Erlangen Program at Large-2.5: Induced Representations and Hypercomplex Numbers

In the search for hypercomplex analytic functions on the half-plane, we review the construction of induced representations of the group G=SL(2,R). Firstly we note that G-action on the homogeneous space G/H, where H is any one-dimensional subgroup of SL(2,R), is a linear-fractional transformation on hypercomplex numbers. Thus we investigate various hypercomplex characters of subgroups H. The correspondence between the structure of the group SL(2,R) and hypercomplex numbers can be illustrated in many other situations as well. We give examples of induced representations of SL(2,R) on spaces of hypercomplex valued functions, which are unitary in some sense. Raising/lowering operators for various subgroup prompt hypercomplex coefficients as well. The paper contains both English and Russian versions. Keywords: induced representation, unitary representations, SL(2,R), semisimple Lie group, complex numbers, dual numbers, double numbers, Moebius transformations, split-complex numbers, parabolic numbers, hyperbolic numbers, raising/lowering operators, creation/annihilation operatorsComment: LaTeX2e; 17 pp + 13 pp of a source code; 5 EPS pictures in two Figures; v2: minor improvements and corrections; v3: a section on raising/lowering operators is added; v4: typos are fixed; v5: Introduction is added, open problems are expanded.v6: Russian translation is added, references areupdated, NoWeb and C++ source codes are added as ancillary files. arXiv admin note: substantial text overlap with arXiv:0707.402

The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces

It is well-known that self-linking is the only Z valued Vassiliev invariant of framed knots in S^3. However for most 3-manifolds, in particular for the total spaces of S^1-bundles over an orientable surface F not S^2, the space of Z-valued order one invariants is infinite dimensional. We give an explicit formula for the order one invariant I of framed knots in orientable total spaces of S^1-bundles over an orientable not necessarily compact surface F not S^2. We show that if F is not S^2 or S^1 X S^1, then I is the universal order one invariant, i.e. it distinguishes every two framed knots that can be distinguished by order one invariants with values in an Abelian group.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-3.abs.htm

Assessing the Complementarity of Preferential Tax Regimes in the Sakhalin Region

State regulation of the anthropogenic impact on nature, including the policy of limiting greenhouse gas emissions, makes it necessary to support those enterprises that are willing to invest in climate projects. The relevance of incentives in this field is confirmed by the task set by the Arctic Council chaired by Russia at the Research and Training Conference on Climate Change and Permafrost Thawing 2023, namely to find reasonable, practical solutions for adapting the global economy to such changes. In the area of taxation, there is a solution prepared by the Russian Ministry of Economic Development willing to provide a package of tax benefits for investors. According to the draft, they should be exempted from paying VAT and income tax. At the same time, the variety of previously introduced preferential ‘investment’ tax regimes calls into question the rationality of new tax incentives due to the assumption of their redundancy. The fact is that they have similarities in the basic idea of support aimed at the growth of regional investment activity. For this reason, the purpose of the article is to answer the following questions: Is it really worthwhile to expand the number of tax regimes once again? Is it possible to use existing incentives instead of introducing new ones? To achieve the purpose, we rely on the results of comprehensive, comparative analysis of the developed incentives and the current tax preferential regimes on the example of the Sakhalin region. It stands out among other regions of Russia by its carbon-neutral pilot project and the greater number of preferences already enjoyed by investors, so we can provide representative and practically significant results. The hypothesis of the study is based on the concept of complementarity, meaning that the newly developed tax incentives will contribute to the complexity of the Russian tax system but will not cross the scope of the other mentioned tax regimes. The results show that climate projects have their own specifics in terms of objectives as well as areas of investment that require special approaches in tax policy, since investors create a useful economic effect in the form of reducing greenhouse gas emissions rather than producing goods, and no taxable profit is generated until the investor profitably sells carbon units in the market

Оценка бюджетных последствий введения необлагаемого минимума в налогообложение личных доходов в России

