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Статті в журналах з теми "Taylors formula"

Автор: Grafiati

Опубліковано: 28 травня 2022

Оновлено: 31 липня 2025

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1

Ma, Lin. "The Taylor's Theorem and Its Application." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 1368–72. http://dx.doi.org/10.54097/98knf072.

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Анотація:

Taylor's theorem is an essential concept in calculus. By constructing polynomials, Taylor's formula can simplify calculations by approximating complex functions so that a variety of functions can be analyzed in detail. This paper explores the form and proof of Taylor's theorem based on Peano and Lagrange remainder forms as well as the Polynomial interpolation. Then, examples of the application of Taylor’s theorem in mathematics fields, such as limit calculation and high-order derivatives computation, are discussed. Additionally, the applications of Taylor’s theorem in other related subjects ar

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2

Aftab, Muhammad Nasim, Saad Ihsan Butt, and Youngsoo Seol. "Fundamentals of Dual Basic Symmetric Quantum Calculus and Its Fractional Perspectives." Fractal and Fractional 9, no. 4 (2025): 237. https://doi.org/10.3390/fractalfract9040237.

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Taylor expansion is a remarkable tool with broad applications in analysis, science, engineering, and mathematics. In this manuscript, we derive a proof of generalized Taylor expansion for polynomials and write its particular case in symmetric quantum calculus. In addition, we define a novel type of calculus that is called symmetric (p,q)- or dual basic symmetric quantum calculus. Moreover, we derive a symmetric (p,q)-Taylor expansion for polynomials based on this calculus. After that, we investigate Taylor’s formulae through an example. Furthermore, we define symmetric definite (p,q)-integral

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3

Pan, Levi Yiwei. "The Application of Taylor formula in Limits and Approximation." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 891–98. http://dx.doi.org/10.54097/a2nzcd87.

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Анотація:

In higher mathematics, the extremely significant content is Taylor’s formula. Simple polynomial functions can be translated from complex functions by this formula. The Taylor formula can be seen as a useful tool to analyze and study many problems in mathematics because of its ability to reduce complexity. The Taylor Formula is an essential mathematical process for solving some problems about limits and approximation and has a unique advantage in rough calculation. The Taylor formula is an important tool in calculus, as it can transform nonlinear problems into linear ones with high accuracy. Th

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4

Wu, Jiacheng. "Application of Taylor Expansion on Calculating Functions." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 464–69. http://dx.doi.org/10.54097/28kn1016.

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The Taylor formula, which approximates some complicated functions as straightforward polynomial functions, is a crucial concept in advanced mathematics. It is an effective tool for studying and analyzing various mathematical topics because of its ability to reduce complexity. The "approximation method" of calculus is embodied in the Taylor formula, which also offers special advantages for approximation calculations. Taylor's formula has significant applications in all areas of calculus because it can accurately convert nonlinear issues into linear problems. The Taylor formula can be used to de

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5

Chaskalovic, Joel, and Hessam Jamshidipour. "A New First Order Expansion Formula with a Reduced Remainder." Axioms 11, no. 10 (2022): 562. http://dx.doi.org/10.3390/axioms11100562.

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Анотація:

This paper is devoted to a new first order Taylor-like formula, where the corresponding remainder is strongly reduced in comparison with the usual one, which appears in the classical Taylor’s formula. To derive this new formula, we introduce a linear combination of the first derivative of the concerned function, which is computed at n+1 equally spaced points between the two points, where the function has to be evaluated. We show that an optimal choice of the weights in the linear combination leads to minimizing the corresponding remainder. Then, we analyze the Lagrange P1- interpolation error

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6

Zhao, Junzhi. "A generalization of the Taylor's theorem." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 885–90. http://dx.doi.org/10.54097/f196n869.

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Анотація:

In mathematics, Taylor's theorem is a formula that uses the information of a function to describe its proximity to a point. If the function is smooth enough, the conductive values can be used to construct a multiform to approximate the the function in the neighboring area of that point, which can even be extended to the convergence radius of the scale. Taylor’s theorem also gives the deviation between this multiform and the actual function value. The essay includes the proof and application of Taylor’s theorem and the Taylor’s theorem in multivariate functions. Special functions are set with u

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7

Odibat, Zaid M., and Nabil T. Shawagfeh. "Generalized Taylor’s formula." Applied Mathematics and Computation 186, no. 1 (2007): 286–93. http://dx.doi.org/10.1016/j.amc.2006.07.102.

