An informal argument shows that common knowledge of rationality implies the iterative elimination of strictly dominated strategies. Rationality here means that players do not play strategies that are strictly dominanted relative to their knowledge. We formalize and prove this claim. When by rationality we mean that players do not play strategies that are weakly dominanted relative to their know...

In this paper we consider a generalization to algebraic number fields of the classical Hermite constant γ n . For this constant we extend the well-known Minkowski bound and study the notion of extreme forms in this setting. Let us briefly recall the definition of Hermite’s constant. Let (a ij ) be a positive definite symmetric real n¬n matrix and let f(x " ,... ,x n ) ̄3 ij a ij x i x j be its a...

It is provided in the paper that the non-conservative dissipative force and asymmetry of time reversal can be naturally introduced into classical statistical mechanics after retarded electromagnetic interaction between charged micro-particles is considered. In this way, the rational dynamic foundation for classical statistical physics can established and the revised Liouville’s equation is obta...

We study the algebra of semigroups Laplacians on Weyl algebra. consider first-order partial differential operators $\nabla^\pm_i$ forming Lie $[\nabla^\pm_j,\nabla^\pm_k]= i\mathcal{R}^\pm_{jk}$ and $[\nabla^+_j,\nabla^-_k] =i\frac{1}{2}(\mathcal{R}^+_{jk}+\mathcal{R}^-_{jk})$ with some anti-symmetric matrices $\mathcal{R}^\pm_{ij}$ define corresponding $\Delta_\pm=g_\pm^{ij}\nabla^\pm_i\nabla^...

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

nearly zero. (3) A watermark is randomized so that a pattern of cyclic cross stripes may disappear and an embedded watermark may be inconspicuous. The embedded watermark is extracted by multiplying the conversely randomized image embedding a watermark by the random sequence. (4) An ID pattern is extracted by summing up the products of any part of the random sequence and the corresponding part o...

1 Roadways, the links of transportation networks, are susceptible to a variety of degradations. 2 Some degradation patterns are severe; they make the network incapable of meeting origin3 destination (OD) demands. Most others are non-severe; they increase the network operational 4 cost while OD demands remain met. In other words, the network structure is resilient to such 5 degradations. It is i...

Consider a N × n random matrix Yn = (Y n ij ) where the entries are given by Y n ij = σ(i/N,j/n) √ n Xn ij , the X n ij being centered i.i.d. and σ : [0, 1] 2 → [0,∞) being a continuous function called a variance profile. Consider now a deterministic N ×n matrix Λn = ( Λij ) whose off-diagonal entries are zero. Denote by Σn the non-centered matrix Yn+Λn and by N ∧n = min(N,n). Then under the as...

We show that solutions of the Bach equation exist which are not conformal Einstein spaces. In connection with fourth order gravitational field equations, cf. e.g. [1, 2] where the breaking of conformal invariance was discussed, the original Bach equation, Bij = 0 , (1) enjoys current interest. Eq. (1) stems from a Lagrangian L = 1 2 √ −gCijklC , and variation gives, cf. Bach [3], 1 √−g δL/δg ij...