Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization

This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López (J. Optim. Theory Appl. 154(2), 2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements—normals and/or subdifferentials.

An act for granting to His Majesty the sum of fifty-five thousand pounds, and for striking the same in bills of credit, in the manner herein after directed..., 1764

Contains an act for collection of taxes to pay the debt by establishing a set fee of fifteen shillings per head and household.

A papist mis-represented and represented or A two-fold charactery of Popery : the one containing a sum of the superstitions, idolatries, cruelties, treacheries and wicked principles of that Popery which ... deserves the hatred of all good Christians, the other laying open that Popery, which the Papists own and profess ... /

Mode of access: Internet.

The Confession of faith, the Larger and Shorter catechisms, with the Scripture-proofs at large. Together with the Sum of saving knowledge (contain'd in the Holy Scriptures, and held forth in the said Confession and Catechisms) and Practical use thereof, Covenants national and Solemn league, Acknowledgement of sins and Engagement to duties, Directories, Form of church-government, & c. Of publick authority in the Church of Scotland. With Acts of Assembly and Parliament, relative to, and approbative of, the same.

Each pt. has special t.-p.

The sum of feminine achievement; a critical and analytical study of woman's contribution to the intellectual progress of the world,

"Table -- The famous women of modern times," (p. 210-237): lists 400 women of achievement in the fields of art, education, geographic exploration, journalism, sociology, philanthropy, religion, suffrage, science, medicine, music, theatre, literature, woman in war, and statesmanship.

The Confession of faith, and the Larger and Shorter catechisms, first agreed upon by the Assembly of divines at Westminster; and now appointed by the General assembly of the Kirk of Scotland, to be a part of uniformity in religion, between the kirks of Christ in the three kingdoms. Together with the Sum of saving knowledge, and the Practical use thereof.

Mode of access: Internet.

Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

Evolution of Sets Systems and Homotopy Groups of Spheres

Симеон Т. Стефанов, Велика И. Драгиева - В работата е изследвана еволюцията на системи от множества върху n-мерната евклидова сфера S^n. Установена е връзката на такива системи с хомотопичните групи на сферите. Получени са някои комбинаторни приложения за многостени.

On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series

MSC 2010: 33C20