Free Action Research Articles

Resolving by a free action linear category and applications to Hochschild-Mitchell (co)homology

Let G be a group acting on a small category C over a field k, that is C is a G-k-category. We first obtain an unexpected result: C is resolvable by a category which is G-k-equivalent to it, on which G acts freely on objects.This resolving category enables to show that if the coinvariants and the invariants functors are exact, then the coinvariants and invariants of the Hochschild-Mitchell (co)homology of C are isomorphic to the trivial component of the Hochschild-Mitchell (co)homology of the skew category C[G].If the action of G is free on objects, then there is a canonical decomposition of the Hochschild-Mitchell (co)homology of the quotient category C/G along the conjugacy classes of G. This way we provide a general frame for monomorphisms which have been described previously in low degrees.

Extending free actions of finite groups on surfaces

The present work introduces new perspectives in order to extend orientation-preserving finite group actions from oriented surfaces to 3-manifolds. We consider the Schur multiplier associated to a finite group G in terms of two-dimensional principal G-bordisms, called G-cobordisms. We are interested in the question of when a free action of a finite group on a closed oriented surface extends to a non-necessarily free action on a 3-manifold. We show the answer to this question is always affirmative for abelian, dihedral, symmetric and alternating groups. As an application of our methods, we show some particular cases for non-necessarily free actions of abelian groups and dihedral groups on surfaces.

The first -betti number and groups acting on trees

AbstractWe generalize results of Thomas, Allcock, Thom–Petersen, and Kar–Niblo to the first $\ell ^{2}$-Betti number of quotients of certain groups acting on trees by subgroups with free actions on the edge sets of the graphs.

Fixed point free actions of spheres and equivariant maps

The concept of index and co-index of a paracompact Hausdorff space X equipped with free involutions relative to the antipodal action on spheres were introduced by Conner and Floyd [2]. In this paper, we extend the notion of index and co-index for free G-spaces X, where X is a finitistic space and G=S1 (with complex multiplication) and G=S3 (with quaternionic multiplication). We prove that the index of X is less than or equal to the mod 2 cohomology index of X. We also compute the ring cohomology of the orbit space X/G, where G=S1 or G=S3 and X is a finitistic space whose cohomology ring is the same as the product of spheres Sn×Sm,1≤n≤m. Using these cohomological calculations, we obtain some Borsuk-Ulam type results.

Interaction of fermionic matter and ECSK black hole leading to bouncing universe

The interactions between the spin of fermionic matter and torsion in the Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity provides a repulsive gravitational potential at the very dense states of fermionic matter, which prevents the formation of black hole singularities inside the deeper horizon. While the fermionic matter in the black hole is attracted by the black hole at the beginning, after a critical point it is repelled to bounce at a critical high density and then expand into other side of the horizon as a newly created space, which may be considered as a nonsingular, closed universe. We constructed the action of these fermions in a black hole with torsion in the framework of ECSK theory of gravity from which the free Dirac action is inferred to obtain the interaction potential. The creation of a bouncing universe with the extremely repulsive potential may be related to the running vacuum and the modified Friedmann equations yield the consistent cosmological parameters with present FRW universe. Finally, this scenario naturally solves the flatness and horizon problems of cosmology without introducing finely tuned scalar fields, or more complicated functions of the Ricci Scalar R in the gravitational action.

The adiabatic groupoid and the Higson–Roe exact sequence

Let \widetilde{X} be a smooth Riemannian manifold equipped with a proper, free, isometric, and cocompact action of a discrete group \Gamma . In this paper, we prove that the analytic surgery exact sequence of Higson–Roe for \widetilde{X} is isomorphic to the exact sequence associated to the adiabatic deformation of the Lie groupoid \widetilde{X}\times_\Gamma\widetilde{X} . We then generalize this result to the context of smoothly stratified manifolds. Finally, we show, by means of the aforementioned isomorphism, that the \varrho -classes associated to a metric with a positive scalar curvature defined by Piazza and Schick (2014) correspond to the \varrho -classes defined by Zenobi (2019).

