WebBy use of the Gordan–Stiemke Theorem of the alternative we demonstrate the similarity of four theorems in combinatorial matrix theory. Each theorem contains five equivalent conditions, one of which is the existence in a given pattern of a line-sum-symmetric or constant-line-sum matrix which is semi-positive or strictly positive for the pattern. WebA Geometric Gordan-Stiemke Theorem G. P. Barker* Department of Mathematics North Carolina State University Raleigh, North Carolina 27650 B. S. Tam Department of …
Vol. 21, No.4, October 1979 - Department of Mathematics
WebAbstract. The purpose of this paper is twofold; first, to present a simple proof of the Farkas theorem (or Farkas lemma or Farkas-Minkowski lemma), proof performed through a nonlinear theorem of the alternative; second, to present various new proofs of the so-called "Tucker key theorem", and to show that these two results are essentially ... WebH. H. HUANG, S. M. ZHANG OPEN ACCESS JMF 125 In this paper, we assume VTj ∈ for j J=1, , .Then 1 J j j j V VTθθ = ∈∑.Our proof must adopt the following notation V VT= ∈∈{θθ J} and V V T [Definition 1] The frictionless market (qV, ) is weakly arbitrage-free if any portfolio θ∈ J of securities has a positive market value qΤθ≥0 whenever it has a positive payoff VTθ black faux leather multi-pocket purses
Stiemke’s Theorem from Farkas
WebJan 1, 1996 · This paper proves compactness from the compactness in Euclidean space by Tychonoff's Theorem, uses the fixed point theorems of Fan (1952) and Glicksberg (1952), and applies the technology taking a diagonal subsequence of some sequence. Stiemke's Lemma is a strict version of Farkas-Minkowski's Lemma. WebStiemke's Theorem [4]. If S is a subspace of Rn and S+ the orthogonal complement of, then SVJS+ contains some vector xS;0, x?^0. In this note we obtain a formula for the number of … WebStiemke's Theorem [4]. If S is a subspace of Rn and S+ the orthogonal complement of, then SVJS+ contains some vector xS;0, x?^0. In this note we obtain a formula for the number of orthants inter-sected by a subspace of R". Stiemke's theorem and ipso the above mentioned transposition theorem will be obtained as a direct conse- ... black faux leather molly skinny fit trousers