Rigidity and volume preserving deformation on degenerate simplices

Given a degenerate $(n+1)$-simplex in a $d$-dimensional space $M^d$ (Euclidean, spherical or hyperbolic space, and $d\geq n$), for each $k$, $1\leq k\leq n$, Radon's theorem induces a partition of the set of $k$-faces into two subsets. We prove that if the vertices of the simplex vary smoothly in $M^d$ for $d=n$, and the volumes of $k$-faces in one subset are constrained only to decrease while in the other subset only to increase, then any sufficiently small motion must preserve the volumes of all $k$-faces; and this property still holds in $M^d$ for $d\geq n+1$ if an invariant $c_{k-1}(\alpha^{k-1})$ of the degenerate simplex has the desired sign. This answers a question posed by the author, and the proof relies on an invariant $c_k(\omega)$ we discovered for any $k$-stress $\omega$ on a cell complex in $M^d$. We introduce a characteristic polynomial of the degenerate simplex by defining $f(x)=\sum_{i=0}^{n+1}(-1)^{i}c_i(\alpha^i)x^{n+1-i}$, and prove that the roots of $f(x)$ are real for the Euclidean case. Some evidence suggests the same conjecture for the hyperbolic case.Comment: 27 pages, 2 figures. To appear in Discrete & Computational Geometr

Психологические трудности пациентов, инфицированных вирусом иммунодефицита человека, при подготовке к антиретровирусной терапии

Objectives: to find out and. analyze the problems of HIV-infected. patients which require additional attention of specialists during counseling before the start of antiretroviral therapy as well as to assess patients' needs in psychological help.Materials and methods: the data are collected, by the questionnaire and. psychometrical screening using The Somatic Symptom. Disorder — B Criteria Scale from 365 HIV-infected. patients, including 155 (42,5%) females who took part in the group psychological counseling for preparing to the start of antiretroviral therapy from July 2017 to July 2018. The average age was 37.2 years old.Results: the difficulties due to HIV-infection, which, are mentioned, by patients before the therapy start, are ranged, by the frequency of their answers as follows: 1) ««need, to conceal HIV diagnosis» — 27,1% answers, 2) ««lack of time for visiting the doctor» — 26,6%; 3) ««depression and/or anxiety» — 26,0%; 4) ««need, to use condom» — 19,5%; 5) ««restrictions in employment» — 10,1%; 6) ««disclosure of HIV diagnosis to the partner» — 8,5%. Less common are ««difficulties to interact with the doctor» (4,4%), ««impossibility to work in the specialty» (4,4%) and. ««the rejection from significant others» (4,1%). The monitoring of HIV treatment adherence showed, that 31,8% of patients were not ready to start taking medications right after the doctor's recommendations, and. 13,4% postpone the start of treatment for more than half a year.Conclusion: in preparation for the start of antiretroviral therapy a patient needs the assistance in time scheduling required. for treatment. The discussion, with patients about their attitudes towards condom use and their self-efficacy to use condom, helps patients to overcome their fear of HIV diagnosis disclosure and. therefore reduces their risky sexual behavior. Psychological screening helps revealing psychological tension and allows offering the consultation of psychiatrist or psychologist with the purpose to correct mental state as well as to facilitate patient's efforts to develop adherence to continual treatment.Цель: выявить и проанализировать трудности у пациентов с ВИЧ-инфекцией перед началом, антиретровирусной терапии, требующие особого внимания специалистов в процессе консультирования, а также оценить потребности пациентов в психологической помощи.Материалы, и методы: проанализированы, данные анкетирования и психометрического скрининга по шкале «The Somatic Symptom. Disorder — B Criteria Scale» 365 ВИЧ-инфицированных пациентов, в том числе 155 (42,5%) женщин, участвовавших в групповом, психологическом консультировании при подготовке к началу антиретровирусного лечения с июля 2017 г. по июль 2018 г. Средний возраст. — 37,2лет.Результаты: трудности в связи с ВИЧ-инфекцией, отмечаемые пациентами перед началом терапии, по частоте ответов распределились следующим образом: 1) ««необходимость скрывать диагноз» — 27,1% ответов, 2) «находить время на посещение врача» — 26,6%; 3) ««депрессия и/или тревога» — 26,0%; 4) «необходимость использовать презервативы.» — 19,5%; 5) «ограничения в трудоустройстве» — 10,1%; 6) ««сообщение диагноза партнеру» — 8,5%. Реже встречаются указания на ««трудности взаимодействия с врачом» (4,4%), «невозможность работать по специальности» (4,4%) и «отвержение со стороны, близких» (4,1%). Мониторинг приверженности лечению ВИЧ-инфекции показал, что 31,8% пациентов не склонны, начинать прием, препаратов сразу после рекомендации врача, а 13,4% откладывают. начало терапии более чем. на полгода.Заключение: при подготовке к началу антиретровирусной терапии пациент нуждается в помощи для планирования времени, связанного с лечением. Снижению рискованного сексуального поведения способствует разговор об отношении и готовности пациента к использованию презерватива, что, в свою очередь, помогает преодолевать страх раскрытия диагноза партнеру. Психологический скрининг позволяет, выявлять психологическую напряженность и предлагать консультации психиатра и психолога для коррекции состояния и облегчения усилий по формированию приверженности непрерывному лечению

