257 research outputs found
The -rational -Catalan polynomials for and their -symmetry
We introduce a new statistic, skip, on rational -Dyck paths and define
a marked rank word for each path when is not a multiple of 3. If a triple
of valid statistics (area,skip,dinv) are given, we have an algorithm to
construct the marked rank word corresponding to the triple. By considering all
valid triples we give an explicit formula for the -rational
-Catalan polynomials when . Then there is a natural bijection on the
triples of statistics (area,skips,dinv) which exchanges the statistics area and
dinv while fixing the skip. Thus we prove the -symmetry of
-rational -Catalan polynomials for .Comment: 11 pages, 4 figure
Rational Convolution Roots of Isobaric Polynomials
In this paper, we exhibit two matrix representations of the rational roots of
generalized Fibonacci polynomials (GFPs) under convolution product, in terms of
determinants and permanents, respectively. The underlying root formulas for
GFPs and for weighted isobaric polynomials (WIPs), which appeared in an earlier
paper by MacHenry and Tudose, make use of two types of operators. These
operators are derived from the generating functions for Stirling numbers of the
first kind and second kind. Hence we call them Stirling operators. To construct
matrix representations of the roots of GFPs, we use the Stirling operators of
the first kind. We give explicit examples to show how the Stirling operators of
the second kind appear in the low degree cases for the WIP-roots. As a
consequence of the matrix construction, we have matrix representations of
multiplicative arithmetic functions under the Dirichlet product into its
divisible closure.Comment: 13 page
DNA Methylation Changes in Response to Sulfur Dioxide Stress in Arabidopsis Plants
AbstractSulfur dioxide (SO2) exposure causes alterations of DNA cytosine methylation in Arabidopsis genome. Analysis of methylation-sensitive amplified polymorphism (MSAP) revealed that SO2 induced methylation changes of cytosine in CCGG sites, in which hypermethylation is more than hypomethylation. Bisulļ¬te sequencing showed that the methyaltion levels of cytosine in promoter regions of Arabidopsis genes encoding 1-aminocyclopropane-1-carboxylic acid synthase 6 and nitrilase 2 decreased accompanying with enhanced transcript levels. The global genome hypermethylation and locus-specific hypomethylation in Arabidopsis cells, which contribute to genome stability and gene regulation, can be considered as a very important regulatory mechanism for plants adaption to environmental stress
Theoretical Analysis of āEco-Manā in Sight of Ecological Civilization
The emergence of a new sort of civilizationāecological civilization, is definitely becoming the historical inevitability symbolizing that human beings have stepped into the era of ecological civilization. As a totally brand new type of civilization, ecological civilization is also in need of a new subject carrierāeco-man. Consequently, the development of ecological civilization is accelerating the establishment of the new type eco-man with personality model. This paper defines the concept and characteristics of āeco-manā. The settlement of āeco-manā theory has significant theoretical importance and practical meaning, and itās especially important and urgent to establish āeco-manā in face of current situation
A dual approach to structure constants for K-theory of Grassmannians
International audienceThe problem of computing products of Schubert classes in the cohomology ring can be formulated as theproblem of expanding skew Schur polynomial into the basis of ordinary Schur polynomials. We reformulate theproblem of computing the structure constants of the Grothendieck ring of a Grassmannian variety with respect to itsbasis of Schubert structure sheaves in a similar way; we address the problem of expanding the generating functions forskew reverse-plane partitions into the basis of polynomials which are Hall-dual to stable Grothendieck polynomials. From this point of view, we produce a chain of bijections leading to Buchās K-theoretic Littlewood-Richardson rule
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Feasibility study for downscaling seasonal tropical cyclone activity using the NCEP regional spectral model
The potential use of the National Centers for Environmental Prediction (NCEP) Regional Spectral Model (RSM) for downscaling seasonal tropical cyclone (TC) activity was analyzed here. The NCEP RSM with horizontal resolution of 50 km, was used to downscale the ECHAM4.5 Atmospheric General Circulation Model (AGCM) simulations forced with observed sea surface temperature (SST) over the western North Pacific. An ensemble of ten runs for JuneāNovember 1994 and 1998 was studied. The representation of the TCs is much improved compared to the low-resolution forcing AGCM, but the TCs are not as intense as observed ones, as the RSM horizontal resolution is not sufficiently high. The large-scale fields of the RSM are examined and compared to both the AGCM and the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis. The large-scale fields of RSM characteristics are in general similar to those of the reanalysis. Various properties of the TCs in the RSM are also examined such as first positions, tracks, accumulated cyclone energy (ACE) and duration. While the RSM does not reproduce the higher number of TCs in 1994 than in 1998, other measures of TC activity (ACE, number of cyclone days) in the RSM are higher in 1994 than in 1998
Hopf algebra of labeled simple graphs arising from super-shuffle product
From the connections between permutations and labeled simple graphs, we generalized the super-shuffle product and the cut-box coproduct on permutations to labeled simple graphs. We then proved that the vector space spanned by labeled simple graphs is a Hopf algebra with these two operations
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