A wide variety of environmental cues, including inflammatory cytokines, ligands for pattern recognition receptors and endogenous danger signals, activate the inducible transcription factor nuclear factorκ B (NFκ B), which is a central regulator of inflammatory and immune responses. Excessive activation of NFκ B results in the development of severe diseases, such as chronic inflammatory disorder...

Let φ1 stand for the statement V = HOD and φ2 stand for the Ground Axiom. Suppose Ti for i = 1, . . . , 4 are the theories “ZFC + φ1 + φ2”, “ZFC + ¬φ1 + φ2”, “ZFC + φ1 + ¬φ2”, and “ZFC + ¬φ1 + ¬φ2” respectively. We show that if κ is indestructibly supercompact and λ > κ is inaccessible, then for i = 1, . . . , 4, Ai =df {δ < κ | δ is an inaccessible cardinal which is not a limit of inaccessible...

The tree property at κ states that there are no Aronszajn trees on κ, or, equivalently, that every κ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible...

We study the approachability ideal I[κ+] in the context of large cardinals and properties of the regular cardinals below a singular κ. As a guiding example consider the approachability ideal I[אω+1] assuming that אω is a strong limit. In this case we obtain that club many points in אω+1 of cofinality אn for some n > 1 are approachable assuming the joint reflection of countable families of stati...

A universal space is one that continuously maps onto all others of its own kind and weight. We investigate when a universal Uniform Eberlein compact space exists for weight κ. If κ = 2<κ, then they exist whereas otherwise, in many cases including κ = ω1, it is consistent that they do not exist. This answers (for many κ and consistently for all κ) a question of Benyamini, Rudin and Wage of 1977.

Starting from the κ-distribution function, obtained by applying the maximal entropy principle to the κ-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical κ-partition function and discuss its main properties. It is shown that all important macroscopical quantities of the system can be expressed employing only the κ-partition function. The relations...

Let T be a complete, first-order theory in a finite or countable language having infinite models. Let I(T, κ) be the number of isomorphism types of models of T of cardinality κ. We denote by μ (respectively μ̂) the number of cardinals (respectively infinite cardinals) less than or equal to κ. Theorem I(T, κ), as a function of κ > א0, is the minimum of 2 κ and one of the following functions: 1. 2...

We show that a strong form of the so called Lindström’s Theorem [4] fails to generalize to extensions of Lκω and Lκκ : For weakly compact κ there is no strongest extension of Lκω with the (κ, κ)-compactness property and the Löwenheim-Skolem theorem down to κ . With an additional set-theoretic assumption, there is no strongest extension of Lκκ with the (κ, κ)-compactness property and the Löwenhe...

Plasma shaping effects on temperature gradient-driven instabilities and geodesic acoustic oscillations are investigated with a gyrokinetic theory and a local magnetohydrodynamics equilibrium model. In specific, we focus on the effect of the elongation κ , including its radial derivative ( )( ) r r s ∂ ∂ = κ κ κ , in the large aspect ratio limit. An analytical formula of the dependence of the GA...