6,687 research outputs found
Dimensions of fractals related to languages defined by tagged strings in complete genomes
A representation of frequency of strings of length K in complete genomes of
many organisms in a square has led to seemingly self-similar patterns when K
increases. These patterns are caused by under-represented strings with a
certain "tag"-string and they define some fractals when K tends to infinite.
The Box and Hausdorff dimensions of the limit set are discussed. Although the
method proposed by Mauldin and Williams to calculate Box and Hausdorff
dimension is valid in our case, a different and simpler method is proposed in
this paper.Comment: 9 pages with two figure
Quantitative K-theory, positive scalar curvature, and band width
We develop two connections between the quantitative framework of operator
-theory for geometric -algebras and the problem of positive scalar
curvature. First, we introduce a quantitative notion of higher index and use it
to give a refinement of the well-known obstruction of Rosenberg to positive
scalar curvature on closed spin manifolds coming from the higher index of the
Dirac operator. We show that on a manifold with uniformly positive scalar
curvature, the propagation at which the index of the Dirac operator vanishes is
related inversely to the curvature lower bound. Second, we give an approach,
using related techniques, to Gromov's band width conjecture, which has been the
subject of recent work by Zeidler and Cecchini from a different point of view.Comment: 30 page
Scalable Preparation of SrTiO3 Submicro-wires from Layered Titanate Nanowires
AbstractSrTiO3 submicro-wires were prepared by the reaction of layered titanate nanowires with Sr (OH)2 powder in an autoclave. The wires were investigated using X-ray diffraction (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), Ultra-violet visible (UV-vis), photoluminescence (PL) and Raman spectroscopy. The XRD measurement shows that the prepared SrTiO3 submicro-wires hardly have impurity phases. The SEM and TEM images demonstrate that the scalable wires, which need to be processed at the reaction temperature of 180 °C for about 48 hours, are not composed of single crystals. The PL shows that the wire-like SrTiO3 has emission peaks at the wavelengths of 568 and 585 nm. Further, the Raman spectroscopy reveals structural changes in the products through different reaction time
Single Inclusive Jet Production in Collisions at NLO in the small- regime
We present the first complete NLO prediction with full jet algorithm
implementation for the single inclusive jet production in collisions
within the CGC effective theory. Our prediction is fully differential over the
final state physical kinematics, which allows the implementation of any IR safe
observable including the jet clustering procedure. The NLO calculation is
organized with the aid of the power counting proposed in [1] which gives rise
to the novel soft contributions in the CGC factorization. We achieve the
fully-differential calculation by constructing suitable subtraction terms to
handle the singularities in the real corrections. The subtraction contributions
can be exactly integrated analytically. We present the NLO cross section with
the jets constructed using the anti- algorithm. The NLO calculation
demonstrates explicitly the validity of the CGC factorization in jet
production. Furthermore, as a byproduct of the subtraction method, we also
derive the fully analytic cross section for the forward jet production in the
small- limit. We show that in the small- approximation, the forward jet
cross section can be factorized into a semi-hard cross section that produces a
parton and the semi-inclusive jet functions. We argue that this feature holds
for generic jet production and jet substructure observables in the CGC
framework. Last, we show numerical analyses of the derived formula to validate
our calculations. We justify when the small- approximation is appropriate.
Like forward hadron production, the obtained NLO result also exhibits the
negativity of the cross section in the large jet transverse regime, which
signals the need for the threshold resummation. A sketch of the threshold
resummation in the CGC framework is presented based on the multiple emission
picture.Comment: 67 pages, multiple figures, comments welcome, reference update
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