We introduce a condition, uniform payoff security, for games with separable metric strategy spaces and payoffs bounded and measurable in players’ strategies. We show that if any such metric game G is uniformly payoff secure, then its mixed extension G is payoff secure. We also establish that if a uniformly payoff secure metric game G has compact strategy spaces, and if its mixed extension G has...

In [4], R. Hamilton has proved that if a compact manifold M of dimension three admits a C Riemannian metric g0 with positive Ricci curvature, then it also admits a metric g with constant positive sectional curvature, and is thus a quotient of the sphere S. In fact, he shows that the original metric can be deformed into the constant-curvature metric by requiring that, for t ≥ 0, x ∈ M and g = g(...

A vertex w of a connected graph G strongly resolves two vertices u, v ∈ V (G), if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension ...

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...

Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in  the unit ball of  the Hilbert space. ...

A family of connected graphs G is said to be a family with constant metric dimension if its metric dimension is finite and does not depend upon the choice of G in G. In this paper, we study the metric dimension of the generalized Petersen graphs P (n, m) for n = 2m + 1 and m ≥ 1 and give partial answer of the question raised in [9]: Is P (n, m) for n ≥ 7 and 3 ≤ m ≤ bn−1 2 c, a family of graphs...

A metric space is often represented as the pair (X,d). An example of metric spaces is (R, Lk), where Lk is the k-norm over R for given n, k ∈ Z≥1. We can represent a finite metric space (X, d) by a symmetric matrix S, of size nxn, where Si,j = d(i, j) and |X| = n. Metric spaces can be visualized using undirected graph G, where S is distance matrix for G. Conversely, given a graph G(V, E), we ca...

In this paper we describe the Einstein-Kähler metric for the Cartan-Hartogs domains which are the special case of the Hua domains. First of all, we reduce the Monge-Ampère equation for the metric to an ordinary differential equation in the auxiliary function X = X(z, w). This differential equation can be solved to give an implicit function in X. Secondly, for some cases, we obtained explicit fo...

Let D be a finite set and g : D × D → R a symmetric function satisfying g(x, x) = 0 and g(x, y) = g(y, x) for all x, y ∈ D. A switch gσ is obtained from g by using a local valuation σ : D → R: gσ(x, y) = σ(x) + g(x, y) + σ(y) for x 6= y. It is shown that every symmetric function g has a unique minimal pseudometric switch, and, moreover, there is a switch gσ of g that is isometric to a finite Ma...

We produce new examples of harmonic maps, having as either source or target manifold the tangent bundle TM on a Riemannian manifold (M,g), equipped with a Riemannian g-natural metric G. In particular, we study the harmonicity of the canonical projection π : (TM,G)→ (M,g), and of the identity map (TM,G)→ (TM,gS) and conversely, gS being the Sasaki metric on TM. A corresponding study is made for ...