On discreteness of subgroups of quaternionic hyperbolic isometries

Let ${{\bf H}_{\mathbb H}}^n$ denote the $n$-dimensional quaternionic hyperbolic space. The linear group ${\rm{Sp}}(n,1)$ acts by the isometries of ${{\bf H}_{\mathbb H}}^n$. A subgroup $G$ of ${\rm {Sp}}(n,1)$ is called \emph{Zariski dense} if it does not fix a point on ${{\bf H}_{\mathbb H}}^n \cup \partial {{\bf H}_{\mathbb H}}^n$ and neither it preserves a totally geodesic subspace of ${{{\bf H}}_{\mathbb H}}^n$. We prove that a Zariski dense subgroup $G$ of ${\rm{ Sp}}(n,1)$ is discrete if for every loxodromic element $g \in G$ the two generator subgroup $\langle f, g f g^{-1} \rangle$ is discrete, where the generator $f \in {\rm{Sp}}(n,1)$ is certain fixed element not necessarily from $G$.Comment: Reformatted, adding new result, and removing some. Removed parts will be subsumed elsewher

GUEST EDITOR’S INTRODUCTION

Indian Philosophical thinking is centered to freedom from problems and the basic problem is identified as ignorance. Ignorance gives birth to all limitations, conflicts, sorrow and suffering. The purpose of philosophical thinking is therapeutic that is, to show ways for getting rid of ignorance to move to the knowledge, mortality to move to the immortality, darkness to the light, mundane to the spiritual, limitations to the infinite. This highest goal for some is freedom from the chains of life, realization of the true nature of one own spirit, discriminating knowledge and for some other a transcendental state beyond description. Different schools and thinkers approach to the highest goal by means of positive (pravṛtti mārga) and negative ways (nivṛtti mārga). The two ways are not conflicting because they approach the same pure knowledge in their own way based on their attitude towards ignorance. Two persons claiming highest knowledge of two disciplines may conflict about their superiority but the aspirants of ‘pure knowledge’ do not because the pure knowledge has no opposition, no conflict, and no contradiction with any. Pure knowledge does not differ with the different approaches to it. Some may take pure knowledge as substance, some as quality of consciousness, some as creativity of soul (kṛtya or karma) and still some other as extinction (śūnya). But they all agree that the state of purity is freedom from worldliness, that is, from ignorance with all its forms and modifications. This issue of the Journal of East-West Thought includes nine articles that representing five trends of Indian Philosophical Studies, can grossly be categorized into – Dharma-centric (article 1, 2, 3), value-centric (article 4, 5, 6), spirit-centric (article 7 & 9), meaning-centric (article 8) and cognition-centric (article 9) approaching ‘pure knowledge’ as its goal. Each of the articles in this volume is a complete statement analyzed well and discussed conclusively. A brief evaluation of the merits of the article as per the trend they represent is given below to draw the attention of the readers

COGNITIVE HOLISM: UNDERSTANDING COGNITIVE HOLISTIC THEORY OF LANGUAGE AND ITS PUBLIC UTILITY

Understanding an indivisible cognition through the analytic part has its own beauty that we can call analytic skill, but that must aim at clarity and conception of the cognition which is a whole approached through individual steps. Composite forms have their own beauty, imposition of the cognition on our different allegiance has a different beauty but if one does not understand clearly the different roles the indivisible cognition plays in causing the pleasure in some and pain in others, amusing in some and an obsession in others, illuminating in some and deviating in others, one cannot enjoy wisdom and bliss. Holism talks about language as power, the potency that works differently in wise and in ignorant in causing different effects that veils and deviates from the indivisible cognition. Interpretation of the cognition needs cognitive holistic approach to realize wisdom

KĀLIDĀSA ON RELATION AND CONDUCT TO NATURE AS DEPICTED IN THE SIMILES OF RAGHUBAMŚAM

In the present time of utilitarianism our strength of collecting more and more civilizational height and imperialistic power, ethical relativism, and pleasure-seeking ideologies that believe in minimizing human rationality and maximizing emotions and passions for maximizing pleasure are defining the rationality. Power of exploiting civilizational progress more and more has created restlessness and misbalance in human societies is keeping the humans engaged in enhancing balance sheets even at the cost of lowering human existence and the values, The argument of Ethical perspective we are discussing here in this paper with reference to Kālidāsa’s famous epic Raghuvamśam is that human rationality cannot be defined in terms of imperialistic power of a man or a nation but with our venerable conduct to the global communities. All richness of wealth and qualities meant for helping others. The term ‘other’ in broader sense is used for nature/environment outside responding to human nature inside. Defining the ethical relation and conduct that exist between man and nature, Kālidāsa establishes a spiritual perspective for which all have existence value that is, all are divinities. Nature responds and shares our conduct to it and our conduct to the other must be venerable for our well-being

Performance Analysis of a signal by removing ICI using Kalman Filter for OFDM Channel

The OFDM communication is very much inspired from the channel frequencies over the network. In such network some kind of orthogonal di stortion occur over the channel called Inter carrier Interference. Here we will improve the ICI using Kalman Filtering improv ed by using repetitive slot and correlated channel tap. The Kalman Filter is been improved by implementing the two stage kalman fil ter. In first stage the Kalman based statistical analysis is performed to estimate the PAPR and the respective Phase variated PAPR reduction is performed. In second stage the ICI reduction is performed by implementing the Kalman filter based carrier offset values. The proposed work of this paper is when data travel over some channel it suffers from the problem of interference. The interf erence results the high signal to noise ratio as well as high bit error rate. The proposed system will improved the si gnal by removing the different kind of impurities over the signal. These impurities includes the ICI, PAPR and the noise over the signal. The signal will be more ef fective than standard OFDM. S o we neednt many pilot symbols in practice, still can ensure the algorithm performance and reduce the time - delay and complexity of this algorith