The social problem of poverty can be mitigated by introduction of a personal tax-free allowance. In this paper the likely effects that a personal tax-free allowance will have on the Russian budget is investigated. It has been assumed that a tax-free allowance will hit regional budgets because they depend greatly on income tax revenue. The indicated effects were estimated by applying a personal tax-free allowance to the data on economic conditions in 2019. Rosstat data on population, poverty, wages and gross regional product and Federal Tax Service data on the number of taxpayers and personal income tax revenues were used. For the purpose of the paper, two scenarios were calculated. In the first scenario, a zero personal income tax rate is applied to wages below the minimum cost of living. We found that under this scenario the consolidated budget of Russia loses over 1 trillion rubles while regional tax revenues reduce by more than 10%. In the second scenario, citizens whose income is below the minimum cost of living are exempt from personal income tax. We found that under this scenario regional tax revenues would be reduced by 1-5%. In both cases the introduction of the personal tax-free allowance puts greater pressure on regions that critically depend on the personal income tax receipts. It was concluded that the negative effect of an introduction of a personal tax-free allowance would be greater, the greater the prevalence of low-income taxpayers in a region. Also considerable regional disparities create a risk that such tax reform will deepen regional inequality and be disruptive for the Russian budgetary system. For citationGromov V.V. Introduction of the personal tax-free allowance in Russia and its budget implications. Journal of Tax Reform. 2021;7(1):20–38. DOI: 10.15826/jtr.2021.7.1.088 Article infoReceived October 7, 2020; Revised January 10, 2021; Accepted January 29, 2021Социальную проблему бедности может смягчить введение необлагаемого подоходным налогом минимума доходов граждан. В статье исследуются вероятные бюджетные потери от введения в России необлагаемого подоходным налогом минимума доходов граждан. Выдвигается гипотеза, что введение необлагаемого минимума негативно скажется на регионах, поскольку зависимость их бюджетов от поступления подоходного налога велика. Расчет последствий введения необлагаемого минимума проводился для экономических условий 2019 г. Источником данных являлись данные Росстата о населении, бедности, заработной плате и валовом региональном продукте, а также данные Федеральной налоговой службы о количестве налогоплательщиков и налоговых поступлениях. Для целей исследования были рассчитаны два сценария. По первому сценарию к заработной плате ниже прожиточного минимума применяется нулевая ставка налога на доходы физических лиц. Мы обнаружили, что при этом сценарии консолидированный бюджет России теряет более 1 трлн р., в то время как налоговые поступления в региональные бюджеты сокращаются более чем на 10%. По второму сценарию не облагаются налогом на доходы физических лиц граждане, чей доход ниже прожиточного минимума. Данные, полученные по второму сценарию, показывают, что региональные налоговые поступления сократятся на 1–5%. В любом случае, введение необлагаемого налогом минимума оказывает более сильное давление на те регионы, которые критически зависят от поступлений подоходного налога с физических лиц. Можно сделать вывод, что введение льготы при преобладании налогоплательщиков с низкими доходами приведет к существенным потерям для региональных бюджетов. Сделан вывод, что негативное влияние введения необлагаемого минимума будет тем больше, чем больше в регионе преобладают малообеспеченные налогоплательщики. Кроме того, значительные региональные диспропорции создают риск того, что такая налоговая реформа усугубит региональное неравенство и подорвет бюджетную систему России.Для цитированияGromov V.V. Introduction of the personal tax-free allowance in Russia and its budget implications. Journal of Tax Reform. 2021;7(1):20–384. DOI: 10.15826/jtr.2021.7.1.088 Информация о статьеДата поступления 7 октября 2020 г.; дата поступления после рецензирования 10 января 2021 г.; дата принятия к печати 29 января 2021 г