A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories

We give an explicit differential equation which is expected to determine the instanton partition function in the presence of the full surface operator in N=2 SU(N) gauge theory. The differential equation arises as a quantization of a certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and Tsuda.Comment: 15 pages, v2: typos corrected and references added, v3: discussion, appendix and references adde

Zonal pressure gradient along the equatorial Atlantic

For three consecutive periods during the summer of 1974, ships of many nations made observations along the Atlantic equator as part of the GATE program [GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment]. Combining these observations, it is found that the zonal pressure gradient over the central Atlantic at the surface and at 50 dbar, relative to 500 dbar, increased from 3.2 to 7.3 and 2.2 to 5.3 × 10-5 dynes/g respectively between June/July and August and then held close to the high values in September...

Limits of Gaudin algebras, quantization of bending flows, Jucys--Murphy elements and Gelfand--Tsetlin bases

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of $n$ copies of the universal enveloping algebra U(\g) of a semisimple Lie algebra \g. This family is parameterized by collections of pairwise distinct complex numbers $z_1,...,z_n$. We obtain some new commutative subalgebras in U(\g)^{\otimes n} as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the hamiltonians of bending flows and to the Gelfand--Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases.Comment: 11 pages, references adde

Leading-order determination of the gluon polarisation from semi-inclusive deep inelastic scattering data

Using a novel analysis technique, the gluon polarisation in the nucleon is re-evaluated using the longitudinal double-spin asymmetry measured in the cross section of semi-inclusive single-hadron muoproduction with photon virtuality $Q^2>1~({\rm GeV}/c)^2$. The data were obtained by the COMPASS experiment at CERN using a 160 GeV/$c$ polarised muon beam impinging on a polarised $^6$LiD target. By analysing the full range in hadron transverse momentum $p_{\rm T}$, the different $p_{\rm T}$-dependences of the underlying processes are separated using a neural-network approach. In the absence of pQCD calculations at next-to-leading order in the selected kinematic domain, the gluon polarisation $\Delta g/g$ is evaluated at leading order in pQCD at a hard scale of $\mu^2= \langle Q^2 \rangle = 3 ({\rm GeV}/c)^2$. It is determined in three intervals of the nucleon momentum fraction carried by gluons, $x_{\rm g}$, covering the range $0.04 \!<\! x_{ \rm g}\! <\! 0.28$~ and does not exhibit a significant dependence on $x_{\rm g}$. The average over the three intervals, $\langle \Delta g/g \rangle = 0.113 \pm 0.038_{\rm (stat.)}\pm 0.036_{\rm (syst.)}$ at $\langle x_{\rm g} \rangle \approx 0.10$, suggests that the gluon polarisation is positive in the measured $x_{\rm g}$ range.Comment: 14 pages, 6 figure

Comparative Study of Bunch Length And Arrival Time Measurements at Flash

Diagnostic devices to precisely measure the longitudinal electron beam profile and the bunch arrival time require elaborate new instrumentation techniques. At FLASH, two entirely different methods are used. The bunch profile can be determined with high precision by a transverse deflecting RF structure, but the method is disruptive and does not allow to monitor multiple bunches in a macro-pulse train. It is therefore complemented by two non-disruptive electrooptical devices, called EO and TEO. The EO setup uses a dedicated diagnostic laser synchronized to the machine RF. The longitudinal electron beam profile is encoded in the intensity profile of a chirped laser pulse and analyzed by looking at the spectral composition of the pulse. The second setup, TEO, utilizes the TiSa-based laser system used for pump-probe experiments. Here, the temporal electron shape is encoded into the spatial dimension of the laser pulse by an intersection angle between the laser and the electron beam at the EO-crystal. In this paper, we present a comparative study of bunch length and arrival time measurements performed simultaneously with all three experimental techniques