10 ENGLISH BOOKS RELATING TO «INFIMUM»
Discover the use of
infimum in the following bibliographical selection. Books relating to
infimum and brief extracts from same to provide context of its use in English literature.
1
Vector Optimization with
Infimum and Supremum
The theory of Vector Optimization is developed by a systematic usage of infimum and supremum.
1.5. Supremum. and. Infimum. The Supremum Let S be a nonempty set of Real
Numbers. We shall now define a number known as the least upper bound of S, or
, in Latin, the supremum of 5*. The best way to describe the supremum of 5* is to
...
3
Infinite Dimensional Analysis: A Hitchhiker's Guide
A lattice is a partially ordered set in which every pair of elements has a
supremum and an infimum. It is easy to show (by induction) that every finite set in
a lattice has a supremum and an infimum. A sublattice of a lattice is a subset that
is closed ...
Charalambos D. Aliprantis, Kim C. Border, 2007
4
A Course in Calculus and Real Analysis
An element m ∈ R is called an infimum or a greatest lower bound of the set S if (i
) m is a lower bound of S,thatis,m ≤ x for all x ∈ S,and (ii) β ≤ m for any lower
bound β of S. Again, it is easy to see from the definition that if S has an infimum, ...
Sudhir R. Ghorpade, Balmohan V. Limaye, 2006
5
Introduction to Set Theory, Third Edition, Revised and Expanded
5.15 Theorem Let (A, <) be an ordered set and let B C A. (a) B has at most one
infimum. (b) If b is the least element of B, then b is the infimum of B, (e) If b is the
infimum of B and 6 C B, then b is the least element of B (d) b 6 A is an infimum of
B ...
Karel Hrbacek, Thomas Jech, 1999
(infimum) of A. The supremum (infimum) of A is often denoted by sup A (inf A). If e
is the supremum (infimum) of {x, y}, then 0 is often called simply the supremum (
infimum) of x and y rather than of (x, y}. DEFINITION. An ordered structure (E, ...
Along any line which is not parallel to the £2-axis, the limit off(x) is +oo in both
directions, so the infimum off relative to such a line is attained. Along any line
parallel to the £2-axis, /(*) is non-increasing as a function of £2 and constant for
large ...
R. Tyrrell Rockafellar, 1997
8
Topics in Distributed Algorithms
The infimum of infinite subsets does not necessarily exist: an easy example is the
poset (Q,£), where the set {x :0<x and 2<x2} does not have an infimum. In all
applications in this book subsets of which an infimum is computed are finite,
hence ...
9
Matrices: Theory and Applications
The quadratic function /, strictly convex, reaches its infimum on the affine sub-
space xo + J#i at a unique vector, which we denote by Xk (same proof as above).
The notation Xk is consistent for k = 0. If x = y + ypk Gio + ^k+l with y G xq + M^, ...
10
Principles of Optimal Design: Modeling and Computation
Although /(*) = 0 for x equal to positive or negative infinity, only the positive one
qualifies as an argument of the infimum. Since x~ <£ P, f(x) is not well bounded
below over P. 6. f(x) = \/x: no g exists, but g0 = g+ = 0 for x~ = oo, so f(x) is not well
...
Panos Y. Papalambros, Douglass J. Wilde, 2000
2 NEWS ITEMS WHICH INCLUDE THE TERM «INFIMUM»
Find out what the national and international press are talking about and how the term
infimum is used in the context of the following news items.
Mental Illness: Our Number One Debilitating Illness
... he was demon possessed,” “We always managed to put up with it until recently,” “I thought I would lose my job if I sought help,” ad infimum. «Valley morning Star, Jun 15»
Holy Grail of Mathematics Pursued in 'The Symphony of Primes …
By an implementation of a binomial coefficient the maximal prime gaps supremum bound is proved, simultaneously establishing the infimum for ... «Broadway World, Oct 13»
