On the group of homeomorphisms on R: A revisit

[EN]  In this article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results known about the group of homeomorphisms on R and about the group of increasing homeomorphisms on R ([2], [6], [7] and [8]), but beyond this there is virtually nothing in the literature concerning the topological structure in the aspects of topological dynamics. In this paper, we analyze this structure in some detail.The first author acknowledges SERB-MATRICS Grant No. MTR/2018/000256 for financial support. The second author acknowledges University of Calicut, Seed Money (U.O. No. 11733/2021/Admn; Dated: 11.10.2021), INDIA for financial support.Ali Akbar, K.; Mubeena, T. (2022). On the group of homeomorphisms on R: A revisit. Applied General Topology. 23(2):269-280. https://doi.org/10.4995/agt.2022.1614326928023

Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups

Given an automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-twisted conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-twisted conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that SL$(n,\mathbb{Z})$ and its congruence subgroups have the $R_\infty$-property. Further we show that any (countable) abelian extension of $\Gamma$ has the $R_\infty$-property where $\Gamma$ is a torsion free non-elementary hyperbolic group, or SL$(n,\mathbb{Z})$, Sp$(2n,\mathbb{Z})$ or a principal congruence subgroup of SL$(n,\mathbb{Z})$ or the fundamental group of a complete Riemannian manifold of constant negative curvature

Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups

Given a group automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that any irreducible lattice in a connected semi simple Lie group having finite centre and rank at least 2 has the $R_\infty$-property.Comment: 6 page

Discretion Preservative Itinerant Health Scrutinising By Haze Succour

Haze-assisted mobile health (mHealth) monitoring,which applies the prevailing mobile communications and Haze computing technologies to provide feedback decision support, has been considered as a revolutionary approach to improving the quality of healthcare service while lowering the healthcare cost. Unfortunately, it  also  poses  a  serious  risk  on  both  clients Confidentiality and intellectual property of monitoring service providers, which could deter the wide adoption of mHealth technology. This paper is to address this important problem and design a Hazeassisted Confidentiality Conserving mobile health monitoring system to protect the Confidentiality of the involved parties and their data. Moreover, the outsourcing decryption technique and a newlyproposed key private proxy re-encryption are adapted to shift the computational complexity of the involved parties to the Haze without compromising clients’ Confidentiality and service providers’ intellectual property. Finally, our security and performance analysis demonstrates the effectiveness of our proposed design

Constraints Encountered by Rural Youth for Establishment of Agri-Enterprises and Elicit Suggestions to Overcome Them

India is with a high level of youth unemployment. Markets have insufficient jobs to absorb young job seekers. The purpose of the study was to identify constraints and suggestions that are faced by the rural youth who are engaged in agri-enterprises. A sample of 240 youth involved in agripreneurshipwasgiven questionnaires. The findings of the study indicated that the youth faced many challenges while establishing their agri-enterprises.The primary constraint faced by rural youth were economic constraints followed by technical constraints, psychological constraints, extension-related constraints, social constraints,and other constraints. The constraints perceived and the suggestions given by the rural youth for the establishment of agri-enterprises to overcome their constraints were observed and depicted

Circulating miRNAs in Women with Polycystic Ovary Syndrome: A Longitudinal Cohort Study

Background: Women with polycystic ovary syndrome (PCOS) often change their metabolic profile over time to decrease levels of androgens while often gaining a propensity for the development of the metabolic syndrome. Recent discoveries indicate that microRNAs (miRNAs) play a role in the development of PCOS and constitute potential biomarkers for PCOS. We aimed to identify miRNAs associated with the development of an impaired metabolic profile in women with PCOS, in a follow-up study, compared with women without PCOS. Methods and materials: Clinical measurements of PCOS status and metabolic disease were obtained twice 6 years apart in a cohort of 46 women with PCOS and nine controls. All participants were evaluated for degree of metabolic disease (hypertension, dyslipidemia, central obesity, and impaired glucose tolerance). MiRNA levels were measured using Taqman® Array cards of 96 pre-selected miRNAs associated with PCOS and/or metabolic disease. Results: Women with PCOS decreased their levels of androgens during follow-up. Twenty-six of the miRNAs were significantly changed in circulation in women with PCOS during the follow-up, and twenty-four of them had decreased, while levels did not change in the control group. Four miRNAs were significantly different at baseline between healthy controls and women with PCOS; miR-103-3p, miR-139-5p, miR-28-3p, and miR-376a-3p, which were decreased in PCOS. After follow-up, miR-28-3p, miR-139-5p, and miR-376a-3p increased in PCOS women to the levels observed in healthy controls. Of these, miR-139-5p correlated with total testosterone levels (rho = 0.50, padj = 0.013), while miR-376-3p correlated significantly with the waist-hip ratio at follow-up (rho = 0.43, padj = 0.01). Predicted targets of miR-103-3p, miR-139-5p, miR-28-3p, and miR-376a-3p were enriched in pathways associated with Insulin/IGF signaling, interleukin signaling, the GNRH receptor pathways, and other signaling pathways. MiRNAs altered during follow-up in PCOS patients were enriched in pathways related to immune regulation, gonadotropin-releasing hormone signaling, tyrosine kinase signaling, and WNT signaling. Conclusions: These studies indicate that miRNAs associated with PCOS and androgen metabolism overall decrease during a 6-year follow-up, reflecting the phenotypic change in PCOS individuals towards a less hyperandrogenic profile