A practical treatise on railway curves and location : for young engineers : containing a full description of the instruments, the manner of adjusting them, and the methods of proceeding in the field, new and simple formulae for compound and reverse curving, rules for calculating excavation and embankment, staking out work, &c., together with tables of natural sines and tangents, radii, chords, ordinates, and others of general use in the profession /

On spine: Shunk on railway curves &c.

The toilet and cosmetic arts in ancient and modern times : with a review of the different theories of beauty, and copious allied information, social, hygienic, and medical, including instructions and cautions respecting the selection and use of perfumes, cosmetics, and other toilet articles, and a comprehensive collection of formulae and directions for their preparation /

Includes bibliographical references and index.

Instructions and cautions respecting the selection and use of perfumes, cosmetics and other toilet articles, with a comprehensive collection of formulae and directions for their preparation.

Running title: The toilet and cosmetic arts. Originally published as the last part of that title.

A collection of arithmetical and algebraic problems and formulae /

Errata bound in.

An elementary treatise on logic ; including pt. I. Analysis of formulae. pt. II. Method. With an appendix of examples for analysis and criticism. And a copious index of terms and subjects. Designed for use in schools and colleges as well as for private study and use /

Mode of access: Internet.

Medical lexicon. A dictionary of medical science; containing a concise explanation of the various subjects and terms of physiology, pathology, hygiene, therapeutics, pharmacology, obstetrics, medical jurisprudence, & c., with the French and other synonymes ; notices of climate, and of celebrated mineral waters; formulae for various officinal, empirical, and dietetic preparations, etc.

Mode of access: Internet.

Fragm. lat. III 1 - Formulae litterarum

Vorbesitzer: Dominikanerkloster Frankfurt am Main

Fragm. lat. III 96 - Formulae litterarum. Nur Tabula

Trägerband: 'War Umschlag von Registrum redituum Domarchiv F,14 aus dem 15ten Jahrh'; Vorbesitzer: Stadtarchiv Frankfurt am Main

Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

On the robustness of random Boolean formulae

Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models. © 2010 IOP Publishing Ltd.

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

MSC 2010: 33E12, 30A10, 30D15, 30E15

Report : school survey to collect data on material performance

A survey of a number of schools in a number of different climates was carried out to determine the condition of building components of interest in the project. Schools in Melbourne, the Victorian Surf Coast, Brisbane, Townsville and the Sunshine Coast were inspected. A rating system was devised to categorise the components and the results collated in tables. Analysis of the data (where sufficient examples permitted) resulted in formulae to predict the service of the components and a database was derived.

Jacobi quartic curves revisited

This paper provides new results about efficient arithmetic on Jacobi quartic form elliptic curves, y 2 = d x 4 + 2 a x 2 + 1. With recent bandwidth-efficient proposals, the arithmetic on Jacobi quartic curves became solidly faster than that of Weierstrass curves. These proposals use up to 7 coordinates to represent a single point. However, fast scalar multiplication algorithms based on windowing techniques, precompute and store several points which require more space than what it takes with 3 coordinates. Also note that some of these proposals require d = 1 for full speed. Unfortunately, elliptic curves having 2-times-a-prime number of points, cannot be written in Jacobi quartic form if d = 1. Even worse the contemporary formulae may fail to output correct coordinates for some inputs. This paper provides improved speeds using fewer coordinates without causing the above mentioned problems. For instance, our proposed point doubling algorithm takes only 2 multiplications, 5 squarings, and no multiplication with curve constants when d is arbitrary and a = ±1/2.

Faster group operations on elliptic curves

This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic scalar multiplication algorithms using previous and current operation counts. Most notably, the best speeds are obtained from Jacobi quartic curves which provide the fastest timings for most scalar multiplication strategies benefiting from the proposed 12M + 5S + 1D point doubling and 7M + 3S + 1D point addition algorithms. Furthermore, the new addition algorithm provides an efficient way to protect against side channel attacks which are based on simple power analysis (SPA). Keywords: Efficient elliptic curve arithmetic,unified addition, side channel attack.

Dynamics of railway wagons subjected to braking/traction torque

Braking or traction torque is regarded as an important source of wheelset skid and a potential source of derailment risk that adversely affects the safety levels of train operations; therefore, this research examines the effect of braking/traction torque to the longitudinal and lateral dynamics of wagons. This paper reports how train operations safety could be adversely affected due to various braking strategies. Sensitivity of wagon dynamics to braking severity is illustrated through numerical examples. The influence of wheel/rail interface friction coefficient and the effects of two types of track geometry defects on wheel unloading ratio and wagon pitch are also discussed in the paper.