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In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function. This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization. The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants. This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.
Convex functions. --- Gamma functions. --- Functions, Convex --- Functions of real variables --- Functions, Gamma --- Transcendental functions --- Difference Equation --- Higher Order Convexity --- Bohr-Mollerup's Theorem --- Principal Indefinite Sums --- Gauss' Limit --- Euler Product Form --- Raabe's Formula --- Binet's Function --- Stirling's Formula --- Euler's Infinite Product --- Euler's Reflection Formula --- Weierstrass' Infinite Product --- Gauss Multiplication Formula --- Euler's Constant --- Gamma Function --- Polygamma Functions --- Hurwitz Zeta Function --- Generalized Stieltjes Constants
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The advancement in manufacturing technology and scientific research has improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical and or mechanical uncertainties of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales.
prestressed concrete cylinder pipe --- external prestressed steel strands --- theoretical study --- wire-breakage --- first-principles calculation --- Heusler compounds --- gapless half metals --- spin gapless semiconductor --- bi-directional functionally graded --- bolotin scheme --- dynamic stability --- elastic foundation --- porosity --- two-axis four-gimbal --- electro-optical pod --- dynamics modeling --- coarse–fine composite --- Carbon-fiber-reinforced plastics (CFRPs) --- fastener --- arc --- Joule heat --- finite element analysis (FEA) --- piezoelectric effect --- bimodular model --- functionally-graded materials --- cantilever --- vibration --- functional reinforcement --- graphene nanoplatelets --- higher-order shear deformable laminated beams --- nanocomposites --- nonlinear free vibration --- sandwich beams --- fractional calculus --- Riemann-Liouville fractional derivative --- viscoelasticity --- pipe flow --- fractional Maxwell model --- fractional Zener model --- fractional Burgers model --- Riemann–Liouville fractional derivative --- fractional Kelvin–Voigt model --- fractional Poynting–Thomson model --- curved sandwich nanobeams --- nonlocal strain gradient theory --- quasi-3D higher-order shear theory --- thermal-buckling --- FG-GPL --- GDQ --- heat transfer equation --- higher-order shear deformation theory --- buckling --- FE-GDQ --- functionally graded materials --- 3D elasticity --- 3D shell model --- steady-state hygro-elastic analysis --- Fick moisture diffusion equation --- moisture content profile --- layer-wise approach --- n/a --- coarse-fine composite --- fractional Kelvin-Voigt model --- fractional Poynting-Thomson model
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The advancement in manufacturing technology and scientific research has improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical and or mechanical uncertainties of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales.
Technology: general issues --- History of engineering & technology --- prestressed concrete cylinder pipe --- external prestressed steel strands --- theoretical study --- wire-breakage --- first-principles calculation --- Heusler compounds --- gapless half metals --- spin gapless semiconductor --- bi-directional functionally graded --- bolotin scheme --- dynamic stability --- elastic foundation --- porosity --- two-axis four-gimbal --- electro-optical pod --- dynamics modeling --- coarse-fine composite --- Carbon-fiber-reinforced plastics (CFRPs) --- fastener --- arc --- Joule heat --- finite element analysis (FEA) --- piezoelectric effect --- bimodular model --- functionally-graded materials --- cantilever --- vibration --- functional reinforcement --- graphene nanoplatelets --- higher-order shear deformable laminated beams --- nanocomposites --- nonlinear free vibration --- sandwich beams --- fractional calculus --- Riemann-Liouville fractional derivative --- viscoelasticity --- pipe flow --- fractional Maxwell model --- fractional Zener model --- fractional Burgers model --- fractional Kelvin-Voigt model --- fractional Poynting-Thomson model --- curved sandwich nanobeams --- nonlocal strain gradient theory --- quasi-3D higher-order shear theory --- thermal-buckling --- FG-GPL --- GDQ --- heat transfer equation --- higher-order shear deformation theory --- buckling --- FE-GDQ --- functionally graded materials --- 3D elasticity --- 3D shell model --- steady-state hygro-elastic analysis --- Fick moisture diffusion equation --- moisture content profile --- layer-wise approach
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This book contains seven reviews and four research articles on the various modern approaches to the problem of quark confinement in quantum chromodynamics (QCD). These approaches include microscopic models of the Yang–Mills vacuum, which are based on the condensation of magnetic monopoles and center vortices, as well as the models of the confining quark-antiquark string. Possible applications of these models to the analysis of the novel superinsulating state, which emerges in such condensed-matter systems as Josephson junction arrays, are further discussed in one of the reviews. Two reviews from this collection discuss the approaches towards the analytic construction of effective confining theories, at the classical level and within the center-vortex model of the Yang–Mills vacuum. Other aspects of non-perturbative physics addressed by this collection include a possible connection between the localization of low-lying Dirac eigenmodes with the deconfinement and the chiral QCD phase transitions, as well as the role of topology in baryon-rich matter. Last but not least, a novel model of dark matter, based on ultralight axion particles, whose masses are arising due to distinct SU(2) Yang–Mills scales and the Planck mass, is suggested and developed in one of the contributed articles.