Discreteness Of Hyperbolic Isometries by Test Maps

Let $\mathbb F=\mathbb R$, $\mathbb C$ or $\mathbb H$. Let ${\bf H}_{\mathbb F}^n$ denote the $n$-dimensional $\mathbb F$-hyperbolic space. Let ${\rm U}(n,1; \mathbb F)$ be the linear group that acts by the isometries. A subgroup $G$ of ${\rm U}(n,1; \mathbb F)$ is called \emph{Zariski dense} if it does not fix a point on the closure of the $\mathbb F$-hyperbolic space, and neither it preserves a totally geodesic subspace of it. We prove that a Zariski dense subgroup $G$ of ${\rm U}(n,1; \mathbb F)$ is discrete if for every loxodromic element $g \in G$, the two generator subgroup $\langle f, g \rangle$ is discrete, where $f \in {\rm U}(n,1; \mathbb F)$ is a test map not necessarily from $G$.Comment: to appear in Osaka J. Mat

Evoluția și etica eugeniei

În acest articol încerc să argumentez opinia că, așa cum este definită eugenia, este foarte dificil de făcut o diferențiere clară între știință (medicină, ingineria genetică) și eugenie. Și de stabilit o linie peste care ingineria genetică nu ar trebui să treacă, conform unor norme morale, juridice și religioase. Atâta timp cât acceptăm ajutorul geneticii în găsirea unor modalități de combatere a cancerului, diabetului sau HIV, acceptăm în mod implicit și eugenia pozitivă, conform definiției actuale. Și atâta timp cât acceptăm screening-ul genetic, și intervenții asupra fătului nenăscut, sau avortul, acceptăm în mod implicit și eugenia negativă. În plus, la nivel de guverne, deși oficial eugenia este repudiată, ea a fost legalizată în foarte multe țări până de curând, și încă mai este acceptată și legalizată, chiar dacă în forme mai subtile, și în prezent. În Introducere definesc termenul și modurile de clasificare. Urmează Istoria eugeniei pornind din perioada antică, introducerea eugeniei de Francis Galton, practica eugeniei ca politică de stat în diverse țări, și eugenia actuală (eugenia liberală). Analizez apoi diverse probleme ridicate de Etica eugeniei liberale, și am dezvoltat o secțiune aparte pentru Viitorul eugeniei, cu accent pe proiectul genomului uman. În final, în secțiunea Concluzii expun opiniile personale cu privire la practica actuală a eugeniei. Am folosit ca surse principale de investigație articolele lui Kenneth M. Ludmerer, ”American Geneticists and the Eugenics Movement: 1905-1935”, Kathy J. Cooke, ”Duty or Dream? Edwin G. Conklin's Critique of Eugenics and Support for American Individualism”, Jonathan Anomaly, ”Defending Eugenics”, John R. Harding Jr. ”Beyond Abortion: Human Genetics and the New Eugenics”, Michael Boulter, ”Bloomsbury Scientists”, Chapter Title: The rise of eugenics, 1901–14, Michael Ruse and Edward O. Wilson, ”Moral Philosophy as Applied Science” și Goering, Sara, "Eugenics"

High Interfacial Hole-Transfer Efficiency at GaFeO3 Thin Film Photoanodes

The photoelectrochemical properties of polycrystalline GaFeO3 (GFO) thin films are investigated for the first time. Thin films prepared by sol–gel methods exhibit phase‐pure orthorhombic GFO with the Pc21n space group, as confirmed by X‐ray diffraction and Raman spectroscopy. Optical responses are characterized by a 2.72 eV interband transition and sub‐bandgap d–d transitions associated with octahedral and tetrahedral coordination of Fe3+ sites. DFT‐HSE06 electronic structure calculations show GFO is highly ionic with very low dispersion in the valence band maximum (VBM) and conduction band minimum (CBM). Electrochemical impedance spectroscopy reveals n‐type conductivity with a flat band potential (Ufb) of 0.52 V versus reversible hydrogen electrode, indicating that GFO has the most positive CBM reported of any ferrite. The photoelectrochemical oxidation of SO32− shows an ideal semiconductor–electrolyte interfacial behavior with no evidence of surface recombination down to the Ufb. Surprisingly, the onset potential for the oxygen evolution reaction also coincides with the Ufb, showing interfacial hole‐transfer efficiency above 50%. The photoelectrochemical properties are limited by bulk recombination due to the short‐diffusion length of minority carriers as well as slow transport of majority carriers. Strategies towards developing high‐efficiency GFO photoanodes are briefly discussed

Nanostructured LaFeO3 Photocathodes with Onset Potentials for the Hydrogen Evolution Reaction Over 1.4 V vs RHE

The photoelectrochemical properties of phase-pure LaFeO3 (LFO) nanostructured films are investigated upon modification with a thin TiO2 film and Pt nanoparticles as a catalyst. LaFeO3 with crystallite domains in the range of 60 nm are prepared by thermolysis of an ionic-liquid precursor and subsequently deposited onto FTO electrode by spin-coating. Deposition of a TiO2 layer by solution-based methods leads to the formation of a heterojunction, attenuating dark current associated with hole-transfer (water oxidation) at potential above 1.4 V. The LFO/TiO2 heterojunction features photocurrent onset potential for the hydrogen evolution reaction of 1.47 V vs the reversible hydrogen electrode (RHE), which is one of the most positive values reported for a single absorber. Deposition of Pt nanoparticles at the LFO/TiO2 heterostructure generates a significant increase in the HER photocurrent, although bulk recombination remains an important challenge in these constructs