Global bifurcation of homoclinic trajectories of discrete dynamical systems

We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving the topological properties of the asymptotic stable bundles

On sigma-subnormality criteria in finite sigma-soluble groups

[EN] Let sigma = {sigma(i) : i is an element of I} be a partition of the set P of all prime numbers. A subgroup X of a finite group G is called sigma-subnormal in G if there is a chain of subgroups X = X-0 subset of X-1 subset of center dot center dot center dot subset of X-n = G where for every j = 1,..., n the subgroup X j-1 is normal in X j or X j /CoreX j ( X j-1) is a si -group for some i. I. In the special case that s is the partition of P into sets containing exactly one prime each, the sigma-subnormality reduces to the familiar case of subnormality. In this paper some sigma-subnormality criteria for subgroups of s-soluble groups, or groups in which every chief factor is a sigma(i)-group, for some sigma(i) sigma s, are showed.The first and third authors are supported by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades and the Agencia Estatal de Investigacion, Spain, and FEDER, European Union and Prometeo/2017/057 of Generalitat (Valencian Community, Spain). The second author was supported by the State Program of Science Researchers of the Republic of Belarus (Grant 19-54 "Convergence-2020").Ballester-Bolinches, A.; Kamornikov, SF.; Pedraza Aguilera, MC.; Pérez-Calabuig, V. (2020). On sigma-subnormality criteria in finite sigma-soluble groups. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-9. https://doi.org/10.1007/s13398-020-00824-4S191142Amberg, B., Franciosi, S., De Giovanni, F.: Products of Groups. Oxford Mathematical Monographs. Clarendon Press, Oxford (1992)Ballester-Bolinches, A., Ezquerro, L.M.: Classes of Finite Groups, Vol. 584 of Mathematics and its Applications. Springer, New York (2006)Ballester-Bolinches, A., Kamornikov, S.F., Pedraza-Aguilera, M.C., Yi, X.: On -subnormal subgroups of factorised finite groups (Preprint)Casolo, C.: Subnormality in factorizable finite soluble groups. Arch. Math. 57, 12–13 (1991)Doerk, K., Hawkes, T.: Finite Soluble Groups. Walter De Gruyter, Berlin (1992)Fumagalli, Francesco: On subnormality criteria for subgroups in finite groups. J. Lond. Math. Soc. 76(2), 237–252 (2007)Kamornikov, S.F., Shemetkova, O.L.: On $${{\cal{F}}}$$-subnormal subgroups of a finite factorised group. Probl. Phys. Math. Tech. 1, 61–63 (2018)Khukhro, E.I., Mazurov, V.D.: Unsolved Problems in Group Theory. The Kourovka notebook. Institut Matematiki SO RAN, Novosibirsk, No. 19 (2018)Lennox, J.C., Stonehewer, S.E.: Subnormal Subgroups of Groups. Clarendon Press, Oxford (1987)Maier, R.: Um problema da teoria dos subgrupos subnormais. Bol. Soc. Bras. Mat. 8(2), 127–130 (1977)Maier, R., Sidki, R.: A note on subnormality in factorizable finite groups. Arch. Math. 42, 97–101 (1984)Skiba, A.N.: A generalization of a Hall theorem. J. Algebra Appl. 15(4), 13 (2016)Skiba, A.N.: On $$\sigma$$-subnormal and $$\sigma$$-permutable subgroups of finite groups. J. Algebra 436, 1–16 (2015)Skiba, A.N.: On -properties of finite groups I. Probl. Phys. Math. Tech. 4, 89–96 (2014)Skiba, A.N.: On -properties of finite groups II. Probl. Phys. Math. Tech. 3(24), 70–83 (2015)Skiba, A.N.: On some arithmetic properties of finite groups. Note Mat. 36, 65–89 (2016)Wielandt, H.: Subnormalität in faktorisierten endlichen Grupppen. J. Algebra 69, 305–311 (1981

Anti‐atherosclerotic effect of the angiotensin 1–7 mimetic AVE0991 is mediated by inhibition of perivascular and plaque inflammation in early atherosclerosis