Research & information: general --- quantum chromodynamics --- confinement --- center vortex model --- vacuum structure --- cooling --- Lattice Gauge Theories --- Effective String Theories --- localization --- QCD --- lattice gauge theory --- finite temperature --- galaxy rotation curves --- low surface brightness --- dark matter --- dark energy --- ultralight axion particles --- cores --- halos --- mass-density --- profiles --- pure Yang–Mills theory --- monopoles --- topological interactions --- ensembles and effective fields --- topological solitons --- higher order theories --- gauge theory --- effective field theory --- magnetic flux symmetry --- chiral symmetry --- monopole --- lattice QCD --- spontaneous symmetry breaking --- Abelian projection --- magnetic catalysis --- magnetic disorder --- confinement models --- center vortices --- magnetic monopoles --- quark condensate --- topology --- lattice field theory --- dense matter --- phase transitions --- n/a --- pure Yang-Mills theory
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This book contains seven reviews and four research articles on the various modern approaches to the problem of quark confinement in quantum chromodynamics (QCD). These approaches include microscopic models of the Yang–Mills vacuum, which are based on the condensation of magnetic monopoles and center vortices, as well as the models of the confining quark-antiquark string. Possible applications of these models to the analysis of the novel superinsulating state, which emerges in such condensed-matter systems as Josephson junction arrays, are further discussed in one of the reviews. Two reviews from this collection discuss the approaches towards the analytic construction of effective confining theories, at the classical level and within the center-vortex model of the Yang–Mills vacuum. Other aspects of non-perturbative physics addressed by this collection include a possible connection between the localization of low-lying Dirac eigenmodes with the deconfinement and the chiral QCD phase transitions, as well as the role of topology in baryon-rich matter. Last but not least, a novel model of dark matter, based on ultralight axion particles, whose masses are arising due to distinct SU(2) Yang–Mills scales and the Planck mass, is suggested and developed in one of the contributed articles.
quantum chromodynamics --- confinement --- center vortex model --- vacuum structure --- cooling --- Lattice Gauge Theories --- Effective String Theories --- localization --- QCD --- lattice gauge theory --- finite temperature --- galaxy rotation curves --- low surface brightness --- dark matter --- dark energy --- ultralight axion particles --- cores --- halos --- mass-density --- profiles --- pure Yang–Mills theory --- monopoles --- topological interactions --- ensembles and effective fields --- topological solitons --- higher order theories --- gauge theory --- effective field theory --- magnetic flux symmetry --- chiral symmetry --- monopole --- lattice QCD --- spontaneous symmetry breaking --- Abelian projection --- magnetic catalysis --- magnetic disorder --- confinement models --- center vortices --- magnetic monopoles --- quark condensate --- topology --- lattice field theory --- dense matter --- phase transitions --- n/a --- pure Yang-Mills theory
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This book contains seven reviews and four research articles on the various modern approaches to the problem of quark confinement in quantum chromodynamics (QCD). These approaches include microscopic models of the Yang–Mills vacuum, which are based on the condensation of magnetic monopoles and center vortices, as well as the models of the confining quark-antiquark string. Possible applications of these models to the analysis of the novel superinsulating state, which emerges in such condensed-matter systems as Josephson junction arrays, are further discussed in one of the reviews. Two reviews from this collection discuss the approaches towards the analytic construction of effective confining theories, at the classical level and within the center-vortex model of the Yang–Mills vacuum. Other aspects of non-perturbative physics addressed by this collection include a possible connection between the localization of low-lying Dirac eigenmodes with the deconfinement and the chiral QCD phase transitions, as well as the role of topology in baryon-rich matter. Last but not least, a novel model of dark matter, based on ultralight axion particles, whose masses are arising due to distinct SU(2) Yang–Mills scales and the Planck mass, is suggested and developed in one of the contributed articles.