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8

Anastassiou, George A. "Distributional Taylor formula." Nonlinear Analysis: Theory, Methods & Applications 70, no. 9 (2009): 3195–202. http://dx.doi.org/10.1016/j.na.2008.04.022.

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9

AGLIĆ ALJINOVIĆ, A., J. PEČARIĆ, and M. RIBIČIĆ PENAVA. "SHARP INTEGRAL INEQUALITIES BASED ON GENERAL TWO-POINT FORMULAE VIA AN EXTENSION OF MONTGOMERY’S IDENTITY." ANZIAM Journal 51, no. 1 (2009): 67–101. http://dx.doi.org/10.1017/s1446181109000315.

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AbstractWe consider families of general two-point quadrature formulae, using the extension of Montgomery’s identity via Taylor’s formula. The formulae obtained are used to present a number of inequalities for functions whose derivatives are fromLpspaces and Bullen-type inequalities.

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10

Pečarić, J., and M. Ribičić Penava. "Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/343191.

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We consider families of general four-point quadrature formulae using a generalization of the Montgomery identity via Taylor’s formula. The results are applied to obtain some sharp inequalities for functions whose derivatives belong to spaces. Generalizations of Simpson’s 3/8 formula and the Lobatto four-point formula with related inequalities are considered as special cases.

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11

Sarkaria, K. S. "Taylor's Formula via Determinants." College Mathematics Journal 32, no. 1 (2001): 54. http://dx.doi.org/10.2307/2687223.

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12

Ang, James S., Gwoduan David Jou, and Tsong-Yue Lai. "Alternative Formulas to Compute Implied Standard Deviation." Review of Pacific Basin Financial Markets and Policies 12, no. 02 (2009): 159–76. http://dx.doi.org/10.1142/s0219091509001599.

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We assume that the call option's value is correctly priced by Black and Scholes' option pricing model in this paper. This paper derives an exact closed-form solution for implied standard deviation under the condition that the underlying asset price equals the present value of the exercise price. The exact closed-form solution provides the true implied standard deviation and has no estimate error. This paper also develops three alternative formulas to estimate the implied standard deviation if this condition is violated. Application of the Taylor expansion on a single call option value derives

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13

Ernst, Thomas. "On Various Formulas with q-integralsand Their Applications to q-hypergeometric Functions." European Journal of Pure and Applied Mathematics 13, no. 5 (2020): 1241–59. http://dx.doi.org/10.29020/nybg.ejpam.v13i5.3755.

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Анотація:

We present three q-Taylor formulas with q-integral remainder. The two last proofsrequire a slight rearrangement by a well-known formula. The first formula has been given in different form by Annaby and Mansour. We give concise proofs for q-analogues of Eulerian integral formulas for general q-hypergeometric functions corresponding to Erd ́elyi, and for two of Srivastavas triple hypergeometric functions and other functions. All proofs are made in a similar style by using q-integration. We find some new formulas for fractional q-integrals including a series expansion. In the same way, the operat

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14

Stancu, Dimitrie D., and Ioana Taşcu. "On some bivariate interpolation procedures." Journal of Numerical Analysis and Approximation Theory 33, no. 1 (2004): 97–106. http://dx.doi.org/10.33993/jnaat331-765.

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In an important paper published in 1966 by the first author [10] a very general interpolation formula for univariate functions, which includes, as special cases, the classical interpolation formulae of Lagrange, Newton, Taylor and Hermite was introduced and investigated. The purpose of the present paper is to extend that formula to the two-dimensional case. The remainders are expressed by means of partial divided differences and derivatives.

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15

Petrovic, Maja, and Branko Malesevic. "The area of Hügelschäffer curves via Taylor series." Filomat 38, no. 23 (2024): 8053–68. https://doi.org/10.2298/fil2423053p.

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In this paper, we give new Taylor approximative formulae for the area of the egg-shaped parts of H?gelsch?ffer curves. Based on a parametrization of the H?gelsch?ffer curve, a formula for the area of the egg-shaped part of such a curve is derived via elliptic integrals of the first and second kind. Furthermore, new approximative formulae for calculating this area derived from standard and double Tay lora pproxima tions ar egiven. A representation of the value 1/? was also obtained using an appropriate series.

