Search results for "8c"
showing 10 items of 34 documents
Quillen superconnections and connections on supermanifolds
2013
Given a supervector bundle $E = E_0\oplus E_1 \to M$, we exhibit a parametrization of Quillen superconnections on $E$ by graded connections on the Cartan-Koszul supermanifold $(M;\Omega (M))$. The relation between the curvatures of both kind of connections, and their associated Chern classes, is discussed in detail. In particular, we find that Chern classes for graded vector bundles on split supermanifolds can be computed through the associated Quillen superconnections.
Automorphisms of the semigroup of endomorphisms of free associative algebras
2005
Let $A=A(x_{1},...,x_{n})$ be a free associative algebra in $\mathcal{A}$ freely generated over $K$ by a set $X=\{x_{1},...,x_{n}\}$, $End A$ be the semigroup of endomorphisms of $A$, and $Aut End A$ be the group of automorphisms of the semigroup $End A$. We investigate the structure of the groups $Aut End A$ and $Aut \mathcal{A}^{\circ}$, where $\mathcal{A}^{\circ}$ is the category of finitely generated free algebras from $\mathcal{A}$. We prove that the group $Aut End A$ is generated by semi-inner and mirror automorphisms of $End F$ and the group $Aut \mathcal{A}^{\circ}$ is generated by semi-inner and mirror automorphisms of the category $\mathcal{A}^{\circ}$. This result solves an open …
Spectroscopy of 253No and its daughters
2011
Abstract New high-statistics data have been obtained on the decay properties of 253 No and its daughters using the reaction 207 Pb( 48 Ca, 2n) 253 No. This was made possible thanks to an improved transmission of fusion–evaporation residues through the VASSILISSA recoil separator and an increased efficiency of the GABRIELA detector setup. The decay schemes of 253 No and 249 Fm have been revisited. The known level scheme of 249 Fm has been confirmed, including a new level at 669 keV excitation energy. The observation of L X-rays in coincidence with the α decay of 249 Fm gives additional support to the ground-state configuration of 1 / 2 + [ 631 ] instead of 5 / 2 + [ 622 ] for 245 Cf. In both…
Controversial roles of methylenetetrahydrofolate reductase polymorphisms and folate in breast cancer disease
2014
Abstract Breast cancer (BC) represents a highly heterogeneous tumour at both the clinical and molecular levels. Single-nucleotide polymorphisms (SNPs) of the folate-metabolising enzyme methylenetetrahydrofolate-reductase (MTHFR) may modify the association between folate intake and BC and influence plasma folate concentration. The role of folate in BC is equivocal, association studies between the common MTHFR SNPs C677T and A1298C and BC risk are controversial. In this study, I have reviewed observed associations between folate intake, as well as its blood levels, and BC. The purpose of this review is to analyse the role of folate and the two SNPs associated with reduced enzyme activity in B…
Consistent large-scale shell-model analysis of the two-neutrino ββ and single β branchings in 48Ca and 96Zr
2020
Abstract Two-neutrino double-beta-decay matrix elements M 2 ν and single beta-decay branching ratios were calculated for 48Ca and 96Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For 48Ca the matrix element M 2 ν = 0.0511 is obtained, which is 5.5% smaller than the previously reported value of 0.0539. For 96Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value M 2 ν = 0.0747 with extreme single-state dominance. These matrix elements, combined with the available ββ-decay half-life data, yield effective values of the weak axial coupling which in turn are u…
Monads in double categories
2010
We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and define what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.
Existence of common zeros for commuting vector fields on 3‐manifolds II. Solving global difficulties
2020
We address the following conjecture about the existence of common zeros for commuting vector fields in dimension three: if $X,Y$ are two $C^1$ commuting vector fields on a $3$-manifold $M$, and $U$ is a relatively compact open such that $X$ does not vanish on the boundary of $U$ and has a non vanishing Poincar\'e-Hopf index in $U$, then $X$ and $Y$ have a common zero inside $U$. We prove this conjecture when $X$ and $Y$ are of class $C^3$ and every periodic orbit of $Y$ along which $X$ and $Y$ are collinear is partially hyperbolic. We also prove the conjecture, still in the $C^3$ setting, assuming that the flow $Y$ leaves invariant a transverse plane field. These results shed new light on t…
Set-valued Brownian motion
2015
Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach space $X$. The present paper is an application of one the paper of the second author in which an embedding result is obtained which considers also the ordered structure of $ck(X)$ and f-algebras.
Singularities of lightlike hypersurfaces in Minkowski four-space
2006
We classify singularities of lightlike hypersurfaces in Minkowski 4-space via the contact invariants for the corresponding spacelike surfaces and lightcones.
The horospherical Gauss-Bonnet type theorem in hyperbolic space
2006
We introduce the notion horospherical curvatures of hypersurfaces in hyperbolic space and show that totally umbilic hypersurfaces with vanishing cur- vatures are only horospheres. We also show that the Gauss-Bonnet type theorem holds for the horospherical Gauss-Kronecker curvature of a closed orientable even dimensional hypersurface in hyperbolic space. + (i1) by using the model in Minkowski space. We introduced the notion of hyperbolic Gauss indicatrices slightly modified the definition of hyperbolic Gauss maps. The notion of hyperbolic indicatrices is independent of the choice of the model of hyperbolic space. Using the hyperbolic Gauss indicatrix, we defined the principal hyperbolic curv…