Research & information: general --- quantum chromodynamics --- confinement --- center vortex model --- vacuum structure --- cooling --- Lattice Gauge Theories --- Effective String Theories --- localization --- QCD --- lattice gauge theory --- finite temperature --- galaxy rotation curves --- low surface brightness --- dark matter --- dark energy --- ultralight axion particles --- cores --- halos --- mass-density --- profiles --- pure Yang-Mills theory --- monopoles --- topological interactions --- ensembles and effective fields --- topological solitons --- higher order theories --- gauge theory --- effective field theory --- magnetic flux symmetry --- chiral symmetry --- monopole --- lattice QCD --- spontaneous symmetry breaking --- Abelian projection --- magnetic catalysis --- magnetic disorder --- confinement models --- center vortices --- magnetic monopoles --- quark condensate --- topology --- lattice field theory --- dense matter --- phase transitions
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Intelligence research is mainly concerned with basic science questions; what is the psychometric structure of intelligence? What are the cognitive bases of intelligence? What are the brain-based correlates of intelligence? What does intelligence predict? Such research is needed, but there are also problems larger than those presented in intelligence tests, including problems of today. What is the role of human intelligence in solving consequential real-world problems? Here, leading scholars in the field of intelligence each address one real-world problem—a problem of their choice—and explain how intelligence has been, or could be, essential for a solution.
Humanities --- Social interaction --- intelligence --- IQ --- giftedness --- transactional giftedness --- transformational giftedness --- critical thinking --- real-world problems --- innovation --- talent selection and development --- gifted education --- social returns --- cognitive aptitudes and creativity --- grand societal challenges --- Sustainable Development Goals --- complex problems --- consequential world problems --- mental tests --- cognitive ageing --- cognitive epidemiology --- mortality --- cognitive development --- wisdom --- education --- conflict resolution --- problem-solving --- decision making --- history-wars --- Wechsler scales --- WAIS-IV --- federal judges --- Supreme Court --- fluid reasoning --- processing speed --- crystallized knowledge --- working memory --- aging-IQ research --- computerized adaptive testing --- test construction --- collective intelligence --- metacognition --- wellbeing --- inequity --- social issues --- functional literacy --- job complexity --- nonadherence to treatment --- noncommunicable disease --- diabetes --- diabetes self-management --- behavioral risk factors --- global burden of disease --- epidemiological transition --- social movements --- theory of social change, cultural evolution, and human development --- social intelligence --- practical intelligence --- abstract intelligence --- COVID-19 --- cultural evolution --- adaptive intelligence --- George Floyd protests --- higher-order thinking --- real-world environments --- infectious diseases
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Exploring quality of vision is one of the most important issues in modern ophthalmology, and research into ophthalmic optics and visual function is essential for making progress in this field. The present Special Issue aims to enlighten readers about the broad range of clinical research in the field of ophthalmic optics and visual function, mainly related to the anterior segment and myopia control. Submissions of original research articles were welcomed that highlight innovative findings with the potential to enhance the clinical capabilities of diagnosing and monitoring ophthalmic conditions and treatments especially of the anterior segment. Review articles of high interest were also considered for publication.
