2,149 research outputs found
Post-critical set and non existence of preserved meromorphic two-forms
We present a family of birational transformations in depending on
two, or three, parameters which does not, generically, preserve meromorphic
two-forms. With the introduction of the orbit of the critical set (vanishing
condition of the Jacobian), also called ``post-critical set'', we get some new
structures, some "non-analytic" two-form which reduce to meromorphic two-forms
for particular subvarieties in the parameter space. On these subvarieties, the
iterates of the critical set have a polynomial growth in the \emph{degrees of
the parameters}, while one has an exponential growth out of these subspaces.
The analysis of our birational transformation in is first carried out
using Diller-Favre criterion in order to find the complexity reduction of the
mapping. The integrable cases are found. The identification between the
complexity growth and the topological entropy is, one more time, verified. We
perform plots of the post-critical set, as well as calculations of Lyapunov
exponents for many orbits, confirming that generically no meromorphic two-form
can be preserved for this mapping. These birational transformations in ,
which, generically, do not preserve any meromorphic two-form, are extremely
similar to other birational transformations we previously studied, which do
preserve meromorphic two-forms. We note that these two sets of birational
transformations exhibit totally similar results as far as topological
complexity is concerned, but drastically different results as far as a more
``probabilistic'' approach of dynamical systems is concerned (Lyapunov
exponents). With these examples we see that the existence of a preserved
meromorphic two-form explains most of the (numerical) discrepancy between the
topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure
Nowhere minimal CR submanifolds and Levi-flat hypersurfaces
A local uniqueness property of holomorphic functions on real-analytic nowhere
minimal CR submanifolds of higher codimension is investigated. A sufficient
condition called almost minimality is given and studied. A weaker necessary
condition, being contained a possibly singular real-analytic Levi-flat
hypersurface is studied and characterized. This question is completely resolved
for algebraic submanifolds of codimension 2 and a sufficient condition for
noncontainment is given for non algebraic submanifolds. As a consequence, an
example of a submanifold of codimension 2, not biholomorphically equivalent to
an algebraic one, is given. We also investigate the structure of singularities
of Levi-flat hypersurfaces.Comment: 21 pages; conjecture 2.8 was removed in proof; to appear in J. Geom.
Ana
Convergence and multiplicities for the Lempert function
Given a domain , the Lempert function is a
functional on the space Hol (\D,\Omega) of analytic disks with values in
, depending on a set of poles in . We generalize its definition
to the case where poles have multiplicities given by local indicators (in the
sense of Rashkovskii's work) to obtain a function which still dominates the
corresponding Green function, behaves relatively well under limits, and is
monotonic with respect to the indicators. In particular, this is an improvement
over the previous generalization used by the same authors to find an example of
a set of poles in the bidisk so that the (usual) Green and Lempert functions
differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for
Matemati
Discovery of Anion Insertion Electrochemistry in Layered Hydroxide Nanomaterials
Electrode materials which undergo anion insertion are a void in the materials innovation landscape and a missing link to energy efficient electrochemical desalination. In recent years layered hydroxides (LHs) have been studied for a range of electrochemical applications, but to date have not been considered as electrode materials for anion insertion electrochemistry. Here, we show reversible anion insertion in a LH for the first time using Co and Co-V layer hydroxides. By pairing in situ synchrotron and quartz crystal microbalance measurements with a computational unified electrochemical band-diagram description, we reveal a previously undescribed anion-insertion mechanism occurring in Co and Co-V LHs. This proof of concept study demonstrates reversible electrochemical anion insertion in LHs without significant material optimization. These results coupled with our foundational understanding of anion insertion electrochemistry establishes LHs as a materials platform for anion insertion electrochemistry with the potential for future application to electrochemical desalination
Consistency Conditions on S-Matrix of Spin 1 Massless Particles
Motivated by new techniques in the computation of scattering amplitudes of
massless particles in four dimensions, like BCFW recursion relations, the
question of how much structure of the S-matrix can be determined from purely
S-matrix arguments has received new attention. The BCFW recursion relations for
massless particles of spin 1 and 2 imply that the whole tree-level S-matrix can
be determined in terms of three-particle amplitudes (evaluated at complex
momenta). However, the known proofs of the validity of the relations rely on
the Lagrangian of the theory, either by using Feynman diagrams explicitly or by
studying the effective theory at large complex momenta. This means that a
purely S-matrix theoretic proof of the relations is still missing. The aim of
this paper is to provide such a proof for spin 1 particles by extending the
four-particle test introduced by P. Benincasa and F. Cachazo in
arXiv:0705.4305[hep-th] to all particles. We show how n-particle tests imply
that the rational function built from the BCFW recursion relations possesses
all the correct factorization channels including holomorphic and
anti-holomorphic collinear limits. This in turn implies that they give the
correct S-matrix of the theory.Comment: 24 pages, 4 figure
Detection of chromosomal inversions using non-repetitive nucleic acid probes
A method for the identification of chromosomal inversions is described. Single-stranded sister chromatids are generated, for example by CO-FISH. A plurality of non-repetitive, labeled probes of relatively small size are hybridized to portions of only one of a pair of single-stranded sister chromatids. If no inversion exists, all of the probes will hybridize to a first chromatid. If an inversion has occurred, these marker probes will be detected on the sister chromatid at the same location as the inversion on the first chromatid
Multiscale analysis of the randomization limits of the chromosomal gene organization between Lepidoptera and Diptera
How chromosome gene organization and gene content evolve among distantly related and structurally malleable genomes remains unresolved. This is particularly the case when considering different insect orders. We have compared the highly contiguous genome assemblies of the lepidopteran Danaus plexippus and the dipteran Drosophila melanogaster, which shared a common ancestor around 290 Ma. The gene content of 23 out of 30 D. plexippus chromosomes was significantly associated with one or two of the six chromosomal elements of the Drosophila genome, denoting common ancestry. Despite the phylogenetic distance, 9.6% of the 1-to-1 orthologues still reside within the same ancestral genome neighbourhood. Furthermore, the comparison D. plexippusâBombyx mori indicated that the rates of chromosome repatterning are lower in Lepidoptera than in Diptera, although still within the same order of magnitude. Concordantly, 14 developmental gene clusters showed a higher tendency to retain full or partial clustering in D. plexippus, further supporting that the physical association between the SuperHox and NK clusters existed in the ancestral bilaterian. Our results illuminate the scope and limits of the evolution of the gene organization and content of the ancestral chromosomes to the Lepidoptera and Diptera while helping reconstruct portions of the genome in their most recent common ancestor
Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds
We consider the dynamics of meromorphic maps of compact K\"ahler manifolds.
In this work, our goal is to locate the non-nef locus of invariant classes and
provide necessary and sufficient conditions for existence of Green currents in
codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and
Theorem 5.3 are adde
Detection of Chromosomal Inversions Using Non-Repetitive Nucleic Acid Probes
A method and a kit for the identification of chromosomal inversions are described. Single-stranded sister chromatids are generated, for example by CO-FISH. A plurality of non-repetitive, labeled probes of relatively small size are hybridized to portions of only one of a pair of single-stranded sister chromatids. If no inversion exists, all of the probes will hybridize to a first chromatid. If an inversion has occurred, these marker probes will be detected on the sister chromatid at the same location as the inversion on the first chromatid
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