A method of iteration of Prikry type forcing notions as well as a forcing for adding clubs is presented. It is applied to construct a model with a measurable cardinal containing a club of former regulars, starting with o(κ) = κ+ 1. On the other hand, it is shown that the strength of above is at least o(κ) = κ. Suppose that κ is an inaccessible cardinal. We wish to find a generic extension (usua...

The polyhomeotic (ph) locus of Drosophila is a complex locus essential for the maintenance of segmental identity. Genetic analysis suggested that two independent units contribute to ph function. Comparison of genomic sequence shows that the ph locus has been duplicated, and that it contains proximal and distal transcription units. The proximal transcription unit encodes two embryonic mRNAs of 6...

Suppose λ > κ is measurable. We show that if κ is either indestructibly supercompact or indestructibly strong, then A = {δ < κ | δ is measurable, yet δ is neither δ+ strongly compact nor a limit of measurable cardinals} must be unbounded in κ. The large cardinal hypothesis on λ is necessary, as we further demonstrate by constructing via forcing two models in which A = ∅. The first of these cont...

In this paper, we propose two algorithms, namely extrapolated proximal iterative hard thresholding (EPIHT) algorithm and EPIHT algorithm with line-search (EPIHT-LS), for solving `0 norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of KurdykaLojasiewicz property, we show that the sequences generated by the two algorithms converge to a local m...

We study several cardinal, and ordinal–valued functions that are relatives of Hanf numbers. Let κ be an infinite cardinality, and let T ⊆ Lκ+,ω be a theory of cardinality ≤ κ, and let γ be an ordinal ≥ κ. Consider (1) μT (γ, κ) := min{μ∗ : ∀φ ∈ L∞,ω , with rk(φ) < γ, if T has the (φ, μ∗)order property then there exists a formula φ ′ (x; y) ∈ Lκ+,ω , such that for every χ ≥ κ, T has the (φ , χ)-...

In this study, by generalizing the notion of fuzzy bi-ideals ordered semirings, (∈,∈∨(κ*,qκ))-fuzzy is established. We prove that are but converse not true, and an example provided to support proof. A condition given under which semirings coincide with bi-ideals. An equivalent certain correspondences between presented. Moreover, (κ*,κ)-lower part described depicted in terms several classes semi...

We present a strongly compact version of the Supercompact Magidor forcing ([3]). A variation of it is used to show that the following is consistent: V ⊇ W are transitive models of ZFC+GCH with the same ordinals such that: 1. κ is an inaccessible in W , 2. κ changes its cofinality to ω1 in V witnessed by a club ⟨κα | α < ω1⟩, 3. for every α < ω1, (κ ++ α ) W < κα , 4. (κ++)W = κ+. 1 Preliminary ...

The effects of a current-limited breakdown (BD) on the post-BD current of MOS capacitors with a thin high-k dielectric stack have been analysed. A strong current reduction after BD and, consequently, a partial recovery of the insulating properties of the dielectric stack is observed. The similarities with the Resistive Switching phenomenon observed in MIM structures for memory applications are ...

In this review, we give a basic introduction to the κ-deformed relativistic phase space and free quantum fields. After review of κ-Poincaré algebra, illustrate construction classical particle using tools Lie bi-algebras Poisson–Lie groups. We then discuss how construct scalar field theory on non-commutative κ-Minkowski associated group valued nature momenta affects propagation.

We consider generalizations of a well-known class of spaces, called by S. Mrówka, N ∪R, where R is an infinite maximal almost disjoint family (MADF) of countable subsets of the natural numbersN . We denote these generalizations by ψ = ψ(κ,R) for κ ≥ ω. Mrówka proved the interesting theorem that there exists an R such that |βψ(ω,R) \ ψ(ω,R)| = 1. In other words there is a unique free z-ultrafilt...