Forced Empowerment and the Paradox of Mobile Dating Apps

New women-focused mobile dating apps purport to empower women by having them “make the first move” and disrupt traditional male-dominated dating norms. Drawing on feminist approaches and technological affordances, we examine how heterosexual cisgender women and men experience this “empowerment” and contrast it to other mobile dating app use. We used a multimethod approach to conducting app walkthroughs, focus groups, and interviews to contrast the mobile dating apps, Tinder and Bumble. The findings reveal that perceptions of free choice and action determine empowerment experiences. Our study reveals that the “forced empowerment” on Bumble was still strongly shaped by heterosexual gender norms that encouraged “good” girls and guys to use the app to look for long-term relationships but continue to use Tinder to hook up, despite the popular misogyny on Tinder identified by both men and women in our study. We conclude by discussing the empowerment paradox of dating apps through popular feminism and misogyny.

Блокчейн и другие технологии в системе традиционных государственно-правовых институтов

Introduction: the technologies of blockchain, cryptocurrencies, and smart contracts in the context of philosophical and legal issues require their understanding. There is a voluminous body of literature on this subject today. However, the main leitmotif of the vast majority of publications is a simple description and further understanding of the structure of these technologies, the order of their implementation, development, and operation. The theoretical and philosophical aspects of the study of these new phenomena are not sufficiently covered. As a rule, the works simply postulate the legal nature of the technologies being studied. But at the same time, all national states have the problem of regulating these regulatory technologies themselves, which are autonomous information and telecommunications systems that do without an intermediary in the person of the state or other official authorities. The purpose of the paper is to clarify the issue of the nature of these technologies, their relationship, and mutual influence with the traditional regulatory institutes. Methods: formal-legal, systematicity, comparison, generalization, and analysis. As a result, the author emphasizes that these digital technologies, although they contain claims to a symbiotic reconciliation with the traditional institutes, are a completely new, alternative regulatory system. The basis of this system is not the legal principle of “if-then-otherwise”, which emphasizes the possibility of free action, but the principle of the physical law of “if-then”, as in the scenario language of a program code, where every event and action is invariant. The paper substantiates the conclusion that these technologies will exist in parallel with the traditional state-legal institutes, competing for the regulation of a significant part of civil law relations, as an appendix to a paper contract in terms of automating the mode of performance, and as the main contract based on the program code.

Nonconsensual neurocorrectives, bypassing, and free action

As neuroscience progresses, we will not only gain a better understanding of how our brains work, but also a better understanding of how to modify them, and as a result, our mental states. An important question we are faced with is whether the state could be justified in implementing such methods on criminal offenders, without their consent, for the purposes of rehabilitation and reduction of recidivism; a practice that is already legal in some jurisdictions. By focusing on a prominent type of view of free action, which I call bypassing views, this paper evaluates how such interventions may negatively impact the freedom of their subjects. The paper concludes that there will be a tension between the goals of rehabilitation and reduction of recidivism, on the one hand, and the negative impact such interventions may have on free action, on the other. Other things equal, the better that a particular intervention is at achieving the former, the more likely it is to result in the latter.

A Comparative Study of Antioxidant Activity between Ethanolic and Aqueous Extract of Cardiospermum halicacabum

Cardiospermum halicacabum is conventionally used in the treatment of stiffness of limbs, chronic bronchitis, and snakebites. The whole plant of Cardiospermum halicacabum has been extracted using ethanol and aqueous solvent and estimation of their antioxidant activity done for predicted current research work. Both ethanol and aqueous extracts illustrate important antioxidant activity in the DPPH method, nitric oxide method, and hydroxyl radical-induced In-vitro assay method. The DPPH radical inhibition (%) was 53.13, 57.13, and 79.12 for EECH, AECH, and Standard ascorbic acid respectively. The Cardiospermum halicacabum extracts (EECH and AECH) showed significant free radical scavenging action against nitric oxide (NO) induced release of free radicals at the concentrations 250μg/ml, showing 29.22% and 63.32% of nitric oxide inhibition, respectively. The EECH and AECH extracts (25-400μg/ml) significantly scavenged the hydroxyl radical generated by the EDTA/HO system, when compared to that of ascorbic acid. The plant Cardiospermum halicacabum has been used to treat different ailments. The present study clearly showed that both the extracts viz. EECH and AECH of the plant possess significant antioxidant activity. Moreover, ethanolic extract was proved as more potent candidature as compared to aqueous extract. The molecular level mechanism is the future interest of the researchers to prove the traditional use of the plant.

