Hereditary approximation property

Abstract If X is a Banach space such that the isomorphism constant to n 2 from n-dimensional subspaces grows sufficiently slowly as n → ∞, then X has the approximation property. A consequence of this is that there is a Banach space X with a symmetric basis but not isomorphic to 2 so that all subspaces of X have the approximation property. This answers a problem raised in 1980. An application of the main result is that there is a separable Banach space X that is not isomorphic to a Hilbert space, yet every subspace of X is isomorphic to a complemented subspace of X. This contrasts with the classical result of Lindenstrauss and Tzafriri that a Banach space in which every closed subspace is complemented must be isomorphic to a Hilbert space

Genericity of Fr\'echet smooth spaces

If a separable Banach space contains an isometric copy of every separable reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach spaces with Fr\'echet smooth dual space. This improves a result of G. Godefroy and N. J. Kalton.Comment: 34 page

Performance and long-term stability of the barley hordothionin gene in multiple transgenic apple lines

Introduction of sustainable scab resistance in elite apple cultivars is of high importance for apple cultivation when aiming at reducing the use of chemical crop protectants. Genetic modification (GM) allows the rapid introduction of resistance genes directly into high quality apple cultivars. Resistance genes can be derived from apple itself but genetic modification also opens up the possibility to use other, non-host resistance genes. A prerequisite for application is the long-term performance and stability of the gene annex trait in the field. For this study, we produced and selected a series of transgenic apple lines of two cultivars, i.e. ‘Elstar’ and ‘Gala’ in which the barley hordothionin gene (hth) was introduced. After multiplication, the GM hth-lines, non-GM susceptible and resistant controls and GM non-hth controls were planted in a random block design in a field trial in 40 replicates. Scab resistance was monitored after artificial inoculation (first year) and after natural infection (subsequent years). After the trial period, the level of expression of the hth gene was checked by quantitative RT-PCR. Four of the six GM hth apple lines proved to be significantly less susceptible to apple scab and this trait was found to be stable for the entire 4-year period. Hth expression at the mRNA level was also stable

Functional analysis and expression profiling of HcrVf1 and HcrVf2 for development of scab resistant cisgenic and intragenic apples

Apple scab resistance genes, HcrVf1 and HcrVf2, were isolated including their native promoter, coding and terminator sequences. Two fragment lengths (short and long) of the native gene promoters and the strong apple rubisco gene promoter (PMdRbc) were used for both HcrVf genes to test their effect on expression and phenotype. The scab susceptible cultivar ‘Gala’ was used for plant transformations and after selection of transformants, they were micrografted onto apple seedling rootstocks for scab disease tests. Apple transformants were also tested for HcrVf expression by quantitative RT-PCR (qRT-PCR). For HcrVf1 the long native promoter gave significantly higher expression that the short one; in case of HcrVf2 the difference between the two was not significant. The apple rubisco gene promoter proved to give the highest expression of both HcrVf1 and HcrVf2. The top four expanding leaves were used initially for inoculation with monoconidial isolate EU-B05 which belongs to race 1 of V. inaequalis. Later six other V. inaequalis isolates were used to study the resistance spectra of the individual HcrVf genes. The scab disease assays showed that HcrVf1 did not give resistance against any of the isolates tested regardless of the expression level. The HcrVf2 gene appeared to be the only functional gene for resistance against Vf avirulent isolates of V. inaequalis. HcrVf2 did not provide any resistance to Vf virulent strains, even not in case of overexpression. In conclusion, transformants carrying the apple-derived HcrVf2 gene in a cisgenic as well as in an intragenic configuration were able to reach scab resistance levels comparable to the Vf resistant control cultivar obtained by classical breeding, cv. ‘Santana’

Self-consistent field theory of polarized BEC: dispersion of collective excitation

We suggest the construction of a set of the quantum hydrodynamics equations for the Bose-Einstein condensate (BEC), where atoms have the electric dipole moment. The contribution of the dipole-dipole interactions (DDI) to the Euler equation is obtained. Quantum equations for the evolution of medium polarization are derived. Developing mathematical method allows to study effect of interactions on the evolution of polarization. The developing method can be applied to various physical systems in which dynamics is affected by the DDI. Derivation of Gross-Pitaevskii equation for polarized particles from the quantum hydrodynamics is described. We showed that the Gross-Pitaevskii equation appears at condition when all dipoles have the same direction which does not change in time. Comparison of the equation of the electric dipole evolution with the equation of the magnetization evolution is described. Dispersion of the collective excitations in the dipolar BEC, either affected or not affected by the uniform external electric field, is considered using our method. We show that the evolution of polarization in the BEC leads to the formation of a novel type of the collective excitations. Detailed description of the dispersion of collective excitations is presented. We also consider the process of wave generation in the polarized BEC by means of a monoenergetic beam of neutral polarized particles. We compute the possibilities of the generation of Bogoliubov and polarization modes by the dipole beam.Comment: 16 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1106.082