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16

Putra, Ikhsan Fachriansyah, Mahdhivan Syafwan, Monika Rianti Helmi, and Admi Nazra. "BENTUK EKSPLISIT RUMUS BEDA MAJU DAN BEDA MUNDUR UNTUK TURUNAN KE-N DENGAN ORDE KETELITIAN KE-N BERDASARKAN DERET TAYLOR." Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 4, no. 3 (2023): 1675–86. http://dx.doi.org/10.46306/lb.v4i3.461.

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Анотація:

In this paper, we aim to derive the explicit forms of forward and backward difference formulas based on the Taylor series. These formulas are employed to approximate the N-th derivative of a single-variable function with N-th order accuracy. The explicit formula is determined by utilizing the properties of the determinant of the Vandermonde matrix. Subsequently, we apply the obtained formulas to an example case involving a first-order ordinary differential equation

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17

Waldron, Shayne. "Multipoint Taylor formulæ." Numerische Mathematik 80, no. 3 (1998): 461–94. http://dx.doi.org/10.1007/s002110050375.

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18

Jin, Ming, Guangbin Ren, and Irene Sabadini. "Slice Dirac operator over octonions." Israel Journal of Mathematics 240, no. 1 (2020): 315–44. http://dx.doi.org/10.1007/s11856-020-2067-z.

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AbstractThe slice Dirac operator over octonions is a slice counterpart of the Dirac operator over quaternions. It involves a new theory of stem functions, which is the extension from the commutative O(1) case to the non-commutative O(3) case. For functions in the kernel of the slice Dirac operator over octonions, we establish the representation formula, the Cauchy integral formula (and, more in general, the Cauchy-Pompeiu formula), and the Taylor as well as the Laurent series expansion formulas.

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19

Poffald, Esteban I. "The Remainder in Taylor's Formula." American Mathematical Monthly 97, no. 3 (1990): 205. http://dx.doi.org/10.2307/2324685.

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20

Anastassiou, George A. "Multivariate fractional Taylor's formula revisited." Sarajevo Journal of Mathematics 5, no. 2 (2024): 159–67. http://dx.doi.org/10.5644/sjm.05.2.03.

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Анотація:

This is a continuation of [2]. Here is established a multivariate fractional Taylor's formula via the Caputo fractional derivative. The fractional remainder is expressed as a composition of two Riemann-Liouville fractional integrals. 2000 Mathematics Subject Classification. 26A33

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21

Poffald, Esteban I. "The Remainder in Taylor's Formula." American Mathematical Monthly 97, no. 3 (1990): 205–13. http://dx.doi.org/10.1080/00029890.1990.11995575.

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22

Mo, Zifei, Yiran Wang, and Jia Wei. "Analysis of Principle and Applications of Series Expansion." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 593–98. http://dx.doi.org/10.54097/47cvvb47.

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Анотація:

As a matter of fact, the series expansion has been widely used in various fields since the proposed. The key reason is that it can be used for simplifying and approximation for complex structure, functions as well as situations. On this basis, it is able to offer an easy routine to calculate some of the values. With this in mind, this study mainly discussed the use of Taylor series expansion in chemistry and daily life, and obtained the freezing point reduction formula, which is not a small challenge for us. However, this expansion of Taylor's series is limited in many other areas of daily lif

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23

Al-Nana, Abeer A., Iqbal M. Batiha, and Shaher Momani. "A Numerical Approach for Dealing with Fractional Boundary Value Problems." Mathematics 11, no. 19 (2023): 4082. http://dx.doi.org/10.3390/math11194082.

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This paper proposes a novel numerical approach for handling fractional boundary value problems. Such an approach is established on the basis of two numerical formulas; the fractional central formula for approximating the Caputo differentiator of order α and the fractional central formula for approximating the Caputo differentiator of order 2α, where 0<α≤1. The first formula is recalled here, whereas the second one is derived based on the generalized Taylor theorem. The stability of the proposed approach is investigated in view of some formulated results. In addition, several numerical examp

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24

Bchir, Amani, Raoul Lemeur, Fethi Ben Mariem, et al. "Estimation and comparison of reference evapotranspiration using different methods to determine olive trees irrigation schedule in different bioclimatic stages of Tunisia." Brazilian Journal of Biological Sciences 6, no. 14 (2019): 615–28. http://dx.doi.org/10.21472/bjbs.061413.

