Paper's Title:

Viability Theory And Differential Lanchester Type Models For Combat.
Differential Systems.

Author(s):

G. Isac and A. Gosselin

Department Of Mathematics, Royal Military College Of Canada,
P.O. Box 17000, Stn Forces, Kingston, Ontario, Canada K7k 7b4
isac-g@rmc.ca
gosselin-a@rmc.ca
URL: http://www.rmc.ca/academic/math_cs/isac/index_e.html
URL: http://www.rmc.ca/academic/math_cs/gosselin/index_e.html

Abstract:

In 1914, F.W. Lanchester proposed several mathematical models based on differential equations to describe combat situations [34]. Since then, his work has been extensively modified to represent a variety of competitions including entire wars. Differential Lanchester type models have been studied from many angles by many authors in hundreds of papers and reports. Lanchester type models are used in the planning of optimal strategies, supply and tactics. In this paper, we will show how these models can be studied from a viability theory stand point. We will introduce the notion of winning cone and show that it is a viable cone for these models. In the last part of our paper we will use the viability theory of differential equations to study Lanchester type models from the optimal theory point of view.

Paper's Title:

Boundedness for Vector-Valued Multilinear Singular Integral Operators on Triebel-Lizorkin Spaces

Author(s):

Liu Lanzhe

College of Mathematics
Changsha University of Science and Technology,
Changsha 410077,
P.R. of China.
lanzheliu@263.net

Abstract:

In this paper, the boundedness for some vector-valued multilinear operators associated to certain fractional singular integral operators on Triebel-Lizorkin space are obtained. The operators include Calderón-Zygmund singular integral operator and fractional integral operator.

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