Vector space structure of finite evolutionary games and its application to strategy profile convergence

2016 ◽  
Vol 29 (3) ◽  
pp. 602-628 ◽  
Author(s):  
Hongsheng Qi ◽  
Yuanhua Wang ◽  
Ting Liu ◽  
Daizhan Cheng
Keyword(s):  
Vector Space ◽  
Evolutionary Games ◽  
Space Structure ◽  
Strategy Profile

scholarly journals FINITE-DIMENSIONAL ORDERED VECTOR SPACES WITH RIESZ INTERPOLATION AND EFFROS–SHEN’S UNIMODULARITY CONJECTURE

2016 ◽  
Vol 101 (2) ◽  
pp. 277-287
Author(s):  
AARON TIKUISIS
Keyword(s):  
Vector Space ◽  
Inductive Limit ◽  
Space Structure ◽  
Vector Spaces ◽  
Ordered Vector Space ◽  
Finite Dimensional ◽  
Ordered Vector Spaces

It is shown that, for any field $\mathbb{F}\subseteq \mathbb{R}$, any ordered vector space structure of $\mathbb{F}^{n}$ with Riesz interpolation is given by an inductive limit of a sequence with finite stages $(\mathbb{F}^{n},\mathbb{F}_{\geq 0}^{n})$ (where $n$ does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with $\mathbb{F}$ replaced by the integers, $\mathbb{Z}$. Indeed, it shows that although Effros and Shen’s conjecture is false, it is true after tensoring with $\mathbb{Q}$.

scholarly journals FOCK SPACE STRUCTURE FOR THE SIMPLEST PARASUPERSYMMETRIC SYSTEM

2001 ◽  
Vol 16 (15) ◽  
pp. 963-971 ◽  
Author(s):  
WEIMIN YANG ◽  
SICONG JING
Keyword(s):  
Vector Space ◽  
State Vector ◽  
Fock Space ◽  
Space Structure ◽  
The State ◽  
Degree Of Freedom ◽  
Basis Vectors

Structure of the state-vector space for a system consisting of one mode para-Bose and one mode para-Fermi degree of freedom with the same parastatistics order p is studied and a complete, orthonormal set of basis vectors in this space is constructed. There is an intrinsic double degeneracy for state vectors with m parabosons and n parafermions, where m ≠ 0, n ≠ 0 and n ≠ p. It is also shown that the degeneracy plays a key role in realization of exact supersymmetry for such a system.

The learning of the vector space structure by sixth grade students

1971 ◽  
Vol 4 (2) ◽  
pp. 166-181 ◽  
Author(s):  
William E. Lamon ◽  
Leslie E. Huber
Keyword(s):  
Vector Space ◽  
Sixth Grade ◽  
Space Structure ◽  
Sixth Grade Students

scholarly journals A New Proof of the Pythagorean Theorem and Its Application to Element Decompositions in Topological Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Fred Greensite
Keyword(s):  
Vector Space ◽  
Algebraic Structure ◽  
Geometric Mean ◽  
Topological Algebra ◽  
Space Structure ◽  
Pythagorean Theorem ◽  
Euclidean Norm ◽  
Topological Algebras

We present a new proof of the Pythagorean theorem which suggests a particular decomposition of the elements of a topological algebra in terms of an “inverse norm” (addressing unital algebraic structure rather than simply vector space structure). One consequence is the unification of Euclidean norm, Minkowski norm, geometric mean, and determinant, as expressions of this entity in the context of different algebras.

Additive reducts of algebraically closed valued fields

2015 ◽  
Vol 27 (2) ◽  
Author(s):  
Fares Maalouf
Keyword(s):  
Vector Space ◽  
Space Structure ◽  
Closed Field ◽  
Valued Fields ◽  
Algebraically Closed Field ◽  
Open Set

AbstractIn this paper we prove a form of the Zilber's trichotomy conjecture for reducts of algebraically closed valued fields of characteristic 0 which are expansions of the valued vector space structure. We prove first that a non-modular reduct of a nontrivially valued algebraically closed field containing the valued vector space structure defines a non-semilinear curve. Then we show that the expansion of such a reduct by a non-semilinear curve defines multiplication on a nonempty open set.

Major subspaces of recursively enumerable vector spaces

1978 ◽  
Vol 43 (2) ◽  
pp. 293-303 ◽  
Author(s):  
Iraj Kalantari
Keyword(s):  
Vector Space ◽  
Space Structure ◽  
Vector Spaces ◽  
Recent Theory ◽  
Essential Difference ◽  
Infinite Dimensional ◽  
Recursively Enumerable ◽  
Partial Recursive Functions ◽  
Initial Work ◽  
Object Of Study

The main point of this paper is a further development of some aspects of the recent theory of recursively enumerable (r.e.) algebraic structures. Initial work in this area is due to Frölich and Shepherdson [4] and Rabin [10]. Here we are only concerned with vector space structure. The previous work on r.e. vector spaces is due to Dekker [2], [3], Metakides and Nerode [8], Remmel [11], Retzlaff [13], and the author [5].Our object of study is V∞ a countably infinite dimensional fully effective vector space over a countable recursive field . By fully effective we mean that V∞. under a fixed Godel numbering has the following properties:(i) Operations of vector addition and scalar multiplication on V∞ are presented by partial recursive functions on the Gödel numbers of elements of V∞.(ii) V∞ has a dependence algorithm, i.e., there is a uniform effective procedure which applied to any n vectors of V∞ determines whether or not they are linearly independent.We also study , the lattice of r.e. subspaces of V∞ (under the operations of intersection, ⋂ and (weak) sum, +). We note that if is not distributive and is merely modular (see [1]). This fact indicates the essential difference between the lattice of r.e. sets and .

scholarly journals A theorem of the alternative and a two-function minimax theorem

2004 ◽  
Vol 2004 (2) ◽  
pp. 169-177 ◽  
Author(s):  
Anton Stefanescu
Keyword(s):  
Vector Space ◽  
Minimax Theorem ◽  
Space Structure ◽  
Theorem Of The Alternative

The two main results of the paper are a theorem of the alternative of Gordan type and a two-function minimax theorem. Both are based on some weakened convexlike properties, without any vector space structure.

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