27 research outputs found
Zero Order Estimates for Analytic Functions
The primary goal of this paper is to provide a general multiplicity estimate.
Our main theorem allows to reduce a proof of multiplicity lemma to the study of
ideals stable under some appropriate transformation of a polynomial ring. In
particular, this result leads to a new link between the theory of polarized
algebraic dynamical systems and transcendental number theory. On the other
hand, it allows to establish an improvement of Nesterenko's conditional result
on solutions of systems of differential equations. We also deduce, under some
condition on stable varieties, the optimal multiplicity estimate in the case of
generalized Mahler's functional equations, previously studied by Mahler,
Nishioka, Topfer and others. Further, analyzing stable ideals we prove the
unconditional optimal result in the case of linear functional systems of
generalized Mahler's type. The latter result generalizes a famous theorem of
Nishioka (1986) previously conjectured by Mahler (1969), and simultaneously it
gives a counterpart in the case of functional systems for an important
unconditional result of Nesterenko (1977) concerning linear differential
systems. In summary, we provide a new universal tool for transcendental number
theory, applicable with fields of any characteristic. It opens the way to new
results on algebraic independence, as shown in Zorin (2010).Comment: 42 page
Exclusive Radiative B-Decays in the Light-Cone QCD Sum Rule Approach
We carry out a detailed study of exclusive radiative rare -decays in the
framework of the QCD sum rules on the light cone, which combines the
traditional QCD sum rule technique with the description of final state vector
mesons in terms of the light-cone wave functions of increasing twist. The
decays considered are: and the corresponding decays of the mesons, and . Based on our estimate of the transition
form factor F_1^{B \to K^*\pg}(0) =0.32\pm0.05, we find for the branching
ratio , which is in
agreement with the observed value measured by the CLEO collaboration. We
present detailed estimates for the ratios of the radiative decay form factors,
which are then used to predict the rates for the exclusive radiative B-decays
listed above. This in principle allows the extraction of the CKM matrix element
from the penguin-dominated CKM-suppressed radiative decays when they
are measured. We give a detailed discussion of the dependence of the form
factors on the -quark mass and on the momentum transfer, as well as their
interrelation with the CKM-suppressed semileptonic decay form factors in , which we also calculate in our approach.Comment: 32 pages, 10 uuencoded figures, LaTeX, preprint CERN-TH 7118/9
Pion and sigma meson properties in a relativistic quark model
A variety of strong and electroweak interaction properties of the pion and
the light scalar sigma meson are computed in a relativistic quark model. Under
the assumption that the resulting coupling of these mesons to the constituent
quarks is identical, the sigma meson mass is determined as M_sigma=385.4 MeV.
We discuss in detail the gauging of the non-local meson-quark interaction and
calculate the electromagnetic form factor of the pion and the form factors of
the pi(0) -> gamma gamma and sigma -> gamma gamma processes. We obtain explicit
expressions for the relevant form factors and evaluate the leading and
next-to-leading orders for large Euclidean photon virtualities. Turning to the
decay properties of the sigma we determine the width of the electromagnetic
sigma -> gamma gamma transition and discuss the strong decay sigma -> pi pi. In
a final step we compute the nonleptonic decays D -> sigma pi and B -> sigma pi
relevant for the possible observation of the sigma meson. All our results are
compared to available experimental data and to results of other theoretical
studies.Comment: 46 page
Identification of alleles of carotenoid pathway genes important for zeaxanthin accumulation in potato tubers
We have investigated the genetics and molecular biology of orange flesh colour in potato (Solanum tuberosum L.). To this end the natural diversity in three genes of the carotenoid pathway was assessed by SNP analyses. Association analysis was performed between SNP haplotypes and flesh colour phenotypes in diploid and tetraploid potato genotypes. We observed that among eleven beta-carotene hydroxylase 2 (Chy2) alleles only one dominant allele has a major effect, changing white into yellow flesh colour. In contrast, none of the lycopene epsilon cyclase (Lcye) alleles seemed to have a large effect on flesh colour. Analysis of zeaxanthin epoxidase (Zep) alleles showed that all (diploid) genotypes with orange tuber flesh were homozygous for one specific Zep allele. This Zep allele showed a reduced level of expression. The complete genomic sequence of the recessive Zep allele, including the promoter, was determined, and compared with the sequence of other Zep alleles. The most striking difference was the presence of a non-LTR retrotransposon sequence in intron 1 of the recessive Zep allele, which was absent in all other Zep alleles investigated. We hypothesise that the presence of this large sequence in intron 1 caused the lower expression level, resulting in reduced Zep activity and accumulation of zeaxanthin. Only genotypes combining presence of the dominant Chy2 allele with homozygosity for the recessive Zep allele produced orange-fleshed tubers that accumulated large amounts of zeaxanthin
Brane effective actions, kappa-symmetry and applications
This is a review on brane effective actions, their symmetries and some of their applications. Its first part covers the Green–Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects: the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry to achieve manifest spacetime covariance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds. Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as Bogomol’nyi–Prasad–Sommerfield (BPS) states carrying (topological) charges in the supersymmetry algebra and the connection between supersymmetry and Hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approximations to infer about the non-trivial dynamics of strongly-coupled gauge theories using the anti de Sitter/conformal field theory (AdS/CFT) correspondence. This includes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description. Its final part briefly discusses effective actions for N D-branes and M2-branes. This includes both Super-Yang-Mills theories, their higher-order corrections and partial results in covariantising these couplings to curved backgrounds, and the more recent supersymmetric Chern–Simons matter theories describing M2-branes using field theory, brane constructions and 3-algebra considerations
Key calculated variables in the AVF P1 in systole (upper row) and diastole (lower row).
The distributions of the velocity magnitude || (A), shear stress τ (B), cumulative shear stress CSS (C) and primed platelets Pa (D) are obtained at the highest parameter values ( = 725 mL/min, N = 100). The blue and red colours correspond to the lowest and highest variable values, respectively. The links for the supporting movies are available in S6 Text.</p