Approximate cost of completing the railway from Port Dalhousie to St. Catharines and an estimate of the cost of the piers at Port Dalhousie signed by William Hamilton Merritt

Approximate cost of completing the railway from Port Dalhousie to St. Catharines and an estimate of the cost of the piers at Port Dalhousie signed by William Hamilton Merritt (5 pages, handwritten), July 8, 1854.

Approximate estimate of the cost of completing the Port Dalhousie Railway to the Grand Central Railway Station at Lock 12

Approximate estimate of the cost of completing the Port Dalhousie Railway to the Grand Central Railway Station at Lock 12. This document is badly torn and burned but most of the text is legible, July 14, 1854.

Approximate estimate of the cost of constructing and completing the Port Dalhousie and Thorold Railway to St. Catharines

Approximate estimate of the cost of constructing and completing the Port Dalhousie and Thorold Railway to St. Catharines signed by S.D. Woodruff (2 pages, handwritten), Jan. 8, 1855.

Approximate estimate of the cost of extending the Port Dalhousie and Thorold Railway from Geneva Street to the Great Western Railway Station at Lock no. 12

Approximate estimate of the cost of extending the Port Dalhousie and Thorold Railway from Geneva Street to the Great Western Railway Station at Lock no. 12 (2 copies) [one appears to be a rough copy] (2 pages, handwritten), Feb. 2, 1855.

Memorandum respecting differences between the approximate and the final estimate

Memorandum respecting differences between the approximate and the final estimate (3 ¼ pages, handwritten), n.d.

Second copy of the memorandum respecting differences between the approximate and final estimate but this one has “memorandum of extras of Brown and McDonall contract” written on the outer page

Second copy of the memorandum respecting differences between the approximate and final estimate but this one has “memorandum of extras of Brown and McDonall contract” written on the outer page (3 pages, handwritten), n.d.

Approximate estimate of the cost of macadamizing, grading, bridging and putting in culverts from Hurst’s Bridge above Thorold to Port Robinson

Approximate estimate of the cost of macadamizing, grading, bridging and putting in culverts from Hurst’s Bridge above Thorold to Port Robinson (2 pages, handwritten), n.d.

Chart of approximate quantity of excavation in slides in the deep cut

Chart of approximate quantity of excavation in slides in the deep cut, July 1, 1848.

Photograph - Young girl, Martha. Approximate age 6-9 years old. Ambrotype?

Young girl, Martha. Approximate age 6-9 years old. Ambrotype? Ca. 1850s? Brass matting with brass border. Wooden case. Photograph very faded. 8.5mm x 9.5mm (yellow sticker with “x” on front of case).

The Wage Rate and the Profit Rate in the Price of Production Equation: a New Solution to an Old Problem

The aim of this paper is to demonstrate that, even if Marx's solution to the transformation problem can be modified, his basic concusions remain valid.

Problèmes de commande optimale stochastique généralisés

Cette thèse est divisée en deux grands chapitres, dont le premier porte sur des problèmes de commande optimale en dimension un et le deuxième sur des problèmes en dimension deux ou plus. Notons bien que, dans cette thèse, nous avons supposé que le facteur temps n'intervient pas. Dans le premier chapitre, nous calculons, au début, l'équation de programmation dynamique pour la valeur minimale F de l'espérance mathématique de la fonction de coût considérée. Ensuite, nous utilisons le théorème de Whittle qui est applicable seulement si une condition entre le bruit blanc v et les termes b et q associés à la commande est satisfaite. Sinon, nous procédons autrement. En effet, un changement de variable transforme notre équation en une équation de Riccati en G= F', mais sans conditions initiales. Dans certains cas, à partir de la symétrie des paramètres infinitésimaux et de q, nous pouvons en déduire le point x' où G(x')=0. Si ce n'est pas le cas, nous nous limitons à des bonnes approximations. Cette même démarche est toujours possible si nous sommes dans des situations particulières, par exemple, lorsque nous avons une seule barrière. Dans le deuxième chapitre, nous traitons les problèmes en dimension deux ou plus. Puisque la condition de Whittle est difficile à satisfaire dans ce cas, nous essayons de généraliser les résultats du premier chapitre. Nous utilisons alors dans quelques exemples la méthode des similitudes, qui permet de transformer le problème en dimension un. Ensuite, nous proposons une nouvelle méthode de résolution. Cette dernière linéarise l'équation de programmation dynamique qui est une équation aux dérivées partielles non linéaire. Il reste à la fin à trouver les conditions initiales pour la nouvelle fonction et aussi à vérifier que les n expressions obtenues pour F sont équivalentes.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Error estimates for approximate approximations on compact intervals

The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in- tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed. In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly.