“…In [1] we have offered a solution to this problem by determining two spatially dependent nPDF sets, EPS09s and EKS98s, using the A-systematics of the earlier global fits EPS09 and EKS98 and an assumption that the spatial dependence can be written as a power series of the nuclear thickness function. For a data comparison, we have calculated the nuclear modification factor of inclusive neutral pion production in d+Au collisions at RHIC in four centrality bins at midrapidity and compared these to a PHENIX measurement. …”
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“…Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. …”
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“…Consider a space M, a map f:M\to M, and a function g:M \to {\mathbb C}. The formal power series \zeta (z) = \exp \sum ^\infty _{m=1} \frac {z^m}{m} \sum _{x \in \mathrm {Fix}\,f^m} \prod ^{m-1}_{k=0} g (f^kx) yields an example of a dynamical zeta function. …”
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“…PREFACEPRELIMINARIES Sets FunctionsREAL NUMBERSField AxiomsOrder Axioms Natural Numbers, Integers, Rational NumbersCompleteness Axiom Decimal Representation of Real Numbers Countable SetsSEQUENCESSequences and ConvergenceProperties of Convergent Sequences Monotonic SequencesThe Cauchy Criterion Subsequences Upper and Lower Limits Open and Closed Sets INFINITE SERIESBasic Properties Convergence TestsLIMIT OF A FUNCTIONLimit of a Function Basic Theorems Some Extensions of the LimitMonotonic Functions CONTINUITY Continuous Functions Combinations of Continuous Functions Continuity on an IntervalUniformContinuityCompact Sets and ContinuityDIFFERENTIATION The DerivativeTheMean Value TheoremL'Hôpital's RuleTaylor's TheoremTHE RIEMANN INTEGRALRiemann Integrability Darboux's Theorem and Riemann SumsProperties of the Integral The Fundamental Theorem of Calculus Improper IntegralsSEQUENCES AND SERIES OF FUNCTIONSSequences of FunctionsProperties of Uniform ConvergenceSeries of FunctionsPower Series LEBESGUE MEASURE Classes of Subsets of R Lebesgue Outer Measure Lebesgue Measure Measurable Functions LEBESGUE INTEGRATIONDefinition of the Lebesgue IntegralProperties of the Lebesgue Integral Lebesgue Integral and Pointwise ConvergenceLebesgue and Riemann IntegralsREFERENCESNOTATIONINDEX.…”
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“…It is based on the same principle of a Taylor expansion (power series), but applied to the complex domain.</p> <p>We will discuss which are the multipoles of the simplest case: the field generated by a current line. …”
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“…A prominent role in the violations of duality seems to belong to the so called exponential terms which, conceptually, may represent the (truncated) tail of the power series. A qualitative model, relying on an instanton background field, is developed allowing one to get an estimate of the exponential terms. …”
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“…In this approach, the solution is considered as a power series expansion that converges rapidly to the nonlinear problem. …”
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“…Although the results of the three methods look different, power series expansions show their consistency.…”
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“…It is based on a formal calculus involving a power series used to deduce a recursive formula for the new coefficients. …”
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“…A simple and easy to implement method for improving the convergence of a power series is presented. We observe that the most obvious or analytically convenient point about which to make a series expansion is not always the most computationally efficient. …”
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“…Fractional coin flipping does not reflect any physical process, being defined as a binomial power series of the transition matrix for “integer” flipping. …”
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“…In the article, we provide a monotonicity rule for the function [Formula: see text] , where [Formula: see text] is a positive differentiable and decreasing function defined on [Formula: see text] ([Formula: see text] ), and [Formula: see text] and [Formula: see text] are two real power series converging on [Formula: see text] such that the sequence [Formula: see text] is increasing (decreasing) with [Formula: see text] and [Formula: see text] for all [Formula: see text] . …”
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“…The solution is created by analytically continuing the divergent power series solution such that it matches the long-time asymptotic behavior of the epidemic model. …”
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“…Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. …”
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“…We work under the assumption that the spatial dependence can be formulated as a power series of the nuclear thickness functions $T_A$. …”
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“…The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. …”
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“…This is not a personal choice: it follows logically from tracking codes overloaded with a truncated power series algebra package. After defining abstractly and briefly what a tracking code is, the author illustrates most of the accelerator perturbation theory using an actual code: PTC. …”
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“…Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. …”
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“…IntroductionCommentsOn the structure of this bookOn mathematical language and notationBackground (elements of theory)SetsFunctionsFUNCTIONS OF ONE REAL VARIABLEElementary properties of functionsElements of theoryFunction definitionBoundednessPeriodicityEven/odd functionsMonotonicityExtremaExercisesLimitsElements of theoryConceptsElementary properties (arithmetic and comparative)ExercisesContinuityElements of theoryLocal propertiesGlobal properties: general resultsGlobal properties: the famous theorems Mapping setsWeierstrass theoremsIntermediate Value theoremUniform continuityExercisesDifferentiationElements of theoryConceptsLocal propertiesGlobal propertiesApplicationsTangent lineMonotonicity and local extremaConvexity and inflectionAsymptotesL'Hospital's ruleExercisesIntegralsElements of theoryIndefinite integralDefinite (Riemann) integralImproper integralsApplicationsExercisesSequences and seriesElements of theoryNumerical sequencesNumerical series: convergence and elementary propertiesNumerical series: convergence testsPower seriesExercisesFUNCTIONS OF TWO REAL VARIABLESLimits and continuityElements of theoryOne-dimensional linksConcepts and local propertiesGlobal propertiesMultidimensional essentialsExercisesDifferentiabilityElements of TheoryOne-dimensional linksConcepts and local propertiesGlobal properties and applicationsMultidimensional essentialsExercisesIntegrabilityElements of theoryOne-dimensional linksMultidimensional essentialsExercisesBibliographySymbol DescriptionIndex.…”
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“…The present study proposes a robust maximum correntropy autoregressive (MCAR) forecasting model by examining the case of actual power series of Hanzhong City, Shaanxi province, China. …”
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