Towards the Intersection Theory on Hurwitz Spaces

Moduli spaces of algebraic curves and closely related to them Hurwitz spaces, that is, spaces of meromorphic functions on the curves, arise naturally in numerous problems of algebraic geometry and mathematical physics, especially in relationship with the string theory and Gromov--Witten invariants. In particular, the classical Hurwitz problem about enumeration of topologically distinct ramified coverings of the sphere with prescribed ramification type reduces to the study of geometry and topology of these spaces. The cohomology rings of such spaces are complicated even in the simplest cases of rational curves and functions. However, the cohomology classes that are the most important from the point of view of applications (namely, the classes Poincar\'e dual to the strata of functions with given singularities) can be expressed in terms of relatively simple ``basic'' classes (which are, in a sense, tautological). The aim of the present paper is to identify these basic classes, to describe relations among them, and to find expressions for the strata in terms of these classes. Our approach is based on R. Thom's theory of universal polynomials of singularities, which has been extended to the case of multisingularities by the first author. Although the general Hurwitz problem still remains open, our approach allows one to achieve a significant progress in its solution, as well as in the understanding of the geometry and topology of Hurwitz spaces.Comment: 29 pages, AMSTe

The charge-dyon bound system in the spherical quantum well

The spherical wave functions of charge-dyon bounded system in a rectangular spherical quantum dot of infinitely and finite height are calculated. The transcendent equations, defining the energy spectra of the systems are obtained. The dependence of the energy levels from the wall sizes is found.Comment: 8 pages, 5 figure

The concept of "Tea" in the language picture of the world (based on Chinese and Russian languages)

This article presents a study of the “tea” concept and its representation in the language picture of the world based on the Russian and Chinese languages and identification of linguistic-cognitive and linguistic-cultural specification of its comprehension by Russian and Chinese people. The following issues were examined in the article: the cultural and historical background of the formation of the “tea” concept, the frequency of occurrence of the “tea” token and also the representation of the “tea” concept in both linguistic worlds. The results were as follows: the language representation of the “tea” concept was described and compared, and the similarities and differences in the content of the concept were revealed. The language representation of the “tea” concept in the Chinese and Russian languages was taken as the material of the study

Direct Interband Light Absorption in Strongly Prolated Ellipsoidal Quantum Dots’ Ensemble

Within the framework of adiabatic approximation, the energy levels and direct interband light absorption in a strongly prolated ellipsoidal quantum dot are studied. Analytical expressions for the particle energy spectrum and absorption threshold frequencies in three regimes of quantization are obtained. Selection rules for quantum transitions are revealed. Absorption edge and absorption coefficient for three regimes of size quantization (SQ) are also considered. To facilitate the comparison of obtained results with the probable experimental data, size dispersion distribution of growing quantum dots by the small semiaxe in the regimes of strong and weak SQ by two experimentally realizing distribution functions have been taken into account. Distribution functions of Lifshits–Slezov and Gaussian have been considered

Spectral properties of a short-range impurity in a quantum dot

The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In the case of a spherically symmetric quantum dot, the dependence of the spectrum on the impurity position and the strength of the impurity potential is analyzed in detail. It is proven that the confinement potential of the dot can be recovered from the spectroscopy data. The consequences of the hidden symmetry breaking by the impurity are considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late

Problem of spreading fake information in the Internet space analysis

Modern Internet space is filled with various kinds of information, including unreliable, fake information. In the current socio-cultural, socio-political, and socio-economic conditions, we should expect further increase in the spread of fakes and, as a consequence, their negative impact on people’s lives. The article analyses results of a sociological study on the attitude of the Kursk region population to fakes spread in the Internet space. The empirical basis of the study is the results of the online questionnaire survey conducted in September 2022 in the Kursk region. The sample population of the study was 521 people living in the territory of Kursk and Kursk region. Fakes are becoming a real part of life in modern society. Residents of the region are constantly faced with inaccurate information. They recognize its danger and note that fakes nevertheless “attract” their attention. The current situation requires additional measures development to regulate dissemination of information in the Internet space

The Updated Zwicky Catalog (UZC)

The Zwicky Catalog of galaxies (ZC), with m_Zw<=15.5mag, has been the basis for the Center for Astrophysics (CfA) redshift surveys. To date, analyses of the ZC and redshift surveys based on it have relied on heterogeneous sets of galaxy coordinates and redshifts. Here we correct some of the inadequacies of previous catalogs by providing: (1) coordinates with <~2 arcsec errors for all of the Nuzc catalog galaxies, (2) homogeneously estimated redshifts for the majority (98%) of the data taken at the CfA (14,632 spectra), and (3) an estimate of the remaining "blunder" rate for both the CfA redshifts and for those compiled from the literature. For the reanalyzed CfA data we include a calibrated, uniformly determined error and an indication of the presence of emission lines in each spectrum. We provide redshifts for 7,257 galaxies in the CfA2 redshift survey not previously published; for another 5,625 CfA redshifts we list the remeasured or uniformly re-reduced value. Among our new measurements, Nmul are members of UZC "multiplets" associated with the original Zwicky catalog position in the coordinate range where the catalog is 98% complete. These multiplets provide new candidates for examination of tidal interactions among galaxies. All of the new redshifts correspond to UZC galaxies with properties recorded in the CfA redshift compilation known as ZCAT. About 1,000 of our new measurements were motivated either by inadequate signal-to-noise in the original spectrum or by an ambiguous identification of the galaxy associated with a ZCAT redshift. The redshift catalog we include here is ~96% complete to m_Zw<=15.5, and ~98% complete (12,925 galaxies out of a total of 13,150) for the RA(1950) ranges [20h--4h] and [8h--17h] and DEC(1950) range [-2.5d--50d]. (abridged)Comment: 34 pp, 7 figs, PASP 1999, 111, 43

Adiabatic description of nonspherical quantum dot models

Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of single-parameter basis functions. The comparison is given and the peculiarities are considered for spectral and optical characteristics of the models with axially symmetric confining potentials depending on their geometric size making use of the total sets of exact and adiabatic quantum numbers in appropriate analytic approximations

Epigenetic characterization of the FMR1 promoter in induced pluripotent stem cells from human fibroblasts carrying an unmethylated full mutation

Silencing of the FMR1 gene leads to fragile X syndrome, the most common cause of inherited intellectual disability. To study the epigenetic modifications of the FMR1 gene during silencing in time, we used fibroblasts and induced pluripotent stem cells (iPSCs) of an unmethylated full mutation (uFM) individual with normal intelligence. The uFM fibroblast line carried an unmethylated FMR1 promoter region and expressed normal to slightly increased FMR1 mRNA levels. The FMR1 expression in the uFM line corresponds with the increased H3 acetylation and H3K4 methylation in combination with a reduced H3K9 methylation. After reprogramming, the FMR1 promoter region was methylated in all uFM iPSC clones. Two clones were analyzed further and showed a lack of FMR1 expression, whereas the presence of specific histone modifications also indicated a repressed FMR1 promoter. In conclusion, these findings demonstrate that the standard reprogramming procedure leads to epigenetic silencing of the fully mutated FMR1 gene