Generic absoluteness and boolean names for elements of a Polish space

It is common knowledge in the set theory community that there exists a duality relating the commutative $C^*$-algebras with the family of $B$-names for complex numbers in a boolean valued model for set theory $V^B$. Several aspects of this correlation have been considered in works of the late $1970$'s and early $1980$'s, for example by Takeuti, and by Jech. Generalizing Jech's results, we extend this duality so as to be able to describe the family of boolean names for elements of any given Polish space $Y$ (such as the complex numbers) in a boolean valued model for set theory $V^B$ as a space $C^+(X,Y)$ consisting of functions $f$ whose domain $X$ is the Stone space of $B$, and whose range is contained in $Y$ modulo a meager set. We also outline how this duality can be combined with generic absoluteness results in order to analyze, by means of forcing arguments, the theory of $C^+(X,Y)$.Comment: 27 page

Strongly outer actions of amenable groups on Z-stable nuclear C*-algebras

Let A be a separable, unital, simple, Z-stable, nuclear C⁎-algebra, and let α:G→Aut(A) be an action of a discrete, countable, amenable group. Suppose that the orbits of the action of G on T(A) are finite and that their cardinality is bounded. We show that the following are equivalent: (1) α is strongly outer; (2) α⊗idZ has the weak tracial Rokhlin property. If G is moreover residually finite, the above conditions are also equivalent to (3) α⊗idZ has finite Rokhlin dimension (in fact, at most 2). If ∂eT(A) is furthermore compact, has finite covering dimension, and the orbit space ∂eT(A)/G is Hausdorff, we generalize results by Matui and Sato to show that α is cocycle conjugate to α⊗idZ, even if α is not strongly outer. In particular, in this case the equivalences above hold for α in place of α⊗idZ. In the course of the proof, we develop equivariant versions of complemented partitions of unity and uniform property Γ as technical tools of independent interest

Humic substances stimulate maize nitrogen assimilation and amino acid metabolism at physiological and molecular level

The effects of a humic substance (HS) extracted from a volcanic soil on the nitrate assimilation pathway of Zea mays seedlings were thoroughly examined using physiological and molecular approaches. Plant growth, the amount of soluble proteins and amino acids, as well as the activities of the enzymes involved in nitrogen metabolism and Krebs cycle, were evaluated in response to different HS concentrations (0, 1 and 5 mg C L−1) supplied to maize seedlings for 48 h. To better understand the HS action, the transcript accumulation of selected genes encoding enzymes involved in nitrogen assimilation and Krebs cycle was additionally evaluated in seedlings grown for 2 weeks under nitrogen (N) sufficient condition and N deprivation. HS at low concentration (1 mg C L−1) positively influenced nitrate metabolism by increasing the content of soluble protein and amino acids synthesis. Furthermore, the activity and transcription of enzymes functioning in N assimilation and Krebs were significantly stimulated. HS treatment influenced the gene expression of Zea mays plants at transcriptional level and this regulation was closely dependent on the availability of nitrate in the growth medium

Pigment in Western Iberian Schematic Rock Art: An analytical approach

This paper explores the processes involved in the production of prehistoric paintings using inorganic pigmentation. The focus for discussion involves a number of rock-shelter sites that contain rock art within the western part of the Iberian Peninsula, with particular reference to the sites that contain Schematic rock art. A direct date cannot be obtained on rock art that is made with inorganic pigments. However, sampling and subsequent analysis has clearly shown that pigments were produced using tried and tested recipes that involved the use of sometimes organic binders. This paper will explore the chemical and mineralogical qualities of sampled pigments from a selected number of sites within Spain and Portugal and suggest that pigmentation was more than just applying paint to rock.info:eu-repo/semantics/publishedVersio