Related papers: Measurable Taylor's Theorem: An Elementary Proof
We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling…
We present a slightly more general version of Boole's additive formula for factorials as a simple consequence of Lagrange's Interpolating Polynomial theorem.
Let $U$ be a bounded open subset of the complex plane and let $A_{\alpha}(U)$ denote the set of functions analytic on $U$ that also belong to the little Lipschitz class with Lipschitz exponent $\alpha$. It is shown that if $A_{\alpha}(U)$…
This paper reexamines the seminal Lagrange multiplier test for cross-section independence in a large panel model where both the number of cross-sectional units n and the number of time series observations T can be large. The first…
In this Letter we extend the proof, by Faraco and Lindberg, of Taylor's conjecture in multiply connected domains to cover arbitrary vector potentials and remove the need to impose conditions on the magnetic field due to gauge invariance.…
We prove a probabilistic Fourier extension theorem that says Fourier extension holds when averaged over certain smooth Alpert multipliers. The proofs use smooth Alpert wavelets with the classical techniques of stationary phase and…
The standard method for the propagation of errors, based on a Taylor series expansion, is approximate and frequently inadequate for realistic problems. A simple and generic technique is described in which the likelihood is constructed…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…
This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some aspects of the theory of such polynomials. We then give a…
Many applications in Lattice field theory require to determine the Taylor series of observables with respect to action parameters. A primary example is the determination of electromagnetic corrections to hadronic processes. We show two…
It is shown that, for stationary isotropic turbulence, Taylor's well known surrogate for the dissipation can be derived directly from the Karman-Howarth equation and is in fact a surrogate for inertial transfer, which becomes equal to the…
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.
According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters provided that the right sides of the differential…
We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…
An outlier is a datapoint that is set apart from a sample population. The outlier theorem in algorithmic information theory states that given a computable sampling method, outliers must appear. We present a simple proof to the outlier…
The present paper is devoted to possible generalizations of the classic Lagrange Mean Value Theorem. We consider a real-valued function of several variables that is only assumed to be continuous. The main concept is to replace the notion of…
In a family of random variables, Taylor's law or Taylor's power law offluctuation scaling is a variance function that gives the variance $\sigma^{2}>0$ of a random variable (rv) $X$ with expectation $\mu >0$ as a powerof $\mu$: $\sigma…
Myriad articles are devoted to Mertens's theorem. In yet another, we merely wish to draw attention to a proof by Hardy, which uses a Tauberian theorem of Landau that "leads to the conclusion in a direct and elegant manner". Hardy's proof is…
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and…
In this paper we establish the pathwise Taylor expansions for random fields that are "regular" in the spirit of Dupire's path-derivatives \cite{Dupire}. Our result is motivated by but extends the recent result of Buckdahn-Bulla-Ma…