Applications of the chiral expansion to generalize the Gerasimov-Drell-Hearn sum rule for finite Q are discussed. The observation of several authors, that the corrections to the leading order contributions are large and limit the applicability to a very small range in Q, are only valid when considering the generalization of the sum rule for protons and neutrons, separately. When using the proto...

The original theme of the paper is the existence proof of “there is η̄ = 〈ηα : α < λ〉 which is a (λ, J)-sequence for Ī = 〈Ii : i < δ〉, a sequence of ideals. This can be thought of as in a generalization to Luzin sets and Sierpinski sets, but for the product ∏ i<δ dom(Ii), the existence proofs are related to pcf. The second theme is when does a Boolean algebraB has free caliber λ (i.e. if X ⊆ B a...

The original theme of the paper is the existence proof of “there is η̄ = 〈ηα : α < λ〉 which is a (λ, J)-sequence for Ī = 〈Ii : i < δ〉, a sequence of ideals”. This can be thought of as a generalization to Luzin sets and to Sierpinski sets, but for the product ∏ i<δ Dom(Ii), the existence proofs are related to pcf. The second theme is when does a Boolean algebra B have a free caliber λ (i.e. if X ...

In the paper two variants of a combinatorial problem for the set F n q of sequences of length n over the alphabet Fq = {0, 1, .., q − 1} are considered, with some applications. The original problem was the following: for a given word w ∈ F n q , what is the smallest integer k such that we can reconstruct w if we know all of its subwords of length k. This problem was solved by Lothaire [8] . We ...

In the paper two variants of a combinatorial problem for the set F q of sequences of length n over the alphabet Fq = {0, 1, .., q − 1} are considered, with some applications. The original problem was the following: what is the smallest k such that every word v ∈ F q is uniquely determined by the set of its subwords of length up to k. This problem was solved by Lothaire [1]. We consider the foll...

We call a comb a map f : I → [0,∞), where I is a compact interval, such that {f ≥ ε} is finite for any ε. A comb induces a (pseudo)-distance d̄f on {f = 0} defined by d̄f (s, t) = max(s∧t,s∨t) f . We describe the completion Ī of {f = 0} for this metric, which is a compact ultrametric space called comb metric space. Conversely, we prove that any compact, ultrametric space (U, d) without isolated p...

Due to enormous applications of metal oxide nanoparticles in research and health-related applications, metal oxide nanoparticles are increasingly being developed through cheaper and more user-friendly approaches. We have formulated a simple route to synthesize zinc oxide nanoparticles (ZNPs) by a sol-gel method at near-room temperatures 25°C, 35°C, 55°C, and 75°C. The results are analyzed by X-...