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...