Medicine --- refractive error --- visual acuity --- myopia --- amplitude of accommodation --- pupillary diameter --- presbyopia --- cataract --- crystalline lens --- subjective refraction --- axial length of the eye --- contrast sensitivity function --- epiphora --- lacrimal passage obstruction --- lacrimal passage intubation --- refraction --- fogging --- monocular/binocular view --- precision --- LASIK --- happiness --- satisfaction --- anisometropia --- axial length --- school children --- light environment --- violet light --- illuminance --- contrast sensitivity --- AULCSF --- intraocular scattering --- higher-order aberrations --- quality of life --- RSVP questionnaire --- presbyLASIK --- excimer laser --- multifocality --- pseudophakic --- glaucoma --- ametropia --- hyperopia --- visual field --- OCT --- SITA standard 24-2 --- pattern deviation --- mean deviation --- spherical equivalent --- phakic intraocular lens --- multicentre study --- 0.01% atropine --- myopia control --- standardized equivalent refraction --- near visual acuity --- standard criterion --- diagnosis --- prevalence of myopia --- degree of myopia --- high-pressure education --- pressure-free education --- Yutori education --- accommodation --- anterior segment optical coherence tomography --- low-concentration atropine --- ocular biometric components --- eyeglasses --- double blinded randomized controlled trial --- n/a
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Exploring quality of vision is one of the most important issues in modern ophthalmology, and research into ophthalmic optics and visual function is essential for making progress in this field. The present Special Issue aims to enlighten readers about the broad range of clinical research in the field of ophthalmic optics and visual function, mainly related to the anterior segment and myopia control. Submissions of original research articles were welcomed that highlight innovative findings with the potential to enhance the clinical capabilities of diagnosing and monitoring ophthalmic conditions and treatments especially of the anterior segment. Review articles of high interest were also considered for publication.
refractive error --- visual acuity --- myopia --- amplitude of accommodation --- pupillary diameter --- presbyopia --- cataract --- crystalline lens --- subjective refraction --- axial length of the eye --- contrast sensitivity function --- epiphora --- lacrimal passage obstruction --- lacrimal passage intubation --- refraction --- fogging --- monocular/binocular view --- precision --- LASIK --- happiness --- satisfaction --- anisometropia --- axial length --- school children --- light environment --- violet light --- illuminance --- contrast sensitivity --- AULCSF --- intraocular scattering --- higher-order aberrations --- quality of life --- RSVP questionnaire --- presbyLASIK --- excimer laser --- multifocality --- pseudophakic --- glaucoma --- ametropia --- hyperopia --- visual field --- OCT --- SITA standard 24-2 --- pattern deviation --- mean deviation --- spherical equivalent --- phakic intraocular lens --- multicentre study --- 0.01% atropine --- myopia control --- standardized equivalent refraction --- near visual acuity --- standard criterion --- diagnosis --- prevalence of myopia --- degree of myopia --- high-pressure education --- pressure-free education --- Yutori education --- accommodation --- anterior segment optical coherence tomography --- low-concentration atropine --- ocular biometric components --- eyeglasses --- double blinded randomized controlled trial --- n/a
Choose an application
Intelligence research is mainly concerned with basic science questions; what is the psychometric structure of intelligence? What are the cognitive bases of intelligence? What are the brain-based correlates of intelligence? What does intelligence predict? Such research is needed, but there are also problems larger than those presented in intelligence tests, including problems of today. What is the role of human intelligence in solving consequential real-world problems? Here, leading scholars in the field of intelligence each address one real-world problem—a problem of their choice—and explain how intelligence has been, or could be, essential for a solution.
intelligence --- IQ --- giftedness --- transactional giftedness --- transformational giftedness --- critical thinking --- real-world problems --- innovation --- talent selection and development --- gifted education --- social returns --- cognitive aptitudes and creativity --- grand societal challenges --- Sustainable Development Goals --- complex problems --- consequential world problems --- mental tests --- cognitive ageing --- cognitive epidemiology --- mortality --- cognitive development --- wisdom --- education --- conflict resolution --- problem-solving --- decision making --- history-wars --- Wechsler scales --- WAIS-IV --- federal judges --- Supreme Court --- fluid reasoning --- processing speed --- crystallized knowledge --- working memory --- aging-IQ research --- computerized adaptive testing --- test construction --- collective intelligence --- metacognition --- wellbeing --- inequity --- social issues --- functional literacy --- job complexity --- nonadherence to treatment --- noncommunicable disease --- diabetes --- diabetes self-management --- behavioral risk factors --- global burden of disease --- epidemiological transition --- social movements --- theory of social change, cultural evolution, and human development --- social intelligence --- practical intelligence --- abstract intelligence --- COVID-19 --- cultural evolution --- adaptive intelligence --- George Floyd protests --- higher-order thinking --- real-world environments --- infectious diseases
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