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Nonextensive Entropy Econometrics for Low Frequency Series provides a new and robust powerlawbased, nonextensive entropy econometrics approach to the economic modelling of illbehaved inverse problems. Particular attention is paid to national accountbased general equilibrium models known for their relative complexity.In theoretical terms, the approach generalizes GibbsShannonGolan entropy models, which are useful for describing ergodic phenomena. In essence, this entropy econometrics approach constitutes a junction of two distinct concepts: Jayne’s maximum entropy principle and the Bayesian generalized method of moments. Rival econometric techniques are not conceptually adapted to solving complex inverse problems or are seriously limited when it comes to practical implementation. Recent literature showed that amplitude and frequency of macroeconomic fluctuations do not substantially diverge from many other extreme events, natural or humanrelated, once they are explained in the same time (or space) scale. Nonextensive entropy is a precious device for econometric modelling even in the case of low frequency series, since outputs evolving within the Gaussian attractor correspond to the Tsallis entropy limiting case of Tsallis qparameter around unity. This book introduces a subdiscipline called Nonextensive Entropy Econometrics or, using a recent expression, Superstar Generalised Econometrics. It demonstrates, using national accountsbased models, that this approach facilitates solving nonlinear, complex inverse problems, previously considered intractable, such as the constant elasticity of substitution class of functions. This new proposed approach could extend the frontier of theoretical and applied econometrics.
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In this work, the Uncertainty Quantification (UQ) approaches combined systematically to analyze and identify systems. The generalized Polynomial Chaos (gPC) expansion is applied to reduce the computational effort. The framework using gPC based on Bayesian UQ proposed in this work is capable of analyzing the system systematically and reducing the disagreement between the model predictions and the measurements of the real processes to fulfill user defined performance criteria.
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Perseverative cognition is defined as the repetitive or sustained activation of cognitive representations of past stressful events or feared events in the future and even at nonclinical levels it causes a “fightorflight” action tendency, followed by a cascade of biological events, starting in the brain and ending as peripheral stress responses. In the past decade, such persistent physiological activation has proven to impact individuals’ health, potentially leading to somatic disease. As such, perseverative cognition has recently been proposed as the missing piece in the relationships between stress, psychopathology, and risk for health. Perseverative cognition is indeed a hallmark of conditions such as anxiety and mood disorders that are at increased though still unexplained cardiovascular risk. Although the pivotal role of ruminative and worrisome thoughts in determining the onset and maintenance of psychopathological disorders has been acknowledged for a long time, its effects on the body via reciprocal influences between mental processes and the body's physiology have been neglected. Moreover, perseverative cognition is definitely not restricted to psychopathology, it is extremely common and likely even omnipresent, pervading daily life. The objective of the Research Topic is to provide an interdisciplinary examination of cuttingedge neuroscientific research on brainbody signatures of perseverative cognition in both healthy and psychopathological individuals. Despite the evident role of the brain in repetitive thinking and the assumption that our mind is embodied, branbody pathways from perseverative cognition to health risk have remained largely unexplored.
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The pricesetting newsvendor model is used to address the single period joint pricing and inventory control problem. The objective is to set the optimal price and replenishment quantity of a single product in order to maximize the expected profit. Products with a short selling season and relatively long replenishment lead times such as fashion goods are the most relevant application areas of the model. The focus of the work is the generalization of the model with respect to the modeling of uncertainty in demand. The author presents an analytical and empirical study which compares different demand models with a more flexible model based on price and inventory optimization. She concludes that using a general model can increase the profits significantly.
Analytical  Arikan  Control  Empirical  Generalized  Inventory  Lagerhaltungsmodell  Model  Nachfrageverhalten  Optimierung  Period  Preispolitik  Pricing  Single  Study
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A topical research activity in statistical physics concerns the study of complex and disordered systems. Generally, these systems are characterized by an elevated level of interconnection and interaction between the parts so that they give rise to a rich structure in the phase space that selforganizes under the control of internal nonlinear dynamics. These emergent collective dynamics confer new behaviours to the whole system that are no longer the direct consequence of the properties of the single parts, but rather characterize the whole system as a new entity with its own features, giving rise to the birth of new phenomenologies. As is highlighted in this collection of papers, the methodologies of statistical physics have become very promising in understanding these new phenomena. This volume groups together 12 research works showing the use of typical tools developed within the framework of statistical mechanics, in nonlinear kinetic and information geometry, to investigate emerging features in complex physical and physicallike systems.A topical research activity in statistical physics concerns the study of complex and disordered systems. Generally, these systems are characterized by an elevated level of interconnection and interaction between the parts so that they give rise to a rich structure in the phase space that selforganizes under the control of internal nonlinear dynamics. These emergent collective dynamics confer new behaviours to the whole system that are no longer the direct consequence of the properties of the single parts, but rather characterize the whole system as a new entity with its own features, giving rise to the birth of new phenomenologies. As is highlighted in this collection of papers, the methodologies of statistical physics have become very promising in understanding these new phenomena. This volume groups together 12 research works showing the use of typical tools developed within the framework of statistical mechanics, in nonlinear kinetic and information geometry, to investigate emerging features in complex physical and physicallike systems.
