For an infinite cardinal μ, MAD(μ) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over μ. Erdős and Hechler proved in [7] the consistency of μ ∈ MAD(μ) for a singular cardinal μ and asked if it was ever possible for a singular μ that μ / ∈ MAD(μ), and also whether 2 μ < μ =⇒ μ ∈ MAD(μ) for every singular cardinal μ. We introduce a new method for controlling ...

We study a free boundary problem modeling tumor growth with T-periodic supply Φ(t) of external nutrients. The model contains two parameters μ and σ˜. first show that (i) zero radially symmetric solution is globally stable if only σ˜⩾1T∫0TΦ(t)dt; (ii) If σ˜<1T∫0TΦ(t)dt, then there exists unique positive σ∗(r,t),p∗(r,t),R∗(t) period T it global attractor all solutions for μ>0. These results are p...

We introduce minimally expansive and GH-stable points for homeomorphisms on metric spaces μ-uniformly expansive, μ-shadowable strong μ-topologically stable Borel measures (with respect to a homeomorphism space). prove that: (i) shadowable point of compact space is topologically GH-stable; (ii) measure μ space) stable.

As part of an educational exercise designed to introduce school students the technique single-crystal X-ray diffraction and enhance their understanding primary secondary bonding, a group nine was given opportunity prepare new compounds solve refine data collected on crystalline materials they had prepared. Their investigation alkali metal salts 4-hydroxybenzoic acid (H 2 hba) yielded structures...

We define analogues of modal Sahlqvist formulas for the modal mucalculus, and prove a correspondence theorem for them.

THE SYMBOLISM of language is, or may be, twofold. By far the greater portion of its recognized content and structure is symbolic in a purely referential sense; in other words, the meaningful combinations of vowels and consonants (words, significant parts of words, and word groupings) derive their functional significance from the arbitrary associations between them and their meanings established...

In this work we present a categorical approach for modeling the pure (i.e., without constants) call-by-value -calculus, defined by Plotkin as a restriction of the classical one. In particular, we study the properties a category must enjoy for give rise to a model of such a language. This definition is enough general for grasping models in different settings.