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The study of olive trees water requirements allows a better water management by using more accurate methods including maximum parameters of the continuum soil-plant- atmosphere. The Penman-Monteith equations is consideredas the most rational approach and the most reliable for calculating evapotranspiration. Only this approach necessarily requires an important number of climate parameters. The use of other equations, less complicated and using less climate parameters may be a reliable and efficient alternative. This experimental study was carried out on two cultivars cv. "Meski" and cv. "Chemla

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25

Alomari, Mohammad W., Iqbal M. Batiha, Wala’a Ahmad Alkasasbeh, Nidal Anakira, Iqbal H. Jebril, and Shaher Momani. "Euler-Maclaurin Method for Approximating Solutions of Initial Value Problems." International Journal of Robotics and Control Systems 5, no. 1 (2025): 366–80. https://doi.org/10.31763/ijrcs.v5i1.1560.

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Анотація:

This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms Taylor’s and Runge–Katta’s methods in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Taylor and Runge-Katta methods. To substantiate our claims, numerical experiments are provided, highlighting the exceptional

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26

Orlová, Alena, and Ferdinand Dobeš. "Contributions to Internal Stress from Free Dislocations and from Substructure Boundaries in Dislocation Structure Formed in High Temperature Creep." Materials Science Forum 567-568 (December 2007): 173–76. http://dx.doi.org/10.4028/www.scientific.net/msf.567-568.173.

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The relation of the internal stress and the parameters of the heterogeneous dislocation structure was suggested in the form of the classical Taylor formula relating the internal stress to the total dislocation density stored in the subgrain interior and in the subgrain boundaries. The other formula combines linearly the stress contribution generated by network dislocations and the stress contribution of the subgrain structure semiempirically related to the subgrain size. The formulas can evaluate the ratio of internal stress components due to sub-boundaries and free dislocations.

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27

MICKELSSON, JOUKO, and SYLVIE PAYCHA. "THE LOGARITHMIC RESIDUE DENSITY OF A GENERALIZED LAPLACIAN." Journal of the Australian Mathematical Society 90, no. 1 (2011): 53–80. http://dx.doi.org/10.1017/s144678871100108x.

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AbstractWe show that the residue density of the logarithm of a generalized Laplacian on a closed manifold defines an invariant polynomial-valued differential form. We express it in terms of a finite sum of residues of classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas provide a pedestrian proof of the Atiyah–Singer formula for a pure Dirac operator in four dimensions and for a twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of pert

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28

Benjemaa, Mondher. "Taylor’s formula involving generalized fractional derivatives." Applied Mathematics and Computation 335 (October 2018): 182–95. http://dx.doi.org/10.1016/j.amc.2018.04.040.

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29

Fahad, Asfand, Saad Ihsaan Butt, Josip Pečarić, and Marjan Praljak. "Generalized Taylor’s Formula and Steffensen’s Inequality." Mathematics 11, no. 16 (2023): 3570. http://dx.doi.org/10.3390/math11163570.

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New Steffensen-type inequalities are obtained by combining generalized Taylor expansions, Rabier and Pečarić extensions of Steffensen’s inequality and Faà di Bruno’s formula for higher order derivatives of the composition.

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30

Sripanich, Yanadet, and Sergey Fomel. "Theory of interval traveltime parameter estimation in layered anisotropic media." GEOPHYSICS 81, no. 5 (2016): C253—C263. http://dx.doi.org/10.1190/geo2016-0013.1.

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Moveout approximations for reflection traveltimes are typically based on a truncated Taylor expansion of traveltime squared around the zero offset. The fourth-order Taylor expansion involves normal moveout velocities and quartic coefficients. We have derived general expressions for layer-stripping second- and fourth-order parameters in horizontally layered anisotropic strata and specified them for two important cases: horizontally stacked aligned orthorhombic layers and azimuthally rotated orthorhombic layers. In the first of these cases, the formula involving the out-of-symmetry-plane quartic

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31

ZHAO, WENHUA. "NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND THE INVERSION PROBLEM." International Journal of Algebra and Computation 18, no. 05 (2008): 869–99. http://dx.doi.org/10.1142/s0218196708004615.

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Let K be any unital commutative ℚ-algebra and z = (z1, z2, …, zn) commutative or noncommutative variables. Let t be a formal central parameter and K[[t]]〈〈z〉〉 the formal power series algebra of z over K[[t]]. In [29], for each automorphism Ft(z) = z - Ht(z) of K[[t]]〈〈z〉〉 with Ht=0(z) = 0 and o(H(z)) ≥ 1, a [Formula: see text] (noncommutative symmetric) system [28] ΩFt has been constructed. Consequently, we get a Hopf algebra homomorphism [Formula: see text] from the Hopf algebra [Formula: see text] [9] of NCSFs (noncommutative symmetric functions). In this paper, we first give a list for the

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32

Dăianu, Dan M. "Taylor type formula with Fréchet polynomials." Aequationes mathematicae 92, no. 4 (2018): 695–707. http://dx.doi.org/10.1007/s00010-018-0574-3.

