Estimates of Z'couplings within data on the A_{FB} for Drell-Yan process at the LHC at s^(1/2) = 7 TeV and 8 TeV

Model-independent search for the Abelian Z' gauge boson in the Drell-Yan process at the LHC at s^{1/2}= 7 TeV and 8 TeV is fulfilled. Estimations of the Z' axial-vector coupling a_f^2 to the standard model fermions, the couplings of the axial-vector to lepton vector currents a_f v_l and the couplings of the axial-vector to quark vector currents a_f v_q are derived within data on the forward-backward asymmetry presented by the CMS Collaboration. The analysis takes into consideration the behaviour of the differential cross-section which exhibits itself if the derived already special relations between the couplings proper to the renormalizable theories are accounted for. In particular, they hold in all the models of Abelian Z' usually considered in the model-dependent analysis of the LHC data. The coupling values are estimated at ~ 92 % CL by means of the maximum likelihood function. They weakly depend on the Z' mass in the investigated interval 1.2 TeV < m_Z' < 5 TeV. Taking into account the dependence of Z-Z' mixing angle theta_0 on m_Z' and the LEP constraints |theta_0|~ 10^{-3}-10^{-4}, the optimistic limits on m_{Z'} are established as 3 < m_Z' < 7-8 TeV. Comparison with the results of other authors is given.Comment: 8 pages, 9 figures, 2 table, 27 reference

Differential symmetry breaking operators I : General theory and F-method

International audienceWe prove a one-to-one correspondence between differential symmetry breaking operators for equivariant vector bundles over two homogeneous spaces and certain homomorphisms for representations of two Lie algebras, in connection with branching problems of the restriction of representations. We develop a new method (F-method) based on the algebraic Fourier transform for generalized Verma modules, which characterizes differential symmetry breaking operators by means of certain systems of partial differential equations. In contrast to the setting of real flag varieties, continuous symmetry breaking operators of Hermitian symmetric spaces are proved to be differential operators in the holomorphic setting. In this case symmetry breaking operators are characterized by differential equations of second order via the F-method

Conformal symmetry breaking operators for differential forms on spheres

We give a complete classification of conformally covariant differential operators between the spaces of $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$. Moreover, we find explicit formul{\ae} for these new matrix-valued operators in the flat coordinates in terms of basic operators in differential geometry and classical orthogonal polynomials. We also establish matrix-valued factorization identities among all possible combinations of conformally covariant differential operators. The main machinery of the proof is the "F-method" based on the "algebraic Fourier transform of Verma modules" (Kobayashi-Pevzner [Selecta Math. 2016]) and its extension to matrix-valued case developed here. A short summary of the main results was announced in [C. R. Acad. Sci. Paris, 2016]

On a Speculated Relation Between Chv\'atal-Sankoff Constants of Several Sequences

It is well known that, when normalized by n, the expected length of a longest common subsequence of d sequences of length n over an alphabet of size sigma converges to a constant gamma_{sigma,d}. We disprove a speculation by Steele regarding a possible relation between gamma_{2,d} and gamma_{2,2}. In order to do that we also obtain new lower bounds for gamma_{sigma,d}, when both sigma and d are small integers.Comment: 13 pages. To appear in Combinatorics, Probability and Computin

RNA content in motor and sensory neurons and surrounding neuroglia of mouse spinal cord under conditions of hypodynamia and following normalization

The differences in the dynamics of reparative processes in RNA metabolism within the neuron-neuroglia unit after the cessation of hyper- and hypodynamia is dicussed. The role of neuroglia is stressed in compensatory, reparative and trophic processes in the nervous system as well as the possibility in an adaptation at the cellular level

RNA content in motor and sensory neurons and surrounding neuroglia of mouse spinal cord under conditions of hypodynamia and following normalization

Male white mice were subjected to two and three week hypodynamia and then decapitated. Cytoplasmic RNA content per cell was measured by means of ultraviolet cytospectrometry. Changes in RNA content are shown, and the dynamics of the reparative processes of cells are discussed