Additive averages of multiplicative correlation sequences and applications

We study sets of recurrence, in both measurable and topological settings, for actions of $(\mathbb{N},\times)$ and $(\mathbb{Q}^{>0},\times)$. In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form $\{(an+b)^{\ell}/(cn+d)^{\ell}: n \in \mathbb{N}\}$ are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function

Averages of completely multiplicative functions over the Gaussian integers -- a dynamical approach

We prove a pointwise convergence result for additive ergodic averages associated with certain multiplicative actions of the Gaussian integers. We derive several applications in dynamics and number theory, including: (i) Wirsing's theorem for Gaussian integers: if $f\colon \mathbb{G} \to \mathbb{R}$ is a bounded completely multiplicative function, then the following limit exists: $$\lim_{N \to \infty} \frac{1}{N^2} \sum_{1 \leq m, n \leq N} f(m + {\rm i} n).$$ (ii) An answer to a special case of a question of Frantzikinakis and Host: for any completely multiplicative real-valued function $f: \mathbb{N} \to \mathbb{R}$, the following limit exists: $$\lim_{N \to \infty} \frac{1}{N^2} \sum_{1 \leq m, n \leq N} f(m^2 + n^2).$$ (iii) A variant of a theorem of Bergelson and Richter on ergodic averages along the $\Omega$ function: if $(X,T)$ is a uniquely ergodic system with unique invariant measure $\mu$, then for any $x\in X$ and $f\in C(X)$, $$\lim_{N\to\infty}\frac{1}{N^2}\sum_{1 \leq m, n \leq N} f(T^{\Omega(m^2 + n^2)}x)=\int_Xf \ d\mu.$$Comment: 32 page

Clustering of Radio Galaxies and Quasars

We compute the cross-correlation between a sample of 14,000 radio-loud AGN (RLAGN) with redshifts between 0.4 and 0.8 selected from the Sloan Digital Sky Survey and a reference sample of 1.2 million luminous red galaxies in the same redshift range. We quantify how the clustering of radio-loud AGN depends on host galaxy mass and on radio luminosity. Radio-loud AGN are clustered more strongly on all scales than control samples of radio-quiet galaxies with the same stellar masses and redshifts, but the differences are largest on scales less than 1 Mpc. In addition, the clustering amplitude of the RLAGN varies significantly with radio luminosity on scales less than 1 Mpc. This proves that the gaseous environment of a galaxy on the scale of its dark matter halo, plays a key role in determining not only the probability that a galaxy is radio-loud AGN, but also the total luminosity of the radio jet. Next, we compare the clustering of radio galaxies with that of radio-loud quasars in the same redshift range. Unified models predict that both types of active nuclei should cluster in the same way. Our data show that most RLAGN are clustered more strongly than radio-loud QSOs, even when the AGN and QSO samples are matched in both black hole mass and radio luminosity. Only the most extreme RLAGN and RLQSOs in our sample, with radio luminosities in excess of 10^26 W/Hz, have similar clustering properties. The majority of the strongly evolving RLAGN population at z~0.5 are found in different environments to the quasars, and hence must be triggered by a different physical mechanism.Comment: 12 pages, 13 Figures, submitted to MNRA

ABA biosynthesis- and signaling-related gene expression differences between sweet cherry fruits suggest attenuation of ABA pathway in bicolored cultivars

Fruit development involves exocarp color evolution. However, signals that control this process are still elusive. Differences between dark-red and bicolored sweet cherry cultivars rely on MYB factor gene mutations. Color evolution in bicolored fruits only occurs on the face receiving sunlight, suggesting the perception or response to color-inducing signals is affected. These color differences may be related to synthesis, perception or response to abscisic acid (ABA), a phytohormone responsible for non-climacteric fruit coloring. This work aimed to determine the involvement of ABA in the coloring process of color-contrasting varieties. Several phenolic accumulation patterns differed between bicolored ‘Royal Rainier’ and dark-red ‘Lapins’. Transcript abundance of ABA biosynthetic genes (PavPSY, PavZEP and PavNCED1) decreased dramatically from the Pink to Red stage in ‘Royal Rainier’ but increased in ‘Lapins’, which correlated with a higher ABA content in this dark-red cultivar. Transcripts coding for ABA signaling (PavPP2Cs, PavSnRKs and PavMYB44.1) were almost undetectable at the Red stage in ‘Royal Rainier’. Field trials revealed that ‘Royal Rainier’ color development was insensitive to exogenous ABA, whereas it increased in ‘Lapins’. Furthermore, ABA treatment only increased transcript levels of signaling genes in ‘Lapins’. Further studies may address if the ABA pathway is attenuated in bicolor cultivar

