We obtain the further characterizations and properties of weakly open functions in bitopological spaces due to Jelić [5]. AMS Mathematics Subject Classification (2000): 54C10, 54E55

Let (Ek)k∈N be a sequence of differential information economies, converging to a limit differential information economy E∞ (written as Ek ⇒ E∞). Denote by C (Ek) the set of all -private core allocations, ≥ 0 (for = 0 we get the private core of Yannelis (1991), denoted by C(Ek)). Under appropriate conditions, we prove the following stability results: (1) (upper semicontinuity): if Ek ⇒ E∞, fk ∈ ...

A stochastic process X is strongly stationary if its fdds are invariant under time shifts, that is, for any (finite) n, for any t0 and for all t1, ..., tn ∈ T , (Xt1 , ..., Xtn) and (Xt1+t0 , ..., Xtn+t0) have the same distribution. A stochastic process X is weakly stationary if its mean function is constant and its covariance function is invariant under time shifts. That is, for all t ∈ T , E(...

We prove that, if M is a weakly 4-connected matroid with |E(M)| 7 and neither M nor M∗ is isomorphic to the cycle matroid of a ladder, then M has a proper minor M ′ such that M ′ is weakly 4-connected and |E(M ′)| |E(M)| − 2 unless M is some 12-element matroid with a special structure. © 2007 Elsevier Inc. All rights reserved.

Given an r-uniform hypergraph H = (V,E) and a weight function ω : E → {1, . . . , w}, a coloring of vertices of H, induced by ω, is defined by c(v) = ∑ e3v w(e) for all v ∈ V . If there exists such a coloring that is strong (that means in each edge no color appears more than once), then we say that H is strongly w-weighted. Similarly, if the coloring is weak (that means there is no monochromati...

Existence of zeros for operators taking their values in the dual of a Banach space BIAGIO RICCERI Throughout the sequel, E denotes a reflexive real Banach space and E * its topological dual. We also assume that E is locally uniformly convex. This means that for each x ∈ E, with x = 1, and each ǫ > 0 there exists δ > 0 such that, for every y ∈ E satisfying y = 1 and x − y ≥ ǫ, one has x + y ≤ 2(...

lut 009 meteorite was found during a trip to lut desert of iran in march,2012, at 30°20.38' n, 59°09.04' e. chemical compositions of equilibrated olivine (fa19.3 ± 0.5) and orthopyroxene (fs16.7 ± 0.6) show that the meteorite sample belongs to h group of ordinary chondrites, while the texture (chondrule petrography and plagioclase size) suggests a petrologic type of 4. the lut 009 has...

We study the weak* lower semicontinuity properties of functionals of the form F (u) = ess sup x∈Ω f(x,Du(x)) where Ω is a bounded open set of R and u ∈ W 1,∞(Ω). Without a continuity assumption on f(·, ξ) we show that the supremal functional F is weakly* lower semicontinuous if and only if it is a level convex functional (i.e. it has convex sub levels). In particular if F is weakly* lower semic...

If G is a locally compact topological group, let BC{G) denote the set of real-valued, bounded, uniformly continuous functions on G with the compact-open topology. Using the fact that the distal (weakly distal) functions are the elements of BC(G) whose orbit closures are compact distal (point-distal) minimal sets, we can characterize compact distal and point-distal minimal transformation groups....

in 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $a_{s}$ over a monoid $s$ that can be described by means of when the functor $a_{s} otimes -$ preserves pullbacks. in this paper, we extend these results to$s$-posets and present equivalent descriptions of weakly kernel po...