Du sucre et de sa fabrication, suivi d'un précis de la législation qui régit cette industrie

"Extrait du Dictionnaire de l'industrie manufacturière, commerciale et agricole, tom. X."

Elegiac extracts from Tibullus and Ovid /

Includes bibliographical footnotes and index.

The history of Nantucket, being a compendious account of the first settlement of the island by the English, together with the rise and progress of the whale fishery; and other historical facts relative to said island and its inhibitants. In two parts.

First edition, 1835.

A manual of medical jurisprudence /

Includes bibliographical references and index.

1879 University of Michigan Football Team

Tomorrow is beautiful /

Mode of access: Internet.

Histoire des Girondins et des massacres de septembre d'après les documents officiels et inédits, accompagnée de plusieurs fac-similé;

Mode of access: Internet.

Dispersive estimates for the Schrödinger equation

In this document we explore the issue of $L^1\to L^\infty$ estimates for the solution operator of the linear Schr\"{o}dinger equation, \begin{align*} iu_t-\Delta u+Vu&=0 &u(x,0)=f(x)\in \mathcal S(\R^n). \end{align*} We focus particularly on the five and seven dimensional cases. We prove that the solution operator precomposed with projection onto the absolutely continuous spectrum of $H=-\Delta+V$ satisfies the following estimate $\|e^{itH} P_{ac}(H)\|_{L^1\to L^\infty} \lesssim |t|^{-\frac{n}{2}}$ under certain conditions on the potential $V$. Specifically, we prove the dispersive estimate is satisfied with optimal assumptions on smoothness, that is $V\in C^{\frac{n-3}{2}}(\R^n)$ for $n=5,7$ assuming that zero is regular, $|V(x)|\lesssim \langle x\rangle^{-\beta}$ and $|\nabla^j V(x)|\lesssim \langle x\rangle^{-\alpha}$, $1\leq j\leq \frac{n-3}{2}$ for some $\beta>\frac{3n+5}{2}$ and $\alpha>3,8$ in dimensions five and seven respectively. We also show that for the five dimensional result one only needs that $|V(x)|\lesssim \langle x\rangle^{-4-}$ in addition to the assumptions on the derivative and regularity of the potential. This more than cuts in half the required decay rate in the first chapter. Finally we consider a problem involving the non-linear Schr\"{o}dinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, \begin{align*} iu_t+d(t) u_{xx}+|u|^2 u=0. \end{align*} We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management solitons. We prove that the dispersion management solitons decay exponentially in $x$ and in the Fourier transform of $x$.

Papers of William Merchant Richardson, 1797-1806

The collection contains a four-page handwritten poem titled "Invention" composed by graduate William Richardson for the 1797 Harvard College Commencement, and an 1806 letter of introduction written by Richardson. The rhyming poem begins, “Long had creations anthem peal been rung…” and contains classical references, and mentions scientists and philosophers including Voltaire, Franklin and Newton. The poem is accompanied by a one-page handwritten letter of introduction for lawyer Benjamin Ames (Harvard AB 1803) written by William M. Richardson to Reverend William Jenks (Harvard AB 1797). The letter is dated November 10, 1806.

William Van Every fonds, 1784, 1804-1806, 1815-1816, 1828, 1832, n.d.

William Van Every, son of McGregory and Mary Wilcox (Jaycocks) Van Every, was born in New York state in 1765. During the Revolutionary War he joined Butler’s Rangers and served under Captain John McDonnell. He was granted three lots of land in the Township of Niagara, with additional lands granted at later dates. William married Elizabeth, daughter of George Young. Elizabeth was the widow of Col. Frederick Dochstader and mother of Catherine Dochstader, b. 1781. William Van Every died in 1832, his wife Elizabeth in 1851. Both are buried in the Warner Cemetery, in present day Niagara Falls. The children of William Van Every and Elizabeth Young were Mary, Elizabeth, Phoebe, John, Peter, William, Rebecca, Samuel and Joseph. Source: Mary Blackadar Piersol, The Records of the Van Every Family, Toronto : Best Printing, 1947. And, Patricia M. Orr, Historic Woodend, sponsored by Niagara Peninsula Conservation Authority, 1980?

[Letter from William Allen to the Corporation of Harvard College], 1806 April 29

Letter requesting a proctor for the west end of Massachusetts Hall.