A remark on singular sets of vector bundle morphisms

If a characteristic class for two vector bundles over the same base space does not coincide, then the bundles are not isomorphic. We give under rather common assumptions a lower bound on the topological dimension of the set of all points in the base over which a morphism between such bundles is not bijective. Moreover, we show that this set is topologically non-trivial

On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

Crystal Structure of the Compound Er3Cu4.8Ga6.2.

Рентгенівським методом полікристалу (дифрактометр ДРОН-3М, проміння Сu Ka) визначено кристалічну структуру сполуки Er3Cu4,8Ga6,2: структурний тип La3Al11, символ Пірсона oI28, просторова група Immm, a = 4,14849(5), b = 12,2345(2), c = 9,7185(1) Å, RI = 0,0819; Rp = 0,1292. У структурі можна виділити пари атомів Купруму (dCu-Cu = 2,367 Å), орієнтовані вздовж [010], і нескінченні стрічки з квадратів атомів Галію (dGa1-Ga2 = 2,765 Å), що простягаються вздовж [100]. The crystal structure of the compound Er 3Cu4,8Ga6,2 (structure type La3Al11, Pearson symbol oI28, space group Immm, a = 4.14849(5), b = 12.2345(2), c = 9.7185(1) Å, RI = 0.0819; Rp = 0.1292) was determined based on X-ray powder diffraction data. In the structure Cu-atom dumbbells ( dCu-Cu = 2.367 Å) oriented along [010] and infinite chains of Ga-atom squares ( dGa1-Ga2 = 2.765 Å) running along [100] can be emphasized

Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha

Crystall Structure Compounds Type Hg5C2X8 (C−Ga, In; X−S, Se, Te) and Solid Solution

Используя методы РФА та РСА анализов, изучена структура соединений состава Hg5C2X8 (C–Ga, In; X–S, Se, Te) и твердых растворов на их основе. Соединения Hg5Ga2Se8, Hg5In2Se8, Hg5Ga2Te8 та Hg5In2Te8 кристализируются в ПГ F 4 3m с параметром элементарной ячейки а = 1,16876(2) нм, 1,18876(2) нм, 1,24738(2) нм и 1,26723(2) нм соответственно. Using X-ray phase and X-ray structure analysis methods, crystal structure compounds type Hg5C2X8 (C–Ga, In; X–S, Se, Te) and solid solution were investigated. Compaunds Hg5Ga2Se8, Hg5In2Se8, Hg5Ga2Te8 and Hg5In2Te8 has crystal structure of the F4 3m with а = 1,16876(2) nm, 1,18876(2) nm, 1,24738(2) nm and 1,26723(2) nm

On manifolds with nonhomogeneous factors

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces

Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

LEETECH facility as a flexible source of low energy electrons

A new versatile facility LEETECH for detector R&D, tests and calibration is designed and constructed. It uses electrons produced by the photoinjector PHIL at LAL, Orsay and provides a powerful tool for wide range R&D studies of different detector concepts delivering "mono-chromatic" samples of low energy electrons with adjustable energy and intensity. Among other innovative instrumentation techniques, LEETECH will be used for testing various gaseous tracking detectors and studying new Micromegas/InGrid concept which has very promising characteristics of spatial resolution and can be a good candidate for particle tracking and identification. In this paper the importance and expected characteristics of such facility based on detailed simulation studies are addressed

Effect of agrotechnological elements on milk thistle (Silynum marianum) productivity

The milk thistle is a highly valuable medicinal plant, widely used in treatment of liver diseases. Soil-climate conditions of the steppe zone of Ukraine are favourable for crop cultivation. The goal of the study was to determine relations between milk thistle productivity and elements of cultivation technology, viz., primary tillage depth (14–16 and 20–22 cm), inter-row spacing (30, 45, 60 cm), timing of sowing (3rd decade of March, middle of April, 3rd decade of April) and mineral fertilizer application doses (no fertilizers, N45P45, N90P90). Field trials were carried out during the period from 2010 to 2012 on the irrigated lands of the Institute of Rice of the National Academy of Agrarian Sciences of Ukraine by using the split plot design method in four replications. The climate of the territory of the trials is typical for the steppe zone. The soil type was dark-chestnut residual solonetz middle-loamy soil. We used the Yuhoslava variety of milk thistle in the trials. Cultivation technology was standard, excluding the studied factors. The results of the trials showed significant impact of all the studied cultivation technology elements on milk thistle seed and oil yields. The maximum average seed (1.66 t/ha) and oil (489 kg/ha) yields were obtained under the primary tillage at the depth of 20–22 cm, inter-row spacing of 60 cm, sowing in the 3rd decade of March, applying mineral fertilizers in a dose of N90P90. The highest input in seed and oil yields rise was made by the mineral fertilizers, which increased milk thistle productivity by 1.57 times comparatively with non-fertilized treatments. We also established a strong direct interrelationship between seed and oil yield: coefficient of determination was 0.96. Results of the current study are slightly limited, so further investigations in the field of milk thistle cultivation technology development and improvement are required to provide Ukrainian farmers with scientifically grounded agrotechnology of this valuable medicinal plant

Proceedings of the third French-Ukrainian workshop on the instrumentation developments for HEP

The reports collected in these proceedings have been presented in the third French-Ukrainian workshop on the instrumentation developments for high-energy physics held at LAL, Orsay on October 15-16. The workshop was conducted in the scope of the IDEATE International Associated Laboratory (LIA). Joint developments between French and Ukrainian laboratories and universities as well as new proposals have been discussed. The main topics of the papers presented in the Proceedings are developments for accelerator and beam monitoring, detector developments, joint developments for large-scale high-energy and astroparticle physics projects, medical applications.Comment: 3rd French-Ukrainian workshop on the instrumentation developments for High Energy Physics, October 15-16, 2015, LAL, Orsay, France, 94 page