Archive for History of Exact Sciences 

About: Archive for History of Exact Sciences is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Philosophy of science & History of science. It has an ISSN identifier of 0003-9519. Over the lifetime, 970 publications have been published receiving 16523 citations.

The Gibbs-Wilbraham phenomenon: An episode in fourier analysis

Abstract: plays an essential r61e in computing the amount of this overshoot. While teaching a course in the theory of functions of a real variable, E. HEWITT found the value 1.71... listed for the integral (1) in HARDY & ROGOSINSKI [271, page 36. This anomaly, as well as others encountered in the literature, led us to a study of the GIBBS phenomenon and its history. In the course of this study we uncovered a maze of forgotten results, interesting and difficult generalizations, faulty constants, and some details about the GIBBS phenomenon that have escaped the attention of many writers on the subject. Despite the familiarity of our theme, we therefore entertain a hope that readers of the Archive will find some interest in a discussion of this corner of FOURIER analysis. The paper is divided into three Parts. In Part I, we examine GIBBS's phenomenon in some detail. In Part II, we take up its curious history and describe briefly some of its congeners. In Part III, we offer some conclusions. The computations given in this paper were carried out on two computers: a Hewlett-Packard 9810 and a Univac 1110. The graphs (barring the simplest) were drawn by a Hewlett-Packard 9862A plotter. All finite decimal expansions are truncated decimal expansions. It is a pleasure to record our indebtedness to GERALD B. FOLLAND, THOMAS L. HANKINS, EINAR HILLE, and STEPHEN P. KEELER, who have made valuable suggestions to us.

The Hill equation and the origin of quantitative pharmacology

Abstract: This review addresses the 100-year-old Hill equation (published in January 22, 1910), the first formula relating the result of a reversible association (e.g., concentration of a complex, magnitude of an effect) to the variable concentration of one of the associating substances (the other being present in a constant and relatively low concentration). In addition, the Hill equation was the first (and is the simplest) quantitative receptor model in pharmacology. Although the Hill equation is an empirical receptor model (its parameters have only physico-chemical meaning for a simple ligand binding reaction), it requires only minor a priori knowledge about the mechanism of action for the investigated agonist to reliably fit concentration-response curve data and to yield useful results (in contrast to most of the advanced receptor models). Thus, the Hill equation has remained an important tool for physiological and pharmacological investigations including drug discovery, moreover it serves as a theoretical basis for the development of new pharmacological models.

Kirchhoff's theory of rods

Abstract: The purpose of this paper is to examine the classical theory of finite displacements of thin rods as developed by KIRCHHOFF [1859, 1876] and CLEBSCH [1862], and presented by LOVE [1892, 1906]. In their work, a rod is a threedimensional body with two dimensions which are very small compared to the third. Their objective was to find an approximate solution of the three-dimensional equations of nonlinear elasticity which is satisfactory for thin rods, within a certain class of boundary conditions, and which is applicable to motions such that the strains relative to the initial configuration are very small, although rotations may be large. Their work suffered from the lack of the well developed nonlinear theory of elasticity which is available today. We will re-examine in this paper the general ideas of KIRCNHOFF-CLEBSCH-LOVE within the framework of modern continuum mechanics 1. The reader who intends to follow through the derivations should begin with appendix A. Contemporary treatments of the bending and twisting of rods are frequently based on some set of hypotheses about the motion and the state of stress such as the following ones. (i) Cross-sections remain plane, undistorted, and normal to the axis of the rod. (ii) The transverse stress is zero. (iii) The bending moments and the twisting moment are proportional to the components of curvature and twist of the axis. Such assumptions are called the KmCHHOFF-LOVE hypotheses. One even sees statements in the current literature about the mutual contradictions within the KIRCHHOFF-LOVE hypotheses. In fact, neither author made such assumptions. KIRCHHOFF viewed the rod as an assembly of short segments. Each segment was regarded as loaded by the contact forces from the adjacent segments. The displacement within each segment was assumed to be small. Continuity between segments was expressed with the help of a redundant system of four space coordi-