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33

Fukushima, Toshio. "Taylor series expansion of prismatic gravitational field." Geophysical Journal International 220, no. 1 (2019): 610–60. http://dx.doi.org/10.1093/gji/ggz449.

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SUMMARY The exact analytical formulae to compute the gravitational field of a rectangular prism suffer from round-off errors when the evaluation point is outside the Brillouin sphere of the prism. The error magnitude grows cubically with respect to the distance from the prism. This phenomenon is eminent in not only the gravitational potential but also the gravity vector and the gravity gradient tensor. Unfortunately, the issue of error increase is not settled efficiently by the rewriting of the formulae using the addition theorems of the transcendental functions. Besides, the computational lab

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34

Sousa, José Vanterler da Costa, and Edmundo Capelas de Oliveira. "Truncated V-fractional Taylor's Formula with Applications." TEMA (São Carlos) 19, no. 3 (2018): 525. http://dx.doi.org/10.5540/tema.2018.019.03.525.

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In this paper, we present and prove a new truncated V-fractional Taylor's formula using the truncated V-fractional variation of constants formula. In this sense, we present the truncated V-fractional Taylor's remainder by means of V-fractional integral, essential for analyzing and comparing the error, when approaching functions by polynomials. From these new results, some applications were made involving some inequalities, specifically, we generalize the Cauchy-Schwartz inequality.

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35

Shokri, Khosro Monsef, Jafar Shaffaf, and Reza Taleb. "Galois groups of Taylor polynomials of some elementary functions." International Journal of Number Theory 15, no. 06 (2019): 1127–41. http://dx.doi.org/10.1142/s1793042119500623.

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Анотація:

Motivated by Schur’s result on computing the Galois groups of the exponential Taylor polynomials, this paper aims to compute the Galois groups of the Taylor polynomials of the elementary functions [Formula: see text] and [Formula: see text]. We first show that the Galois groups of the [Formula: see text]th Taylor polynomials of [Formula: see text] are as large as possible, namely, [Formula: see text] (full symmetric group) or [Formula: see text] (alternating group), depending on the residue of the integer number [Formula: see text] modulo [Formula: see text]. We then compute the Galois groups

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36

Sun, Min, Maoying Tian, and Yiju Wang. "Discrete-Time Zhang Neural Networks for Time-Varying Nonlinear Optimization." Discrete Dynamics in Nature and Society 2019 (April 8, 2019): 1–14. http://dx.doi.org/10.1155/2019/4745759.

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As a special kind of recurrent neural networks, Zhang neural network (ZNN) has been successfully applied to various time-variant problems solving. In this paper, we present three Zhang et al. discretization (ZeaD) formulas, including a special two-step ZeaD formula, a general two-step ZeaD formula, and a general five-step ZeaD formula, and prove that the special and general two-step ZeaD formulas are convergent while the general five-step ZeaD formula is not zero-stable and thus is divergent. Then, to solve the time-varying nonlinear optimization (TVNO) in real time, based on the Taylor series

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37

Panda, Anton, and Ján Duplák. "Comparison of Theory and Practice in Analytical Expression of Cutting Tools Durability for Potential Use at Manufacturing of Bearings." Applied Mechanics and Materials 616 (August 2014): 300–307. http://dx.doi.org/10.4028/www.scientific.net/amm.616.300.

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Анотація:

The problem effective and economical management of the cutting tools is often the factor that manufacturing enterprises do not attach much importance. Any manufacturer of cutting tools states in promotional and marketing materials, and also in many catalogs data about cutting tools, excluding those subject know-how. Among the following data are also recommended cutting conditions and their dependent of durability of the instrument. If the company uses different cutting parameters, knows the durability of knowledge by F.W. Taylor contained in standard ISO 3685, which can be fast deduced, becaus

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38

SUZUKI, MASUO. "GENERAL FORMULATION OF QUANTUM ANALYSIS." Reviews in Mathematical Physics 11, no. 02 (1999): 243–65. http://dx.doi.org/10.1142/s0129055x9900009x.