ЭКОЛОГИЧЕСКИЕ НАЛОГИ: КЛАССИЧЕСКОЕ И СОВРЕМЕННОЕ ПОНИМАНИЕ СУЩНОСТИ

Modern practice of taxation necessarily concerns environmental taxes that are one of the basic instruments for environmental quality improvement in developed countries. Russia also tries to use its tax system to promote environmental protection policy. Against this background, understanding of what environmental tax is and past and present notion of its nature is very essential.Современная практика налогообложения не обходится без обращения к экологическим налогам, которые в экономике развитых стран служат одним из основных инструментов повышения качества экологии. Россия тоже стремится задействовать налоговую систему для реализации своей природоохранной политики. На этом фоне особо важное значение приобретает понимание того, что такое экологический налог, и каковы были и остаются представления о его сущности

Assessment of the degree of violations of hemostasis parameters, rheology, markers of inflammation in patients with arterial hypertension and different risks of venous thromboembolic complications

The aim of the work is to investigate the parameters of hemostasis, electrical and viscoelastic parameters of red blood cells and markers of inflammation in persons suffering from arterial hypertension to determine the possibility of assessing the severity of hemorheological disorders. Material and methods. The study included 203 patients (156 patients with arterial hypertension and 47 patients without hypertension). The parameters of hemostasis, markers of inflammation and red blood cells were studied. Results. The possibilities of assessing the severity of hemorheological disorders in patients with arterial hypertension, based on the study of parameters: hemostasis, erythrocytes (by dielectrophoresis). In patients with hypertension, as the risk of venous thromboembolic complications increased, acceleration of leukocyte-platelet aggregation, increased fibrinogen level and decreased activity of XII-dependent fibrinolysis, which creates prerequisites for rheological disturbances, were revealed. The most accurate prediction of result according to severity of hemorheological disorders (differentiation moderate and expressed disorders from the lungs) is provided by such indicators of electric and viscoelastic parameters of erythrocytes, as the polarizability of red blood cells at a frequency of 106 Hz (AUC = 0,750 in), the speed of movement of cells to the electrodes (AUC = 0,746), deformation degree at a frequency of 5 × 105 Hz (AUC = 0,733), conductivity cell (AUC = 0,730), the generalized viscosity (AUC = 0,729), the index of aggregation of erythrocytes (AUC = 0,716), graduation according to the degree of strain at all frequencies (AUC = 0,716), generalized stiffness (AUC = 0,714), the deformation amplitude at frequency of 106 Hz (AUC = 0,711), the capacity of the cells (AUC = 0,693). The measure of specificity for different indices of erythrocytes is 75.4–99,3 % and a sensitivity of 84.1–98.6 %. Conclusions. The study of the parameters of hemostasis, markers of inflammation, red blood cells allowed us to determine the key indicators for assessing the severity of hemorheological disorders in patients with arterial hypertension. The work was carried out within the framework of the budgetary theme under the State Assignment No. 121090800102-4

Baxter Q-Operators and Representations of Yangians

We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang-Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang-Baxter equation serve as elementary, "partonic" building blocks for other solutions via the standard fusion procedure. As a first example of the method we consider sl(n) compact spin chains and derive the full hierarchy of operatorial functional equations for all related commuting transfer matrices and Q-operators. This leads to a systematic and transparent solution of these chains, where the nested Bethe equations are derived in an entirely algebraic fashion, without any reference to the traditional Bethe ansatz techniques.Comment: 27 pages, 5 figures; v2: typos fixed, references updated and adde

On subgroups of minimal topological groups

A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. The Roelcke uniformity (or lower uniformity) on a topological group is the greatest lower bound of the left and right uniformities. A group is Roelcke-precompact if it is precompact with respect to the Roelcke uniformity. Many naturally arising non-Abelian topological groups are Roelcke-precompact and hence have a natural compactification. We use such compactifications to prove that some groups of isometries are minimal. In particular, if U_1 is the Urysohn universal metric space of diameter 1, the group Iso(U_1) of all self-isometries of U_1 is Roelcke-precompact, topologically simple and minimal. We also show that every topological group is a subgroup of a minimal topologically simple Roelcke-precompact group of the form Iso(M), where M is an appropriate non-separable version of the Urysohn space.Comment: To appear in Topology and its Applications. 39 page