Background and Purpose: Inflammation plays a key role in atherosclerosis. A protective role of angiotensin-(1-7) in vascular pathologies opened a possibility for therapeutic use of small molecule non-peptide Ang-(1-7) mimetics, such as AVE0991. The mechanisms of these vaso-protective effects of a Mas receptor agonist, AVE0991, remain unclear. Experimental approach: We investigated the effects of AVE0991 on the spontaneous atherosclerosis in ApoE-/- mice, in the context of vascular inflammation and plaque stability. Key Results: AVE0991 has significant anti-atherosclerotic properties in ApoE-/- mice and increases plaque stability, by reducing plaque macrophage content, without effects on collagen. Using descending aorta of chow fed ApoE-/- mice, before significant atherosclerotic plaque develops, we gained insight to early events in atherosclerosis. Interestingly, perivascular adipose tissue (pVAT) and adventitial infiltration with macrophages and T cells precedes atherosclerotic plaque or the impairment of endothelium-dependent NO bioavailability as a measure of endothelial function. AVE0991 inhibited perivascular inflammation, through the reduction of chemokine expression in pVAT, as well as through direct actions on monocytes/macrophages inhibiting their activation, characterized by IL-1β, TNF-α, MCP-1 and CXCL10 and differentiation to M1 phenotype. Pre-treatment with AVE0991 inhibited migration of THP-1 monocytes towards supernatants of activated adipocytes (SW872). Mas receptors were expressed in pVAT and in THP-1 cells in vitro and anti-inflammatory effects of AVE0991 were partially Mas dependent. Conclusions & implications: Selective Mas receptor agonist AVE0991 possesses anti-atherosclerotic and anti-inflammatory properties, affecting monocyte/macrophage differentiation and recruitment to perivascular space at early stages of atherosclerosis in ApoE-/- mice

On X-saturated formations of finite groups

This is an Author's Original Manuscript of an article submitted for consideration in Communications in Algebra 33(4):1053-1064 (2005) (copyright Taylor & Francis). Communications in Algebra is available online at http://www.tandfonline.com/10.1081/AGB-200053809 DOI 10.1081/AGB-200053809 The final publication is available at link.springer.com[EN] In the paper, a Frattini-like subgroup associated with a class X of simple groups is introduced and analysed. The corresponding X-saturated formations are exactly the X-local ones introduced by Förster. Our techniques are also very useful to highlight the properties and behaviour of omega-local formations. In fact, extensions and improvements of several results of Shemetkov are natural consequences of our study.This work has been supported by Proyecto BFM2001-1667-C03-03, MCyT (Spain) and FEDER (European Union).http://www.tandfonline.com/10.1081/AGB-200053809Ballester Bolinches, A.; Calvo Lopez, C.; Esteban Romero, R. (2005). On X-saturated formations of finite groups. Communications in Algebra. 4(33). doi:10.1081/AGB-20005380943

Blow-off mechanisms of turbulent premixed bluff-body stabilised flames operated with vapourised kerosene fuels

The lean blow-off (LBO) behaviour of unconfined lean premixed blu -body stabilised flames with various fuels was investigated. Methane and vapourised ethanol, heptane, Jet-A1, and an alternative alcohol-derived kerosene (Gevo) were used. OH* chemiluminescence (5 kHz), OH- and Fuel-PLIF (5 kHz), and CH2O-PLIF (10 Hz) were deployed. For all fuels, as the flame approached LBO fragmentation was observed downstream, the two sides of the flame merged at the axis, pockets of OH and CH2O were found in the recirculation zone (RZ), and eventually the individual fragments extinguished. The CH2O seemed to enter into the RZ from downstream early in the LBO process, with reactants following suit at times closer to LBO. During LBO, the integrated OH* signal decreased slowly to zero and the duration of this transition was 25 (d=UBO) in the methane and ethanol flames and 60 (d=UBO) in flames operated with heptane and the two kerosenes (where d is the blu -body diameter and UBO the LBO velocity). This large di erence could be due to re-ignitions of partially-quenched fluid inside the RZ during the LBO event. Additionally, for the same bulk velocity, the kerosene flames blow-o at higher equivalence ratios than the single-component fuelled flames, which is possibly due to the higher Lewis number and lower extinction strain rates of these fuels. The results suggest that the blow-o mechanism is qualitatively similar for each of the fuels; however, the complex chemistry associated with heavy hydrocarbons appears to result in a prolonged LBO event.Cambridge Trust