3,026 research outputs found
Lineability, spaceability, and additivity cardinals for Darboux-like functions
We introduce the concept of maximal lineability cardinal number, mL(M), of a subset M of a topological vector space and study its relation to the cardinal numbers known as: additivity A(M), homogeneous lineability HL(M), and lineability L(M) of M. In particular, we will describe, in terms of L, the lineability and spaceability of the families of the following Darboux-like functions on R-n, n >= 1: extendable, Jones, and almost continuous function
Chemical Synthesis at Surfaces with Atomic Precision: Taming Complexity and Perfection
Scanning probe microscopy (SPM) is a powerful tool to study the structure and dynamics of molecules at surfaces and interfaces as well as to precisely manipulate atoms and molecules by applying an external force, by inelastic electron tunneling, or by means of an electric field. The rapid development of these SPM manipulation modes made it possible to achieve fineâcontrol over fundamental processes in the physics of interfaces as well as chemical reactivity, such as adsorption, diffusion, bond formation, and bond dissociation with precision at the single atom/molecule level. Their controlled use for the fabrication of atomicâscale structures and synthesis of new, perhaps uncommon, molecules with programmed properties are reviewed. Opportunities and challenges towards the development of complex chemical systems are discussed, by analyzing potential future impacts in nanoscience and nanotechnology.journal articlereview2019 Dec 192019 11 28importe
An undecidable case of lineability in R^R
Recently it has been proved that, assuming that there is an almost disjoint
family of cardinality (2^{\mathfrak c}) in (\mathfrak c) (which is assured, for
instance, by either Martin's Axiom, or CH, or even 2^{<\mathfrak c=\mathfrak
c}) one has that the set of Sierpi\'nski-Zygmund functions is
(2^{\mathfrak{c}})-strongly algebrable (and, thus,
(2^{\mathfrak{c}})-lineable). Here we prove that these two statements are
actually equivalent and, moreover, they both are undecidable. This would be the
first time in which one encounters an undecidable proposition in the recently
coined theory of lineability.Comment: 5 page
Maximal -regularity for stochastic evolution equations
We prove maximal -regularity for the stochastic evolution equation
\{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t),
\qquad t\in [0,T],
U(0) & = u_0, {aligned}. under the assumption that is a sectorial
operator with a bounded -calculus of angle less than on
a space . The driving process is a cylindrical
Brownian motion in an abstract Hilbert space . For and
and initial conditions in the real interpolation space
\XAp we prove existence of unique strong solution with trajectories in
L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities
F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to
\g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their
second variables with small enough Lipschitz constants. Extensions to the case
where is an adapted operator-valued process are considered as well.
Various applications to stochastic partial differential equations are worked
out in detail. These include higher-order and time-dependent parabolic
equations and the Navier-Stokes equation on a smooth bounded domain
\OO\subseteq \R^d with . For the latter, the existence of a unique
strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi
Four-nucleon shell-model calculations in a Faddeev-like approach
We use equations for Faddeev amplitudes to solve the shell-model problem for
four nucleons in the model space that includes up to 14 hbar Omega
harmonic-oscillator excitations above the unperturbed ground state. Two- and
three-body effective interactions derived from the Reid93 and Argonne V8'
nucleon-nucleon potentials are used in the calculations. Binding energies,
excitations energies, point-nucleon radii and electromagnetic and strangeness
charge form factors for 4He are studied. The structure of the Faddeev-like
equations is discussed and a formula for matrix elements of the permutation
operators in a harmonic-oscillator basis is given. The dependence on
harmonic-oscillator excitations allowed in the model space and on the
harmonic-oscillator frequency is investigated. It is demonstrated that the use
of the three-body effective interactions improves the convergence of the
results.Comment: 22 pages, 13 figures, REVTe
Solutions of the Faddeev-Yakubovsky equations for the four nucleons scattering states
The Faddeev-Yakubowsky equations in configuration space have been solved for
the four nucleon system. The results with an S-wave interaction model in the
isospin approximation are presented. They concern the bound and scattering