Polynomial Entropy of Subsets for Free Semigroup Actions

Polynomial Entropy of Subsets for Free Semigroup Actions

Measurable Hall’s theorem for actions of abelian groups

We prove a measurable version of the Hall marriage theorem for actions of finitely generated abelian groups. In particular, it implies that for free measure-preserving actions of such groups and measurable sets which are suitably equidistributed with respect to the action, if they are are equidecomposable, then they are equidecomposable using measurable pieces. The latter generalizes a recent result of Grabowski, Máthé and Pikhurko on the measurable circle squaring and confirms a special case of a conjecture of Gardner.

Assessment of irradiated TiO2 nanoparticles on the growth and nutritional components of broccoli

Broccoli is highly tremendously as it is enriched with healthy promoting phytochemicals. This research was undertaken to study the feedback of broccoli to different concentrations of un-irradiated and irradiated (50 kGy of gamma rays) titanium dioxide nanoparticles (TiO2NPs). Un-irradiated and irradiated titanium dioxide characterization was accomplished by FT-IR, XRD, TGA, SEM and TEM. Foliar spray of titanium dioxide was applied to the broccoli in regards to the results of the characterizations. The growth traits; plant height, leaves No. per plant as well as stem diameter of plants and physical quality of heads were measured. Also, nutritional components of heads were determined. The results detailed that vegetative growth and physical quality of heads positively responded to foliar application of titanium dioxide compared to those obtained from control and 50 ppm from irradiated titanium dioxide (ITiO2NPs) gave the highest values of all traits. Regarding to nutritional components of heads, the efficiency of photosynthesis increased by using TiO2 (un-irradiated and irradiated) specially, 50 ppm ITiO2NPs. Application of Ti significantly increased the osmolytes concentrations such as proline, total free amino acids and soluble sugars as well as the extracts of heads sprayed with TiO2NPs concentrations displayed a prospective DPPH free radical scavenging action. Likewise, absorption of other nutrient elements and amino acids pool increased by spraying TiO2NPs. It was found that there are several phytochemical constituents identified by GC-MS that contribute to the biological activity of the methanol extract of broccoli heads that were affected by the use of TiO2NPs. It is clear that from above results, the using of ITiO2NPs specially; 50 ppm stimulated growth, resulting in improved quality of broccoli heads which is ultimately reflected in productivity.

Variational Principle for Topological Pressure on Subsets of Free Semigroup Actions

Variational Principle for Topological Pressure on Subsets of Free Semigroup Actions

Human life and self-realization according to Edith Stein

The aim of this article is to analyse the Edith Stein’s phenomenological-metaphysical anthropologyand its moral aspects. Her enquiry shifts from the study of those aspects common to both humanbeings and animals to an aspect that is specifically and exclusively human, i.e., spirituality. Theperson only is a spiritual subject, because he has an intellectual knowledge and he can freely act. Inthis investigation, Stein moves from outcomes achieved thanks to the phenomenological method,which leads her to focus on a description of the bodily, psychical and spiritual sphere of the humanbeing. Accordingly, Stein reflects on the ethical consequences of her anthropological research.Following Augustine, she perceives originary self-consciousness as interiority, from which to beginexplicating intellectual knowledge, and especially free action and hence ethics. Action is not onlyexpressed outwards, first of all it is self-actuation – acting and being are mutually implied. Thedirection of moral actions is thus already present in each one’s individual ‘essence’ (Wesen) and thisessence, thanks to the creative ‘essentiality’ (Wesenheiten), is ab eterno in Logos. In view of thiscomplex theological node, Stein recognizes Christ as the archetype of the only possible ethics.

