Factorization of leading chiral logarithms in the pion form factors

In the recently proposed framework of hard pion chiral perturbation theory, the leading chiral logarithms are predicted to factorize with respect to the energy dependence in the chiral limit. We have scrutinized this assumption in the case of vector and scalar pion form factors FV;S(s) by means of standard chiral perturbation theory and dispersion relations. We show that this factorization property is valid for the elastic contribution to the dispersion integrals for FV;S(s) but it is violated starting at three loops when the inelastic four-pion contributions arise.

Notebook on logarithms, ca. 1714-1718, 1747

This notebook is missing at least one page, as it begins in the midst of a problem. It contains extensive notes on logarithms and various related examples, problems, and calculations. Prince made notes on the addition, subtraction, multiplication, and division of logarithms, as well as some notes on navigation. The last two pages of this notebook contain a draft of a letter from Prince to an unnamed gentleman in London, thanking him for his financial support. This is believed to have been written in June 1747, when Prince arrived in Portsmouth, England "without one six pence in [his] pocket & without Hat, Coat, Breeches, Shirts, Stockings or shoes fit to come up to London with." In the letter, he thanks this donor for his support and describes in detail his situation and the challenges facing him in leaving the Navy and beginning missionary work. He refers several times to Dr. Philip Bearcroft, the Secretary of the Society for the Propagation of the Gospel, who was responsible for his approval as a Missionary to the Moskito tribe.

Arithmetical exercises and examination papers : with an appendix containing questions in logarithms and mensuration /

Includes section with answers.

Tables of the common logarithms and trigonometrical functions to six places of decimals.

"With an appendix containing a table of natural functions and circular measures of angles to each minute of arc to five places of decimals."

Table of natural logarithms ... /

"One in a series of mathematical tables prepared by the Project for the Computation of Mathematical Tables."--Volume I., Pref.

Mathematics for the practical man explaining simply and quickly all the elements of algebra, geometry, trigonometry, logarithms, coördinate geometry, calculus,

Mode of access: Internet.

Mathematics for the practical engineer. Engineers' study course from Power; a mathematical manual for the power plant engineer. Contains simplified lessons for home-study in fractions, ratio and proportion, percentage, involution and evolution, square root, cube root, formulas, logarithms, mensuration and plane trigonometry,

Mode of access: Internet.

An elementary treatise on algebra : to which are added exponential equations and logarithms /

Mode of access: Internet.

A treatise of plane trigonometry : to which is prefixed a summary view of the nature and use of logarithms : being the second part of a course of mathematics, adapted to the method of instruction in the American colleges /

Mode of access: Internet.

Binomial theorem and logarithms. For the use of the midshipmen at the naval school, Philadelphia.

Preface signed: William Chauvenet.

New mathematical tables containing the factors, squares, cubes, square roots, cube roots, reciprocals, and hyperbolic logarithms, of all numbers from 1 to 10000; tables of powers and prime numbers; an extensive table of formulæ, or general synopsis of the most important particulars relating to the doctrines of equations, series, fluxions, fluents, &c. &c. &c.

Mode of access: Internet.

A system of plane and spherical trigonometry : to which is added a treatise on logarithms /

Mode of access: Internet.