states below the first three-body threshold. The elastic phase-shifts for the
N+NNN reaction in different () channels are given and the corresponding
low energy expansions are discussed. Particular attention is payed to the n+t
elastic cross section. Its resonant structure is well described in terms of a
simple NN interaction. First results concerning the S-matrix for the coupled
N+NNN-NN+NN channels and the strong deuteron-deuteron scattering length are
obtained.Comment: latex.tar.gz, 36 pages, 10 figures, 11 tables. To be published in
Physical Review
Structural rearrangements in the mitochondrial genome of Drosophila melanogaster induced by elevated levels of the replicative DNA helicase
Pathological conditions impairing functions of mitochondria often lead to compensatory upregulation of the mitochondrial DNA (mtDNA) replisome machinery, and the replicative DNA helicase appears to be a key factor in regulating mtDNA copy number. Moreover, mtDNA helicase mutations have been associated with structural rearrangements of themitochondrial genome. To evaluate the effects of elevated levels of the mtDNA helicase on the integrity and replication of the mitochondrial genome, we overexpressed the helicase in Drosophila melanogaster Schneider cells and analyzed the mtDNA by two-dimensional neutral agarose gel electrophoresis and electron microscopy. We found that elevation of mtDNA helicase levels increases the quantity of replication intermediates and alleviates pausing at the replication slow zones. Though we did not observe a concomitant alteration in mtDNA copy number, we observed deletions specific to the segment of repeated elements in the immediate vicinity of the origin of replication, and an accumulation of species characteristic of replication fork stalling. We also found elevated levels of RNA that are retained in the replication intermediates. Together, our results suggest that upregulation of mtDNA helicase promotes the process of mtDNA replication but also results in genome destabilization.Peer reviewe
Structure of boson systems beyond the mean-field
We investigate systems of identical bosons with the focus on two-body
correlations. We use the hyperspherical adiabatic method and a decomposition of
the wave function in two-body amplitudes. An analytic parametrization is used
for the adiabatic effective radial potential. We discuss the structure of a
condensate for arbitrary scattering length. Stability and time scales for
various decay processes are estimated. The previously predicted Efimov-like
states are found to be very narrow. We discuss the validity conditions and
formal connections between the zero- and finite-range mean-field
approximations, Faddeev-Yakubovskii formulation, Jastrow ansatz, and the
present method. We compare numerical results from present work with mean-field
calculations and discuss qualitatively the connection with measurements.Comment: 26 pages, 6 figures, submitted to J. Phys. B. Ver. 2 is 28 pages with
modified figures and discussion
The Price of WMAP Inflation in Supergravity
The three-year data from WMAP are in stunning agreement with the simplest
possible quadratic potential for chaotic inflation, as well as with new or
symmetry-breaking inflation. We investigate the possibilities for incorporating
these potentials within supergravity, particularly of the no-scale type that is
motivated by string theory. Models with inflation driven by the matter sector
may be constructed in no-scale supergravity, if the moduli are assumed to be
stabilised by some higher-scale dynamics and at the expense of some
fine-tuning. We discuss specific scenarios for stabilising the moduli via
either D- or F-terms in the effective potential, and survey possible
inflationary models in the presence of D-term stabilisation.Comment: 15 pages, 6 figures, plain Late
Total 4He Photoabsorption Cross Section Revisited: Correlated HH versus Effective Interaction HH
Two conceptually different hyperspherical harmonics expansions are used for
the calculation of the total 4He photoabsorption cross section. Besides the
well known method of CHH the recently introduced effective interaction approach
for the hyperspherical formalism is applied. Semi-realistic NN potentials are
employed and final state interaction is fully taken into account via the
Lorentz integral transform method. The results show that the effective
interaction leads to a very good convergence, while the correlation method
exhibits a less rapid convergence in the giant dipole resonance region. The
rather strong discrepancy with the experimental photodisintegration cross
sections is confirmed by the present calculations.Comment: LaTeX, 7 pages, 3 ps figure
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