Generalized statistical mechanics  information theory  anomalous diffusion  stochastic processes  collective phenomena  disordered systems
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"This book introduces formal grammar theories that play a role in current linguistic theorizing (Phrase Structure Grammar, Transformational Grammar/Government & Binding, Generalized Phrase Structure Grammar, Lexical Functional Grammar, Categorial Grammar, HeadDriven Phrase Structure Grammar, Construction Grammar, Tree Adjoining Grammar). The key assumptions are explained and it is shown how the respective theory treats arguments and adjuncts, the active/passive alternation, local reorderings, verb placement, and fronting of constituents over long distances. The analyses are explained with German as the object language.The second part of the book compares these approaches with respect to their predictions regarding language acquisition and psycholinguistic plausibility. The nativism hypothesis, which assumes that humans posses genetically determined innate languagespecific knowledge, is critically examined and alternative models of language acquisition are discussed. The second part then addresses controversial issues of current theory building such as the question of flat or binary branching structures being more appropriate, the question whether constructions should be treated on the phrasal or the lexical level, and the question whether abstract, nonvisible entities should play a role in syntactic analyses. It is shown that the analyses suggested in the respective frameworks are often translatable into each other. The book closes with a chapter showing how properties common to all languages or to certain classes of languages can be captured.The book is a translation of the German book Grammatiktheorie, which was published by Stauffenburg in 2010. "
generalized phrase structure grammar  lexical functional grammar  categorial grammar  headdriven phrase structure grammar  construction grammar  formal grammar theories  phrase structure grammar  transformational grammar/government & binding  tree adjoining grammar
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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 transSasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds). We wish to mention that among the authors, there are both wellknown 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.
Euclidean submanifold  position vector field  concurrent vector field  concircular vector field  rectifying submanifold  Tsubmanifolds  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 pseudoangle  L2harmonic forms  Hodge–Laplacian  manifold with singularity  L2Stokes theorem  capacity  kth generalized Tanaka–Webster connection  nonflat complex space form  real hypersurface  lie derivative  shape operator  conical surface  developable surface  generalized 1type Gauss map  cylindrical hypersurface  inextensible flow  lightlike surface  ruled surface  Darboux frame  CBochner tensor  generalized normalized ?Casorati curvature  Sasakian manifold  slant  invariant  antiinvariant  transSasakian 3manifold  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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Since the end of the 19th century when the prominent Norwegian mathematician Sophus Lie created the theory of Lie algebras and Lie groups and developed the method of their applications for solving differential equations, his theory and method have continuously been the research focus of many wellknown mathematicians and physicists. This book is devoted to recent development in Lie theory and its applications for solving physically and biologically motivated equations and models. The book contains the articles published in two Special Issue of the journal Symmetry, which are devoted to analysis and classification of Lie algebras, which are invariance algebras of realword models; Lie and conditional symmetry classification problems of nonlinear PDEs; the application of symmetrybased methods for finding new exact solutions of nonlinear PDEs (especially reactiondiffusion equations) arising in applications; the application of the Lie method for solving nonlinear initial and boundaryvalue problems (especially those for modelling processes with diffusion, heat transfer, and chemotaxis).
