On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Letter from Robert Bell to Edward Wigglesworth, 1781 June 16

This brief letter from Robert Bell in Boston, Massachusetts, to Professor Edward Wigglesworth concerns the donation of books to the College Library.

Binding cost estimates, 1801

This six-page undated list contains volume titles and estimates for the cost of binding them. The list is undated, but one of the first entries contains the note, "from the year 1774 to the present time [1801]."

Classed book list, undated

This four-page undated list contains book titles primarily arranged into classes. The last page is titled, "Books for the red stamp."

Diplomas from Harvard College and Yale University, 1750

The diplomas are accompanied by a silver case in which the documents were stored.

Letter from Samuel Willard, Harvard College, Cambridge, Massachusetts, to Catherine Willard, Petersham, Massachusetts, May 1, 1801

Willard alludes to a situation regarding his father and praises him profusely.

Letter from Samuel Willard, Harvard College, Cambridge, Massachusetts, to Abigail Willard, Petersham, Massachusetts, May 1, 1801

Willard thanks his sister for writing to him and asks her to write as often as possible. He also mentions his cousin Sophia Chadwick, who has been living with President Willard.

Letter from Samuel Willard, Harvard College, Cambridge, Massachusetts, to William Willard, Petersham, Massachusetts, October 16, 1801

Willard reports on President Willard’s travels and general well-being and asks his father to apologize to his sister for not writing to her often enough. He also tells his father that he is in debt, details his purchases, and asks for money.

Letter from Samuel Willard, Harvard College, Cambridge, Massachusetts, to William Willard, Petersham, Massachusetts, February 28, 1802

Willard describes his trip back to Harvard from Petersham, reports that President Willard and family were doing well, although “he has had an ill turn since, but has recovered,” and concludes the letter by asking for more money.

Letter from Samuel Willard, Harvard College, Cambridge, Massachusetts, to William Willard, Petersham, Massachusetts, November 30, 1802

Willard discusses President Willard’s son Sheafe, who he has been tutoring, explains his education and argues for well-rounded studies. He also mentions that Doctor Aaron Dexter, a lecturer on chemistry, gave him a recipe for paint “which I enclose [separately] in this letter,” as well as a recipe for mortar. He explains that his vacation plans are to teach at a school in Groton for eighteen dollars a month, and asks for a loan from his parents to pay a bill.

Letter from Samuel Willard, Harvard College, Cambridge, Massachusetts, to Catherine Willard, Petersham, Massachusetts, June 22, 1803

Willard mentions his brother’s poor health, his plans to go to teach at Phillips Exeter, and describes various objects that he has sent to different family members, including a razor and books. In his post script, he asks to have a shirt mended.

Account book of the executors of the Henry Flynt estate, 1760-1767

The volume contains acknowledgements of the disbursements of Harvard Tutor Henry Flynt's estate written in the hands of the respective beneficiaries. The entries begin on February 27, 1760 following Flynt's death on February 13, 1760, and continue through May 9, 1767. Each receipt includes the date, name of the executors, description of the property, beneficiary's name, and signature. The beneficiaries include the wife of Sol. Davy, Dorothy Jackson, Edmund Quincy, J. Henry Quincy, Esther and Stephen Richard (received by attorney Nicholas Boylston), Dorothy Skinner (also received for her by her husband Richard Skinner), John Wendell, Edmund Wendell, Katherine Wendell, and Oliver Wendell, as well as Harvard College (received by Harvard Treasurer Thomas Hubbard), and the Deacons of the First Church of Cambridge. The volume also includes a loose document titled "Account from Messrs Edmund & Josiah Quincy Settled & Ballanced March 31, 1749."

University of Michigan Class of 1889

On verso: Taken Saturday A.M.; May 11, 1889; Property of Minnie H. Newby. Randall, Photographer ... Fine Art Goods (?) 30 E. Huron St. Ann Arbor, Mich. Additional documentation (re: names and provenance) available in folder