Human life and self-realization according to Edith Stein

The aim of this article is to analyse the Edith Stein’s phenomenological-metaphysical anthropologyand its moral aspects. Her enquiry shifts from the study of those aspects common to both humanbeings and animals to an aspect that is specifically and exclusively human, i.e., spirituality. Theperson only is a spiritual subject, because he has an intellectual knowledge and he can freely act. Inthis investigation, Stein moves from outcomes achieved thanks to the phenomenological method,which leads her to focus on a description of the bodily, psychical and spiritual sphere of the humanbeing. Accordingly, Stein reflects on the ethical consequences of her anthropological research.Following Augustine, she perceives originary self-consciousness as interiority, from which to beginexplicating intellectual knowledge, and especially free action and hence ethics. Action is not onlyexpressed outwards, first of all it is self-actuation – acting and being are mutually implied. Thedirection of moral actions is thus already present in each one’s individual ‘essence’ (Wesen) and thisessence, thanks to the creative ‘essentiality’ (Wesenheiten), is ab eterno in Logos. In view of thiscomplex theological node, Stein recognizes Christ as the archetype of the only possible ethics.

Minimal model-universal flows for locally compact Polish groups

Let G be a locally compact Polish group. A metrizable G-flow Y is called model-universal if by considering the various invariant probability measures on Y, we can recover every free action of G on a standard Lebesgue space up to isomorphism. Weiss has shown that for countable G, there exists a minimal, model-universal flow. In this paper, we extend this result to all locally compact Polish groups.

Anti-oxidant and Anti-microbial activities of 2’’, 4’’-thiazolidindione derivatives of 7-flavonols

Objective: The synthesized compounds of 2’’,4’’-thiazolidindione derivatives of 7-flavonols*, after characterization, aimed to be tested for their anti-oxidant and anti-microbial effects. Methods: i) Free radical scavenging actions tested by hydrogen peroxide- nitric oxide- and by alkaline DMSO- methods and ii) anti-microbial effects against various bacterial pathogens and against candida albicans by disc diffusion method. Results: Data were found to be dose dependent and IC50 value was 30-60 µg/ml and the results revealed that the dinitro-, trinitro- and acetyl, dinitro derivatives showed better and/or equipotent activity to that of the standard, ascorbic acid. The synthesized compounds exerted variable inhibitory activities at a concentration of 1μg /10μl /disc with inhibition zone ranging from 7-26 mm in diameter and a good antifungal activity against Candida albicans at the concentration of (1μg /10μl /disc) with inhibition of 10-24 mm. Klebsiella tribatta are more susceptible to the action of the formylated samples, giving high inhibition values comparing to the other organisms. Compounds Ie and Ih resulted to a higher activity index (AI>1); compounds Id, Ig and Ii showed an equal value (AI=1); whereas, Ia, Ib, Ic and If showed only a moderate activity (AI<1) compared to the standard, Amikacin. Conclusion: The findings confirmed that the synthetic compounds of 3-formyl, 7-flavonol derivatives have significant anti-oxidant and anti-microbial activities.

Topological Pressure of Free Semigroup Actions For Non-Compact Sets and Bowen’s Equation, II

Inspired to the work of Ma and Wu (Discrete Contin Dyn Syst 31:545–557, 2011) and Climenhaga (Ergodic Theory Dyn Syst 31(4):1163–1182, 2011), we introduce the new notions of topological pressure and upper (lower) capacity topological pressure of a free semigroup action of maps for finite potential functions by using the Carathéodory–Pesin structure (C-P structure) with respect to non-compact sets in this paper. Meanwhile, we also give some properties of these notions. Moreover, by Bowen’s equation, we characterize the Hausdorff dimension of certain sets, whose points have the positive lower Lyapunov exponents and satisfy a so-called tempered contraction condition.

Free dihedral actions on abelian varieties

We give a simple construction for hyperelliptic varieties, defined as the quotient of a complex torus by the action of a finite group \(G\) that contains no translations and acts freely, with \(G\) any dihedral group. This generalizes a construction given by Catanese and Demleitner for \(D_4\) in dimension three.