Separability within alternating groups and randomness

This thesis promotes known residual properties of free groups, surface groups, right angled Coxeter groups and right angled Artin groups to the situation where the quotient is only allowed to be an alternating group. The proofs follow two related threads of ideas. The first thread leads to `alternating' analogues of extended residual finiteness in surface groups \cite{scott1978subgroups}, right angled Artin groups and right angled Coxeter groups \cite{haglund2008finite}. Let $W$ be a right-angled Coxeter group corresponding to a finite non-discrete graph $\mathcal{G}$ with at least $3$ vertices. Our main theorem says that $\mathcal{G}^c$ is connected if and only if for any infinite index convex-cocompact subgroup $H$ of $W$ and any finite subset $\{ \gamma_1, \ldots , \gamma_n \} \subset W \setminus H$ there is a surjective homomorphism $f$ from $W$ to a finite alternating group such that $f (\gamma_i) \notin f (H)$ . A corollary is that a right-angled Artin group splits as a direct product of cyclic groups and groups with many alternating quotients in the above sense. Similarly, finitely generated subgroups of closed, orientable, hyperbolic surface groups can be separated from finitely many elements in an alternating quotient, answering positively a conjecture of Wilton \cite{wilton2012alternating}. The second thread uses probabilistic methods to provide `alternating' analogues of subgroup conjugacy separability and subgroup into-conjugacy separability in free groups \cite{bogopolski2010subgroup}. Suppose $H_1, \ldots H_k$ are infinite index, finitely generated subgroups of a non-abelian free group $F$. Then there exists a surjective homomorphism $f:F \longrightarrow A_m$ such that if $H_i$ is not conjugate into $H_j$, then $f(H_i)$ is not conjugate into $f(H_j)$.EPSRC International Doctoral Scholar schem

Bias crimes charges in the United States: bias homicides in the U.S. between 1990 and 2016

CRISP analyzed data from bias crimes in the United States to examine links between bias crimes and bias crime charges. The findings have policy implications, including the fact that effectiveness of bias crime legislation should be further evaluated for impact and operation.The Indiana General Assembly introduced 10 bills related to bias (or hate) crimes in the 2019 session. Indiana is 1 of 5 states in the U.S. without a bias crimes statute. The 10 bills are similar in that each of them allows for a criminal penalty enhancement for bias crimes offenses. Penalty enhancement statutes enable courts to impose a longer sentence if the predicate crime—the underlying crime committed by an offender—is proven to have been motivated by bias as defined by the particular statute. Marginalized communities are convicted of predicate crimes at higher rates. Given that racial disparities also exist within sentencing decisions for equal crimes, there is evidence of discretion within the legal process that disproportionately (and negatively) impacts marginalized groups. The following brief presents an objective analysis of bias homicide charges in the U.S. with the goal of understanding possible policy implications of Indiana’s proposed bias crimes legislation

Mind Mapping Technique in Language Learning

The current study aims to describe meaningful, powerful and effective tool, used to encourage technical students to apply mind mapping techniques in the language classroom. For this purpose, we overview the previous and the present studies, concerning the problem and describe the implementation of mind mapping techniques in the learning process. The results of this study showed that mind maps help students solve problems, brainstorm creative ideas, remember new vocabulary, take notes, enhance their reading skills, organize the tasks and prepare presentations. This study concludes that mind mapping technique invented in the XX century is considered to be up-to-date, creative, useful and available tool for students, educators and researchers

Prospects of Blended Learning Implementation at Technical University

The present paper explores the integration of a blended learning course in the process of learning English as a second language at the technical university. We overview the difference between traditional, web facilitated, blended learning and online course; the implementation of the blended learning course in the process of learning English at the technical university. The article also investigates the benefits and drawbacks of blended learning and the possibilities of a blended learning course integration in the educational process. The results of the survey conducted prove that the integration of a blended learning course can be implemented successfully through a combination of online learning and face-to-face classes. The findings described will be useful to teachers and researchers working in this field to overcome the barriers, become more experienced and understand the main concept of blended learning

A Seat at the Table : The Norwegian Board Gender Quota: A Study on Indirect Effects

Twenty years ago, Norway led the way with the first board gender quota on ASA1 and is now considering extending the legislation to AS. This paper examines if the existing board gender quota has fulfilled one of its main objectives – increasing opportunities for all women, also those outside the boardroom. First, we find little to no evidence of an external spillover onto AS boards, as the quota had a negligible impact on increasing the gender ratio for AS. Second, we find some evidence of internal spillover from the quota onto management, causing a slight short-term boost of increased female representation in management, but with modest longterm effects. However, comparing with Sweden, neither of these findings are likely to be significant due to a probable underlying societal trend. Third, we fail to find a general internal spillover effect from boards to management or vice versa. An AS quota will undoubtingly increase the number of female seats in the boardroom. Hence, if the main objective of the quota is to increase the female share of AS boards, we recommend that the policymakers implement a quota for AS companies. However, based on our findings, we urge them not to use increased labour opportunities for women as a motivation for enacting such a quota.nhhma

One or Nothing: Anti-unification over the Simply-Typed Lambda Calculus

Generalization techniques have many applications, such as template construction, argument generalization, and indexing. Modern interactive provers can exploit advancement in generalization methods over expressive-type theories to further develop proof generalization techniques and other transformations. So far, investigations concerned with anti-unification (AU) over lambda terms and similar type theories have focused on developing algorithms for well-studied variants. These variants forbid the nesting of generalization variables, restrict the structure of their arguments, and are unitary. Extending these methods to more expressive variants is important to applications. We consider the case of nested generalization variables and show that the AU problem is nullary (using capture-avoiding substitutions), even when the arguments to free variables are severely restricted.Comment: 12 pages, submitted to Journal (a revised version of the previous submission with more precise proofs

The Implementation of the Feedback Principle in Science and Technics

In this study positive and negative influence of the feedback have been examined. A feedback principle in the alternating current amplifier and in the speed regulator of the turbine rotation was described. The main conclusion of the positive and negative effect was obtained. Negative feedback worsens the properties of an object, reducing a strengthening factor, delaying regulatory action. Positive feedback considerably raises device work stability. This research will enable to identify the importance and effectiveness of the feedback principle in science and technics

Gold(i)/Zn(ii) catalyzed tandem hydroamination/annulation reaction of 4-yne-nitriles

The tandem hydroamination-annulation reaction of 4-pentyne-nitriles in the presence of amine nucleophiles and a cooperatively operating catalyst system, consisting of Ph3PAuCl and Zn(ClO4)2, provides an efficient route to 2-aminopyrroles. Two regioisomeric 2-aminopyrroles were formed in moderate to good yields. © 2010 The Royal Society of Chemistry.TÜBİTAK; TÜBA and MET