Subsequences of Real Valued Sequences and Convergence

Convergence of real valued sequences is a classical subject of study for many mathematicians and it continues to be studied in recent years. Different types of convergence including ordinary, statistical, almost and ideal convergence, and related properties have been researched. In some studies, the relationship of a sequence and its subsequences regarding some type of convergence is investigated, using Lebesgue measure and Baire category. In this paper we revisit ordinary convergence and study the properties of subsequences of a real valued sequence using measure and category. We state and prove some simple theorems offering fresh insights into a classical subject

Van Raalte Family Genealogical Records

Genealogical records of the Van Raalte family members. I use the date of 1811 here because of the year of Albertus C. Van Raalte\u27s birth.https://digitalcommons.hope.edu/vrp_1810s/1004/thumbnail.jp

Contraceptie als methode in het beheer van hoefdierpopulaties

Bezorgdheid over dierenwelzijn en praktische problemen met lethale methoden hebben geleid tot de ontwikkeling van contraceptiemiddelen om hoefdierpopulaties te beheren. Vroege studies hebben enkele chemische sterilisatiemiddelen getest, maar de meeste daarvan zijn niet geschikt gebleken om in het wild levende hoefdieren mee te behandelen. Sommige zijn onpraktisch vanwege de noodzaak van herhaalde toediening of de grote volumes die geïnjecteerd moeten worden om effect te verkrijgen (o.a. (synthetische) hormonen), terwijl andere afvallen vanwege negatieve bijwerkingen op de gezondheid van behandelde dieren (o.a. DES, levonorgestrel). Een ander probleem van de meeste chemocontraceptiemiddelen is hun resistentie tegen biologische afbraak, waardoor de middelen via de voedselketen overgedragen kunnen worden of zich ophopen in het milieu. Het meest veelbelovende chemocontraceptiemiddel is waarschijnlijk de GnRH-agonist leuprolide, dat wel biologisch afbreekbaar is

Time-symmetric fluctuations in nonequilibrium systems

For nonequilibrium steady states, we identify observables whose fluctuations satisfy a general symmetry and for which a new reciprocity relation can be shown. Unlike the situation in recently discussed fluctuation theorems, these observables are time-reversal symmetric. That is essential for exploiting the fluctuation symmetry beyond linear response theory. Besides time-reversal, a crucial role is played by the reversal of the driving fields, that further resolves the space-time action. In particular, the time-symmetric part in the space-time action determines second order effects of the nonequilibrium driving.Comment: 4 page