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent polynomials  (p,q)analogue of tangent numbers and polynomials  (p,q)analogue of tangent zeta function  symmetric identities  zeros  Lommel functions  univalent functions  starlike functions  convex functions  inclusion relationships  analytic function  Hankel determinant  exponential function  upper bound  nonlinear boundary value problems  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint boundary conditions  advanced and deviated arguments  existence of at least one solution  Fredholm integral equation  Schauder fixed point theorem  Hölder condition  generalized Kuramoto–Sivashinsky equation  modified Kudryashov method  exact solutions  Maple graphs  analytic function  Hadamard product (convolution)  partial sum  Srivastava–Tomovski generalization of Mittag–Leffler function  subordination  differential equation  differential inclusion  Liouville–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev polynomials  orthogonality property  symmetric  encryption  password  hash  cryptography  PBKDF  q–Bleimann–Butzer–Hahn operators  (p,q)integers  (p,q)Bernstein operators  (p,q)Bleimann–Butzer–Hahn operators  modulus of continuity  rate of approximation  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  analytic functions  Mittag–Leffler functions  starlike functions  convex functions  Hardy space  vibrating string equation  initial conditions  spectral decomposition  regular solution  the uniqueness of the solution  the existence of a solution  analytic  ?convex function  starlike function  stronglystarlike function  subordination  q Sheffer–Appell polynomials  generating relations  determinant definition  recurrence relation  q Hermite–Bernoulli polynomials  q Hermite–Euler polynomials  q Hermite–Genocchi polynomials  Volterra integral equations  highly oscillatory Bessel kernel  Hermite interpolation  direct Hermite collocation method  piecewise Hermite collocation method  differential operator  qhypergeometric functions  meromorphic function  Mittag–Leffler function  Hadamard product  differential subordination  starlike functions  Bell numbers  radius estimate  (p, q)integers  Dunkl analogue  generating functions  generalization of exponential function  Szász operator  modulus of continuity  function spaces and their duals  distributions  tempered distributions  Schwartz testing function space  generalized functions  distribution space  wavelet transform of generalized functions  Fourier transform  analytic function  subordination  Dziok–Srivastava operator  nonlinear boundary value problem  nonlocal  multipoint  multistrip  existence  Ulam stability  functions of bounded boundary and bounded radius rotations  subordination  functions with positive real part  uniformly starlike and convex functions  analytic functions  univalent functions  starlike and qstarlike functions  qderivative (or qdifference) operator  sufficient conditions  distortion theorems  Janowski functions  analytic number theory  ?generalized Hurwitz–Lerch zeta functions  derivative properties  recurrence relations  integral representations  Mellin transform  natural transform  Adomian decomposition method  Caputo fractional derivative  generalized mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential equations  fuzzy general linear method  fuzzy differential equations  generalized Hukuhara differentiability  spectrum symmetry  DCT  MFCC  audio features  anuran calls  analytic functions  convex functions  starlike functions  strongly convex functions  strongly starlike functions  uniformly convex functions  Struve functions  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.
Fubini polynomials  wtorsion Fubini polynomials  fermionic padic integrals  symmetric identities  Chebyshev polynomials  sums of finite products  hypergeometric function  Fubini polynomials  Euler numbers  symmetric identities  elementary method  computational formula  two variable qBerstein polynomial  two variable qBerstein operator  qEuler number  qEuler polynomial  Fubini polynomials  Euler numbers  congruence  elementary method  qBernoulli numbers  qBernoulli polynomials  two variable qBernstein polynomials  two variable qBernstein operators  padic integral on ?p  the degenerate gamma function  the modified degenerate gamma function  the degenerate Laplace transform  the modified degenerate Laplace transform  Fibonacci  Lucas  linear form in logarithms  continued fraction  reduction method  sums of finite products of Chebyshev polynomials of the third and fourth kinds  Hermite  generalized Laguerre  Legendre  Gegenbauer  Jacobi  thirdorder character  classical Gauss sums  rational polynomials  analytic method  recursive formula  fermionic padic qintegral on ?p  qEuler polynomials  qChanghee polynomials  symmetry group  Apostoltype Frobenius–Euler polynomials  threevariable Hermite polynomials  symmetric identities  explicit relations  operational connection  qVolkenborn integral on ?p  Bernoulli numbers and polynomials  generalized Bernoulli polynomials and numbers of arbitrary complex order  generalized Bernoulli polynomials and numbers attached to a Dirichlet character ?  Changhee polynomials  Changhee polynomials of type two  fermionic padic integral on ?p  Chebyshev polynomials of the first, second, third, and fourth kinds  sums of finite products  representation  catalan numbers  elementary and combinatorial methods  recursive sequence  convolution sums  wellposedness  stability  acoustic wave equation  perfectly matched layer  Fibonacci polynomials  Lucas polynomials  trivariate Fibonacci polynomials  trivariate Lucas polynomials  generating functions  central incomplete Bell polynomials  central complete Bell polynomials  central complete Bell numbers  Legendre polynomials  Laguerre polynomials  generalized Laguerre polynomials  Gegenbauer polynomials  hypergeometric functions 1F1 and 2F1  Euler polynomials  Bernoulli polynomials  elementary method  identity  congruence  new sequence  Catalan numbers  elementary and combinatorial methods  congruence  conjecture  fluctuation theorem  thermodynamics of information  stochastic thermodynamics  mutual information  nonequilibrium free energy  entropy production
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