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 /

With: A Practical application of The Principles of geometry to the mensuration of superficies and solids: being the third part of a Course of mathematics, ...

An elementary essay on the computation of logarithms : containing a view of the most expeditious methods of constructing a table of those numbers /

Mode of access: Internet.

Tables of logarithms of numbers and of sines and tangents for every ten seconds of the quadrant, with other useful tables.

Mode of access: Internet.

Logarithms of the values of all vulgar fractions, with numerator and denominator not exceeding 100, arranged in order of magnitude.

"Excerpt Minutes of proceedings of the Institution of Civil Engineers, vol. lxv. Session 1880-81. Part iii."

Table of the logarithms of the natural numbers from 1 to 108000 /

Mode of access: Internet.

A new manual of logarithms to seven places of decimals,

Mode of access: Internet.

Powers and Logarithms

There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers of logarithmic and antilogarithmic mappings or powers of logarithms and antilogarithms (cf. for instance, the survey of Schinzel S[1].

Teaching basic finance with Excel, and without pain

The five quantities of interest in elementary finance problems are present value, future value, amount of periodic payment, number of periods and the rate of compound interest per period. A recursive approach to computing each of these five quantities in a modern version of Excel, for the case of ordinary annuities, is described. The aim is to increase student understanding and build confidence in the answer obtained, and this may be achieved with only linear relationships and in cases where student knowledge of algebra is essentially zero. Annuity problems may be solved without use of logarithms and black-box intrinsic functions; these being used only as check mechanisms. The author has had success with the method at Bond University and surrounding high schools in Queensland, Australia.

Predicting mortality of phosphine-resistant adults of Sitophilus oryzae (L) (Coleoptera: Curculionidae) in relation to changing phosphine concentration

Adults of a phosphine-resistant strain of Sitophilus oryzae (L) were exposed to constant phosphine concentrations of 0.0035-0.9 mg litre(-1) for periods of between 20 and 168 h at 25 °C, and the effects of time and concentration on mortality were quantified. Adults were also exposed to a series of treatments lasting 48, 72 or 168 h at 25 °C, during which the concentration of phosphine was varied. The aim of this study was to determine whether equations from experiments using constant concentrations could be used to predict the efficacy of changing phosphine concentrations against adults of S oryzae. A probit plane without interaction, in which the logarithms of time (t) and concentration (C) were variables, described the effects of concentration and time on mortality in experiments with constant concentrations. A derived equation of the form C^nt = k gave excellent predictions of toxicity when applied to data from changing concentration experiments. The results suggest that for resistant S oryzae adults there is nothing inherently different between constant and changing concentration regimes, and that data collected from fixed concentrations can be used to develop equations for predicting mortality in fumigations in which phosphine concentration changes. This approach could simplify the prediction of efficacy of typical fumigations in which concentrations tend to rise and then fall over a period of days.

Tools for compositional data with a total

Compositional data analysis usually deals with relative information between parts where the total (abundances, mass, amount, etc.) is unknown or uninformative. This article addresses the question of what to do when the total is known and is of interest. Tools used in this case are reviewed and analysed, in particular the relationship between the positive orthant of D-dimensional real space, the product space of the real line times the D-part simplex, and their Euclidean space structures. The first alternative corresponds to data analysis taking logarithms on each component, and the second one to treat a log-transformed total jointly with a composition describing the distribution of component amounts. Real data about total abundances of phytoplankton in an Australian river motivated the present study and are used for illustration.

Determination of alpha(s)(M-tau(2)) from improved fixed order perturbation theory

We revisit the extraction of alpha(s)(M-tau(2)) from the QCD perturbative corrections to the hadronic tau branching ratio, using an improved fixed-order perturbation theory based on the explicit summation of all renormalization-group accessible logarithms, proposed some time ago in the literature. In this approach, the powers of the coupling in the expansion of the QCD Adler function are multiplied by a set of functions D-n, which depend themselves on the coupling and can be written in a closed form by iteratively solving a sequence of differential equations. We find that the new expansion has an improved behavior in the complex energy plane compared to that of the standard fixed-order perturbation theory (FOPT), and is similar but not identical to the contour-improved perturbation theory (CIPT). With five terms in the perturbative expansion we obtain in the (MS) over bar scheme alpha(s)(M-tau(2)) = 0.338 +/- 0.010, using as input a precise value for the perturbative contribution to the hadronic width of the tau lepton reported recently in the literature.

Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

We examine the large-order behavior of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard ``contour-improved'' expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behavior of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the hadronic width of the tau lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, alpha(s)(M-tau(2)) = 0.3189(-0.0151)(+0.0173), which translates to alpha(s)(M-Z(2)) = 0.1184(-0.0018)(+0.0021). DOI: 10.1103/PhysRevD.87.014008

Single Spin Asymmetry in Charmonium Production

We present estimates of single spin asymmetry (SSA) in the electroproduction of taking into account the transverse momentum dependent (TMD) evolution of the gluon Sivers function and using Color Evaporation Model of charmonium production. We estimate SSA for JLab, HERMES, COMPASS and eRHIC energies using recent parameters for the quark Sivers functions which are fitted using an evolution kernel in which the perturbative part is resummed up to next-to-leading logarithms accuracy. We find that these SSAs are much smaller as compared to our first estimates obtained using DGLAP evolution but are comparable to our estimates obtained using TMD evolution where we had used approximate analytical solution of the TMD evolution equation for the purpose.

Transformation empirique des tables numeriques de Galton en tables des probits

Comparison between Galton equation and preston normal logarithms models allowed an empirical reconstitution of probits tables.