Discurso empleado en el ambiente escolar por los estudiantes de los grados 6-1 y 6-7 de la instituci?n t?cnica educativa Francisco de Paula Santander de la ciudad de Ibagu? una aproximaci?n ling??stica

108 p. Recurso Electr?nicoEste trabajo de grado consiste en realizar una aproximaci?n ling??stica hacia el discurso originado a partir de los enunciados verbales y no verbales creados por los estudiantes de los grados 6-1 y 6-7 de la Instituci?n T?cnica Francisco de Paula Santander, de la ciudad de Ibagu?, en espacios escolares con el fin de divulgarlos y realizarles un an?lisis l?xico, pragm?tico, semi?tico y socioling??stico en pro de mostrar los cambios que permanentemente sufre el lenguaje y como este influye en las estructuras sociales y culturales. El trabajo consta de tres etapas b?sicamente, por medio de las cuales se desarroll? el dise?o metodol?gico, la primera de ellas va enfocada a la contextualizaci?n de la Instituci?n T?cnica Educativa Francisco de Paula Santander de la ciudad de Ibagu? y la zona residencial en donde esta se encuentra. La segunda etapa da a conocer todo lo relacionado a las fases que se implementaron, con base al documento ?Redescubrir la Escuela? que se dieron a trav?s, de los diferentes semestres de la carrera universitaria ?Licenciatura en Educaci?n B?sica con ?nfasis en Lengua Castellana?. La ?ltima secci?n presenta ?el taller?, como estrategia metodol?gica en la intervenci?n realizada en el aula de clases, con un fin espec?fico y, es el de elaborar expresiones orales y graficas propias del discurso de los alumnos mencionados anteriormente, a partir de la implementaci?n de medios tem?ticos como lo son la m?sica, la literatura y el cortometraje. Palabras Claves: Discurso, Estudiantes, Contexto Socio Cultural, Simbolismo, intenciones comunicativas.This degree work is to conduct a linguistic approach to speech originated from verbal statements and nonverbal created by students in grades 6-1 and 6-7 of the Technical Institution Francisco de Paula Santander, city Ibague, in school areas in order to disseminate and have a follow lexical, pragmatic and sociolinguistic analysis in favor of showing the changes permanently suffer the language and how it affects the social and cultural structures. The work consists of three stages basically, through which the methodological design was developed, the first one is focused on the contextualization of the Educational Technical Institution Francisco de Paula Santander city of Ibague and the residential area where this is find. The second stage disclosed everything related to the phases that were implemented, based on the document "Rediscovering School" that got through, the different semesters of university studies "Degree in Basic Education with Emphasis in Spanish Language" . The final section presents "workshop" as a methodological strategy for intervention in the classroom, with a specific purpose and is to develop oral expressions and graphs own speech of students mentioned above, from the implementation thematic media such as music, literature and film. Keywords: Speech, Students, Socio-Cultural Context, Symbolism, Communicative intentions

The cross-fertilization of jurisprudence and the principle of proportionality : process and result from a canadian perspective

Modern comparative constitutionalism traces back at least to the practice of some states in the post-World War II era of adopting democratic regimes as well as constitutionally entrenched bills of rights. It has since been fueled by the proliferation of international human rights instruments, which has increased with the end of the Cold War. Significant attention was first paid to comparative constitutional structure, but many states have now reached another stage. As notably witnessed by the works of the Council of Europe and especially those of the Venice Commission in the domain of constitutional justice, the question now is no longer about constitutionalism, including whether rights should be constitutionally protected, as much as it is about constitutional justice: how to effectively implement constitutions. Both on a regional and a global level, mutual inspiration is increasingly drawn from the case-law of peer Courts of other countries and even other continents, which gives rise to a cross-fertilisation phenomenon. One constitutional principle that emerges from, and which is still being forged by, such cross-fertilisation is the principle according to which the limitation of human rights and freedoms must be proportional to states’ objectives, that is, the principle of proportionality. More specifically, our topic is about both the historical process of jurisprudential cross-fertilisation and its functional result as far as the principle of proportionality is concerned. We speak from a Canadian perspective. The aim here is to be able to distinguish between what is common and what is distinctive about the Canadian approach