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A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the Gâteaux derivative or commutators. This yields a unified formulation of quantum analysis, namely the invariance of quantum derivatives, which are expressed by multiple integrals of ordinary higher derivatives with hyperoperator variables. Multivariate quantum analysis is also formulated in the present unified scheme by introducing a partial inner derivation and a rearrangement formula. Operator Taylo

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39

Pečarić, J. E., Gh Tudor, B. Crstici, and B. Savić. "Note on Taylor's formula and some applications." Journal of Approximation Theory 51, no. 1 (1987): 47–53. http://dx.doi.org/10.1016/0021-9045(87)90093-1.

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Luc, Dinh The. "Taylor’s Formula for $C^{k,1} $ Functions." SIAM Journal on Optimization 5, no. 3 (1995): 659–69. http://dx.doi.org/10.1137/0805032.

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Butt, Saad Ihsan, Ljiljanka Kvesić, and Josip Pečarić. "Generalization of majorization theorem via Taylor's formula." Mathematical Inequalities & Applications, no. 4 (2016): 1257–69. http://dx.doi.org/10.7153/mia-19-92.

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Jing, Si-Cong, and Hong-Yi Fan. "q -Taylor's Formula with Its q -Remainder." Communications in Theoretical Physics 23, no. 1 (1995): 117–20. http://dx.doi.org/10.1088/0253-6102/23/1/117.

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Trujillo, J. J., M. Rivero, and B. Bonilla. "On a Riemann–Liouville Generalized Taylor's Formula." Journal of Mathematical Analysis and Applications 231, no. 1 (1999): 255–65. http://dx.doi.org/10.1006/jmaa.1998.6224.

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Nečasová, Gabriela, Jiří Kunovský, Václav Šátek, Jan Chaloupka, and Petr Veigend. "Taylor Series Based Differential Formulas." IFAC-PapersOnLine 48, no. 1 (2015): 705–6. http://dx.doi.org/10.1016/j.ifacol.2015.05.209.

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王, 泽军. "Application of Taylor Formula and Taylor Series for Single Variable Function." Pure Mathematics 12, no. 06 (2022): 1067–73. http://dx.doi.org/10.12677/pm.2022.126117.

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Rempała, Jan A. "A semi-global Taylor formula for manifolds." Annales Polonici Mathematici 48, no. 2 (1988): 131–38. http://dx.doi.org/10.4064/ap-48-2-131-138.

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Bonfiglioli, Andrea. "Taylor formula for homogenous groups and applications." Mathematische Zeitschrift 262, no. 2 (2008): 255–79. http://dx.doi.org/10.1007/s00209-008-0372-z.

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McAneney, K. J., and B. Itier. "Operational limits to the Priestley-Taylor formula." Irrigation Science 17, no. 1 (1996): 37–43. http://dx.doi.org/10.1007/s002710050020.

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Ruan, Xiaozhou. "Note on the Bulk Estimate of the Energy Dissipation Rate in the Oceanic Bottom Boundary Layer." Fluids 7, no. 2 (2022): 82. http://dx.doi.org/10.3390/fluids7020082.

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Анотація:

The dissipation of the kinetic energy (KE) associated with oceanic flows is believed to occur primarily in the oceanic bottom boundary layer (BBL), where bottom drag converts the KE from mean flows to heat loss through irreversible mixing at molecular scales. Due to the practical difficulties associated with direct observations on small-scale turbulence close to the seafloor, most up-to-date estimates on bottom drag rely on a simple bulk formula (CdU3) proposed by G.I. Taylor that relates the integrated BBL dissipation rate to a drag coefficient (Cd) as well as a flow magnitude outside of the

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Gisler, Alois. "THE RESERVE UNCERTAINTIES IN THE CHAIN LADDER MODEL OF MACK REVISITED." ASTIN Bulletin 49, no. 03 (2019): 787–821. http://dx.doi.org/10.1017/asb.2019.18.

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Анотація:

AbstractWe revisit the “full picture” of the claims development uncertainty in Mack’s (1993) distribution-free stochastic chain ladder model. We derive the uncertainty estimators in a new and easily understandable way, which is much simpler than the derivation found so far in the literature, and compare them with the well known estimators of Mack and of Merz–Wüthrich.Our uncertainty estimators of the one-year run-off risks are new and different to the Merz–Wüthrich formulas. But if we approximate our estimators by a first order Taylor expansion, we obtain equivalent but simpler formulas. As re

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