Normalizers of maximal tori and real forms of Lie groups

Given a complex connected reductive Lie group G with a maximal torus H⊂G, Tits defined an extension WTG of the corresponding Weyl group WG. The extended group is supplied with an embedding into the normalizer NG(H) such that WTG together with H generate NG(H). In this paper we propose an interpretation of the Tits classical construction in terms of the maximal split real form G(R)⊂G, which leads to a simple topological description of WTG. We also consider a variation of the Tits construction associated with compact real form U of G. In this case we define an extension WUG of the Weyl group WG, naturally embedded into the group extension U˜:=U⋊Γ of the compact real form U by the Galois group Γ=Gal(C/R). Generators of WUG are squared to identity as in the Weyl group WG. However, the non-trivial action of Γ by outer automorphisms requires WUG to be a non-trivial extension of WG. This gives a specific presentation of the maximal torus normalizer of the group extension U˜. Finally, we describe explicitly the adjoint action of WTG and WUG on the Lie algebra of G

Psychological Status of Perimenopausal Women with Climacteric Syndrome

Introduction. Women’s health is an important goal of modern medical, psychological, and social research. Unfavorable external and internal negative factors, which worsen psychoemotional status and lead to psychophysiological disadaptation, and also the increase in life expectancy determine the importance of the issue. Perimenopausal women with the so-called climacteric syndrome are at special risk. The novelty of the research lies in studying psychological characteristics of perimenopause complicated with climacteric syndrome. Methods. The study used the following techniques: (a) “Your Health”, a questionnaire developed by O. S. Kopina and L. Reader; (b) “Assessing Neuropsychic Stress”, a technique by T. A. Nemchin; (c) the Rapid Diagnosis of Predisposition to Unwarranted Anxiety by V. V. Boyko; (d) the State-Trait Anxiety Inventory (STAI) by Ch. D. Spielberg and Yu. L. Khanin; (e) the Individual Typological Questionnaire (ITQ) by L. N. Sobchik; (f) and a technique for diagnosing health, activity, and mood – HAM test – developed by V. A. Doskin and co-authors. The participants comprised 143 menopausal women aged 45–55 years. Results. The study revealed the insufficiently explored personality characteristics in menopausal women with and without climacteric syndrome. Personal anxiety and climacteric syndrome had a statistically significant relationship in perimenopausal women. Discussion. The findings contribute to a better understanding of the psychology of menopause and help in improving methods for diagnosis and psychocorrection of climacteric syndrome. Further research will concentrate on the bioelectric and bioenergetic processes forming the basis for personality characteristics in women with climacteric syndrome

Neuro-Energetic Correlates of Mental and Emotional Phenomena (Manifestations) of the Climacteric Syndrome

Introduction. Studying psychoneurophysiological correlates in perimenopausal women is of great theoretical and practical importance, since it may help in identifying common and gender-specific patterns of aging. The menopausal syndrome and the neurophysiological substrate underlying the phenomena of psychological maladjustment in menopausal women merit special attention. This study reveals previously unknown neuro-energetic correlates of psycho-emotional characteristics of the climacteric syndrome. Methods. This study involved menopausal women with and without manifestations of the menopausal syndrome and reproductive-age women with the normal menstrual cycle. Using the questioning method the authors examined the respondents’ personality traits. After averaging over groups, these personality characteristics were compared with the constant potential level (CPL) in frontal, central, occipital, right and left temporal regions of the cortex, which was registered by the Neuro-energo-cartograph NEC-5 hardware/software complex. The CPL was assessed by means of a special embedded math program. This helped to distinguish the local and the average CPLs, CPL gradients between unipolar values and to map the obtained data on the computer screen. Results. The findings of the study indicated a positive correlation between the expression of situational anxiety and unmotivated aggressiveness and the increased CPL in the occipital and temporal cortex in women with the climacteric syndrome. Discussion. For the first time in the study of the female climacterium, the use of registration and neuro-energetic mapping of the CPLs in various regions of the cerebral cortex and their correlations with psycho-emotional characteristics helped to identify the intensity and topography of energy metabolism in the brain, which is an integral neurophysiological substrate for psycho-emotional manifestations of the climacteric syndrome. The registration of the CPLs enabled authors to correlate the intensity and topography of energy metabolism in various regions of the cortex with psycho-emotional characteristics of the climacteric syndrome

Majorana Anyon Composites in Magneto-Photoluminescence Spectra of Natural Quantum Hall Puddles

In magneto-photoluminescence (magneto-PL) spectra of quasi two-dimensional islands (quantum dots) having seven electrons and Wigner–Seitz radius rs~1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts, and jumps of the energy of the emission components for filling factors ν > 1 (B < 10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on rs. Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock–Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the rs-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having an equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed ν~5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and rs. Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, the Majorana anyon origin of the states having even ν, i.e., composite fermions, which provide new opportunities for topological quantum computing

Сhanges in the organ of view, lucious sheets and skin in respiratory diseases

In the lecture, possible changes from the side of the visual organ, the mucous membranes of the oral cavity and the skin with respiratory diseases are considered. These changes can be a direct manifestation of the disease, and in a number of clinical situations they are even an additional differential diagnostic criterion, and can also arise against the background of drug therapy of these diseases as a manifestation of drug disease

Nano-photoluminescence of natural anyon molecules and topological quantum computation

International audienceThe proposal of fault-tolerant quantum computations, which promise to dramatically improve the operation of quantum computers and to accelerate the development of the compact hardware for them, is based on topological quantum field theories, which rely on the existence in Nature of physical systems described by a Lagrangian containing a non-Abelian (NA) topological term. These are solid-state systems having two-dimensional electrons, which are coupled to magnetic-flux-quanta vortexes, forming complex particles, known as anyons. Topological quantum computing (TQC) operations thus represent a physical realization of the mathematical operations involving NA representations of a braid group B$_{n}$, generated by a set of n localized anyons, which can be braided and fused using a “tweezer” and controlled by a detector. For most of the potential TQC material systems known so far, which are 2D-electron–gas semiconductor structure at high magnetic field and a variety of hybrid superconductor/topological-material heterostructures, the realization of anyon localization versus tweezing and detecting meets serious obstacles, chief among which are the necessity of using current control, i.e., mobile particles, of the TQC operations and high density electron puddles (containing thousands of electrons) to generate a single vortex. Here we demonstrate a novel system, in which these obstacles can be overcome, and in which vortexes are generated by a single electron. This is a ~ 150 nm size many electron InP/GaInP$_{2}$ self-organized quantum dot, in which molecules, consisting of a few localized anyons, are naturally formed and exist at zero external magnetic field. We used high-spatial-resolution scanning magneto-photoluminescence spectroscopy measurements of a set of the dots having five and six electrons, together with many-body quantum mechanical calculations to demonstrate spontaneous formation of the anyon magneto-electron particles (e$^{ν}$) having fractional charge ν = n/k, where n = 1–4 and k = 3–15 are the number of electrons and vortexes, respectively, arranged in molecular structures having a built-in (internal) magnetic field of 6–12 T. Using direct imaging of the molecular configurations we observed fusion and braiding of e$^{ν}$-anyons under photo-excitation and revealed the possibility of using charge sensing for their control. Our investigations show that InP/GaInP$_{2}$ anyon-molecule QDs, which have intrinsic transformations of localized e$^{ν}$-anyons compatible with TQC operations and capable of being probed by charge sensing, are very promising for the realization of TQC