs and Symptoms, Neurobehavioral --- Cognitive Manifestation --- Cognitive Symptom --- Manifestation, Cognitive --- Manifestation, Neurobehavioral --- Manifestations, Cognitive --- Manifestations, Neurobehavioral --- Neurobehavioral Manifestation --- Symptom, Cognitive --- Symptoms, Cognitive --- Retrocochlear Hearing Loss --- Disease, Retrocochlear --- Diseases, Retrocochlear --- Hearing Loss, Retrocochlear --- Retrocochlear Disease --- Allocortex --- Archipallium --- Cortex Cerebri --- Cortical Plate --- Insular Cortex --- Paleocortex --- Periallocortex --- Insula of Reil --- Allocortices --- Archipalliums --- Cerebral Cortices --- Cerebri, Cortex --- Cerebrus, Cortex --- Cortex Cerebrus --- Cortex, Cerebral --- Cortex, Insular --- Cortical Plates --- Cortices, Cerebral --- Cortices, Insular --- Insular Cortices --- Paleocortices --- Periallocortices --- Plate, Cortical --- Plates, Cortical --- Reil Insula --- Natural Sciences --- Physical Sciences --- Discipline, Natural Science --- Disciplines, Natural Science --- Natural Science --- Natural Science Discipline --- Physical Science --- Science, Natural --- Science, Physical --- Sciences, Natural --- Sciences, Physical --- Neural Interconnections --- Interconnection, Neural --- Interconnections, Neural --- Neural Interconnection --- Neural Pathway --- Pathway, Neural --- Pathways, Neural --- Peripheral Nervous System --- Brain Disorders --- CNS Disorders, Intracranial --- Central Nervous System Disorders, Intracranial --- Central Nervous System Intracranial Disorders --- Encephalon Diseases --- Encephalopathy --- Intracranial CNS Disorders --- Intracranial Central Nervous System Disorders --- Brain Disease --- Brain Disorder --- CNS Disorder, Intracranial --- Encephalon Disease --- Encephalopathies --- Intracranial CNS Disorder --- Acquired Communication Disorders --- Childhood Communication Disorders --- Communication Disabilities --- Communication Disorders, Childhood --- Communication Disorders, Developmental --- Communication Disorders, Neurogenic --- Communicative Disorders --- Communicative Dysfunction --- Developmental Communication Disorders --- Neurogenic Communication Disorders --- Acquired Communication Disorder --- Childhood Communication Disorder --- Communication Disability --- Communication Disorder --- Communication Disorder, Acquired --- Communication Disorder, Childhood --- Communication Disorder, Developmental --- Communication Disorder, Neurogenic --- Communication Disorders, Acquired --- Communicative Disorder --- Communicative Dysfunctions --- Developmental Communication Disorder --- Disabilities, Communication --- Disability, Communication --- Dysfunction, Communicative --- Dysfunctions, Communicative --- Neurogenic Communication Disorder --- Afferent Pathway --- Pathway, Afferent --- Pathways, Afferent --- Sensory Processing --- Processing, Sensory --- Sensation --- Auditory Pathway --- Pathway, Auditory --- Pathways, Auditory --- Trapezoid Body --- Biologic Sciences --- Biological Science --- Science, Biological --- Sciences, Biological --- Biological Sciences --- Life Sciences --- Biologic Science --- Biological Science Discipline --- Discipline, Biological Science --- Disciplines, Biological Science --- Life Science --- Science Discipline, Biological --- Science Disciplines, Biological --- Science, Biologic --- Science, Life --- Sciences, Biologic --- Sciences, Life --- Hemisensory Neglect --- Sensory Neglect --- Somatosensory Discrimination Disorder --- Hemispatial Neglect --- Discrimination Disorder, Somatosensory --- Discrimination Disorders, Somatosensory --- Hemisensory Neglects --- Hemispatial Neglects --- Neglect, Hemisensory --- Neglect, Hemispatial --- Neglect, Sensory --- Neglects, Hemisensory --- Perceptual Disorder --- Sensory Neglects --- Somatosensory Discrimination Disorders --- Perceptual Distortion --- Acquired Language Disorders --- Language Disorders, Acquired --- Acquired Language Disorder --- Language Disorder --- Language Disorder, Acquired --- Speech Disorders --- Verbal Behavior --- Verbal Learning --- Overinclusion --- Disorder, Cognition --- Disorders, Cognition --- Cognitive Aging --- Fusiform Gyrus --- Gyrus Fusiformis --- Gyrus Temporalis Superior --- Inferior Horn of Lateral Ventricle --- Inferior Horn of the Lateral Ventricle --- Lateral Occipito-Temporal Gyrus --- Lateral Occipitotemporal Gyrus --- Occipitotemporal Gyrus --- Planum Polare --- Superior Temporal Gyrus --- Temporal Cortex --- Temporal Gyrus --- Temporal Horn --- Temporal Horn of the Lateral Ventricle --- Temporal Operculum --- Temporal Region --- Temporal Sulcus --- Cortex, Temporal --- Cortices, Temporal --- Fusiformi, Gyrus --- Fusiformis, Gyrus --- Gyrus Fusiformi --- Gyrus Temporalis Superiors --- Gyrus, Fusiform --- Gyrus, Lateral Occipito-Temporal --- Gyrus, Lateral Occipitotemporal --- Gyrus, Occipitotemporal --- Gyrus, Superior Temporal --- Gyrus, Temporal --- Horn, Temporal --- Horns, Temporal --- Lateral Occipito Temporal Gyrus --- Lobe, Temporal --- Lobes, Temporal --- Occipito-Temporal Gyrus, Lateral --- Occipitotemporal Gyrus, Lateral --- Operculum, Temporal --- Operculums, Temporal --- Planum Polares --- Polare, Planum --- Polares, Planum --- Region, Temporal --- Regions, Temporal --- Sulcus, Temporal --- Superior, Gyrus Temporalis --- Superiors, Gyrus Temporalis --- Temporal Cortices --- Temporal Gyrus, Superior --- Temporal Horns --- Temporal Lobes --- Temporal Operculums --- Temporal Regions --- Temporalis Superior, Gyrus --- Temporalis Superiors, Gyrus --- Auditory Dysfunction, Central --- Auditory Pathway Disorders, Central --- Central Auditory Pathway Disorders --- Auditory Cortex Disorder --- Central Auditory Diseases --- Auditory Cortex Disorders --- Auditory Disease, Central --- Central Auditory Disease --- Central Auditory Dysfunction --- Cortex Disorder, Auditory --- Cortex Disorders, Auditory --- Dysfunction, Central Auditory --- Dysfunctions, Central Auditory --- Language Development Disorders. --- Auditory Perceptual Disorders. --- physiopathology. --- physiology.