Integrals, quantum Galois extensions and the affineness criterion for quantum Yetter-Drinfel'd modules

We introduce and study a general concept of integral of a threetuple (H, A, C), where H is a Hopf algebra acting on a coalgebra C and coacting on an algebra A. In particular, quantum integrals associated to Yetter-Drinfel'd modules are defined. Let A be an H-bicomodule algebra, $^H {\cal YD}_A$ be the category of (generalized) Yetter-Drinfel'd modules and $B$ the subalgebra of coinvariants of the Verma structure of $A$. We introduce the concept of quantum Galois extensions and we prove the affineness criterion in a quantum version.Comment: latex 32 pg. J. Algebra, to appea

Serre Theorem for involutory Hopf algebras

We call a monoidal category ${\mathcal C}$ a Serre category if for any $C$, $D \in {\mathcal C}$ such that C\ot D is semisimple, $C$ and $D$ are semisimple objects in ${\mathcal C}$. Let $H$ be an involutory Hopf algebra, $M$, $N$ two $H$-(co)modules such that $M \otimes N$ is (co)semisimple as a $H$-(co)module. If $N$ (resp. $M$) is a finitely generated projective $k$-module with invertible Hattory-Stallings rank in $k$ then $M$ (resp. $N$) is (co)semisimple as a $H$-(co)module. In particular, the full subcategory of all finite dimensional modules, comodules or Yetter-Drinfel'd modules over $H$ the dimension of which is invertible in $k$ are Serre categories.Comment: a new version: 8 page

New types of bialgebras arising from the Hopf equation

New types of bialgebras arising from the Hopf equation (pentagonal equation) are introduced and studied. They will play from the Hopf equation the same role as the co-quasitriangular do from the quantum Yang Baxter equation.Comment: Latex2e, Comm Algebra, in pres

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor

The Hopf modules category and the Hopf equation

We study the Hopf equation which is equivalent to the pentagonal equation, from operator algebras. A FRT type theorem is given and new types of quantum groups are constructed. The key role is played now by the classical Hopf modules category. As an application, a five dimensional noncommutative noncocommutative bialgebra is given.Comment: 30 pages, Letax2e, Comm. Algebra in pres

Clinical chemistry, haematology, immune response and histological evaluation of rabbits after immunisation and challenge with rabbit haemorrhagic disease (RHD) virus

[EN] Following their immunisation and infection with a VSHI-CN-6 viral strain, a group of 15 rabbits were examined in a study of Rabbit Haemorrhagic Disease (RHD). Serum samples were collected from the external ear vein at 0, 15, 30 and 60 days post-immunisation. The recorded platelet numbers were closer to the lower physiological limit, indicating a mild thrombocytopenia, with values ranging from 26.6 to 30.43×104/mm3. The phagocytic index revealed significant differences (P<0.001) between the mean values obtained before vaccination (day 0) and the 3 post-vaccination measurements, confirming the increase in phagocytic capacity after immunisation. Additionally, the serum lysozyme average value equalled 9.14 mg/mL post-vaccination. The analysis of variance revealed significant statistical differences (P<0.05) between the average values obtained before vaccination (0) and the post-vaccination values, measured on day 14 and 30, respectively. The morphology of the samples collected from the main organs involved in immune protection, spleen and gastric and portal lymph nodes highlighted changes corresponding to the post-vaccination immunological response. The white pulp of the spleen appeared as a diffuse lymphoid tissue, presenting with primary and secondary lymphoid follicles. The ratio of white/red pulp was in favour of the white pulp and multiple lymphoid follicles were present, indicating their reactivation. In the medullary area of gastric and portal lymph nodes, narrow lymphoid cords, circumscribed by relatively large lymphatic sinuses, and well defined lymphocytolysis were observed. Moreover, the exudate and lymphoid follicles during activation were noted in the cortical area. Furthermore, the inflammatory processes were identified, morphologically manifested by the thickening of connective tissue in the lymph node capsule, dilacerations of the connective fibres and the presence of light acidophilic serous exudate with rare inflammatory cells (serous lymphoreticulitis).Stancu, CA.; Cărpinișan, L.; Ghișe, A.; Marcu, A.; Pentea, MC.; Dumitrescu, E.; Muselin, F.... (2017). Clinical chemistry, haematology, immune response and histological evaluation of rabbits after immunisation and challenge with rabbit haemorrhagic disease (RHD) virus. World Rabbit Science. 25(4):357-365. doi:10.4995/wrs.2017.7500SWORD35736525

Suppressing Recoil Heating in Levitated Optomechanics using Squeezed Light

We theoretically show that laser recoil heating in free-space levitated optomechanics can be arbitrarily suppressed by shining squeezed light onto an optically trapped nanoparticle. The presence of squeezing modifies the quantum electrodynamical light-matter interaction in a way that enables us to control the amount of information that the scattered light carries about a given mechanical degree of freedom. Moreover, we analyze the trade-off between measurement imprecision and back-action noise and show that optical detection beyond the standard quantum limit can be achieved. We predict that, with state-of-the-art squeezed light sources, laser recoil heating can be reduced by at least 60% by squeezing a single Gaussian mode with an appropriate incidence direction, and by 98% by squeezing a properly mode-matched mode. Our results, which are valid both for motional and librational degrees of freedom, will lead to improved feedback cooling schemes as well as boost the coherence time of optically levitated nanoparticles in the quantum regime.Comment: 16 pages, 5 figure

Comportarea unor soiuri noi de măr la atacul focului bacterian

Fireblight -Erwinia amylovora Burill. Winslow is one of the most damaging for the apple culture in the many apple producing countries. Under ideal microclimate conditions it can destroy a young apple orchard in a single growing season, and by consequence it is very devastating not only for the apple production growing industry but for nurseries sector as well. In order to restrain and control the disease spread and damages, intensive researches are carried out in many fruit growing countries. This work aim was to assess the infection risks and early warning possibilities for the fire blight infections, under specific climatic conditions, using modern computer software, to assess the behavior of some new released and introduced apple varieties and to establish their susceptibility to natural occurred infections on active growing lateral shoots, in the latest years. According to the software forecast model, in the latest years, the infection risk with Erwinia amylovora on apples was high and very high from May to October. Under the given natural and technological conditions, the most sensitive apple varieties to fireblight attack were: Auriu de Bistrita (ROM) DD%=45.0; Dalinco and Dalinred (FRA) DD%=30-45.0; Topaz (CEH) DD%=35.0; Crimson Crisp and Idared (USA) DD%=35.0; Red Jonaprince (NL), Fuji Kiku Clone 8 (JPN) DD%=15.0.During the identified risk periods the apple trees need special prunings and preventive treatments with plant protection products including copper hydroxide and fosetil-aluminium, to keep them in good phytosanitary status. In order to better manage the fireblight disease, breeding o new tolerant or resistant apple varieties is always actual and a constant request