On the Livingstone-Wagner Theorem

The case of equality in the Livingstone-Wagner Theorem

Let G be a permutation group acting on a set of size n ∈ N and let 1 ≤ k < (n− 1)/2. Livingstone and Wagner proved that the number of orbits of G on k-subsets of is less than or equal to the number of orbits on (k + 1)-subsets. We investigate the cases when equality occurs.

An Improved WAGNER-WHITIN Algorithm

We present an improved implementation of the Wagner-Whitin algorithm for economic lot-sizing problems based on the planning-horizon theorem and the Economic- Part-Period concept. The proposed method of this paper reduces the burden of the computations significantly in two different cases. We first assume there is no backlogging and inventory holding and set-up costs are fixed. The second model ...

Left ventricular hypertrophy and sudden death.

trans, GM Robertson GE, Livingstone E, Livingstone M, eds. Edinburgh, Scotland: E&S Livingstone, 1921:139. 5. Rosenthal NE, Sack DA, Gillin JC, et al. Seasonal affective disorder: a description of the syndrome and preliminary findings with light therapy. Arch Gen Psychiatry 1984;41:72–80. 6. Kasper S, Wehr TA, Bartko JJ, Gaist P, Rosenthal NE. Epidemiological findings of seasonal changes in moo...

Book Review: Pharmacology by Rang HP, Dale MM, Ritter JM and Moore PK. Fifth edition Churchill Livingstone, Edinburgh, 2003

On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...