Prime Fano threefolds of genus 12 with a GmG_m-action

We give an explicit construction of prime Fano threefolds of genus 12 with a $G_m$-action, describe their isomorphism classes and automorphism groups.Comment: 14 pages, LaTeX, updated version, to appear in \'Epijournal de G\'eom\'etrie Alg\'ebrique, Vol. 2 (2018), Article Nr.

Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations

In this paper we perform the parameter-dependent center manifold reduction near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf bifurcations in delay differential equations (DDEs). This allows us to initialize the continuation of codimension one equilibria and cycle bifurcations emanating from these codimension two bifurcation points. The normal form coefficients are derived in the functional analytic perturbation framework for dual semigroups (sun-star calculus) using a normalization technique based on the Fredholm alternative. The obtained expressions give explicit formulas which have been implemented in the freely available numerical software package DDE-BifTool. While our theoretical results are proven to apply more generally, the software implementation and examples focus on DDEs with finitely many discrete delays. Together with the continuation capabilities of DDE-BifTool, this provides a powerful tool to study the dynamics near equilibria of such DDEs. The effectiveness is demonstrated on various models

Practical initialization of homoclinic orbits from a Bogdanov-Takens point

In a recent paper [IJBC, 24(04):1450057, 2014], we improved the theoretical base for the initialization of homoclinic orbits. However, practical application of this method is not very robust without the consideration of some numerical issues. We deal with these issues and provide examples from a robust implementation of the initialization procedure in the software package MatCont [ACM Trans. Math. Software, 29(2):141–164, 2003]

Rationality over non-closed fields of Fano threefolds with higher geometric Picard rank

We prove rationality criteria over algebraically non-closed fields of characteristic $0$ for five out of six types of geometrically rational Fano threefolds of Picard number $1$ and geometric Picard number bigger than $1$. For the last type of such threefolds we provide a unirationality criterion and prove stable non-rationality under additional assumptions.Comment: 34 pages, late

Dynamics of Cellular Factors of the Immune System of Arctic Foxes (Vulpes lagopus) on the Background of Mixtinvasion

The article presents data on the dynamics of cellular immune system factors of the arctic foxes (Vulpes lagopus) while being affected by mixtinvasion of protozoa (Isospora vulpina) and helminth (Toxascaris leonina). The changes in the blood cell composition, in particular those responsible for the body’s immunity and immune status, reflect the pathological effect of the endoparasites on the animal’s body. The development of the invasive process during mixtinvasions causes and is accompanied by a decrease in the level of nonspecific resistance of the host organism. In addition, a significant process of inhibition of the lysozyme complementary activity in the blood serum and the development of secondary immunodeficiencies is observed. The aim of our work was to study the development of the pathological process in arctic foxes, caused by previously detected mixtinvasion by eimeriidoses and helminthiases, as well as to identify dynamical patterns of the immune system cellular factors. Intravital diagnostics of parasitoses was carried out by means of coproscopic studies with the help of conventional flotation methods. 127 arctic foxes participated in the experiment. Among them individuals with double invasion, an invasion with both protozoa (placeI. vulpina) and helminth (T. leonina), were selected for the experiment. Healthy animals served as the control group. Arctic foxes which took part in the experiment were divided into three groups of 10 animals each. Groups were formed by the method of balanced analogous groups. Evaluation of the T-system of immunity was carried out by the method of spontaneous rosetting according to Jondal (1972). Isolation of lymphocytes by the method of A. Boyum (1968), B-lymphocytes were determined by the method of E. Mendes (1973), theophylline-resistant and theophylline-sensitive T-lymphocytes were determined using the method of S. Limatibul et.al. (1978). The immunoregulation index was calculated by the ratio of T-helpers to T-suppressors. During the experiment, it was found that in infected animals the total number of lymphocytes was significantly 10.2 % higher than in animals in the control group, however, there was a tendency to a sharp decrease in the total number of lymphocytes in patients with I. vulpina + T. leonina. The T-helper dynamics in infected foxes was 18.9 ± 0.9 (P≤0.05), which is 21.9 % less than in the control – 24.2 ± 0.6 (P≤0, 05). The dynamics of T-suppressors turned out to be directly opposite to the dynamics of the T-helpers. The dynamics of B-lymphocytes in the 2nd group turned out to be 1.76 times higher than in animals from the control. In the 3rd group same indicator was comparable with the control values of 2.9 ± 0.3, against 2.5 ± 0.4 in the control group. The study showed that mixtinvasion with placeI. vulpina + T. leonina leads to immunosuppression in the arctic foxes. Interestingly the specific therapy did not straighten the immune state of the animals, but on the contrary it became more pronounced, which suggests that antiparasitic drugs have an immunosuppressive nature on the body of arctic foxes as evidenced by violations of the parameters of the body’s natural resistance, the content of T-E-ROCK lymphocytes

On higher-dimensional del Pezzo varieties

We study del Pezzo varieties, higher-dimensional analogues of del Pezzo surfaces. In particular, we introduce ADE classification of del Pezzo varieties, show that in type A the dimension of non-conical del Pezzo varieties is bounded by $12 - d - r$, where $d$ is the degree and $r$ is the rank of the class group, and classify maximal del Pezzo varieties.Comment: 60 pages, LaTe