1,088 research outputs found
The double Ringel-Hall algebra on a hereditary abelian finitary length category
In this paper, we study the category of semi-stable
coherent sheaves of a fixed slope over a weighted projective curve. This
category has nice properties: it is a hereditary abelian finitary length
category. We will define the Ringel-Hall algebra of and
relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type
theorem to describe the indecomposable objects in this category, i.e. the
indecomposable semi-stable sheaves.Comment: 29 page
Deep levels in a-plane, high Mg-content MgxZn1-xO epitaxial layers grown by molecular beam epitaxy
Deep level defects in n-type unintentionally doped a-plane MgxZn1−xO, grown by molecular beam epitaxy on r-plane sapphire were fully characterized using deep level optical spectroscopy (DLOS) and related methods. Four compositions of MgxZn1−xO were examined with x = 0.31, 0.44, 0.52, and 0.56 together with a control ZnO sample. DLOS measurements revealed the presence of five deep levels in each Mg-containing sample, having energy levels of Ec − 1.4 eV, 2.1 eV, 2.6 V, and Ev + 0.3 eV and 0.6 eV. For all Mg compositions, the activation energies of the first three states were constant with respect to the conduction band edge, whereas the latter two revealed constant activation energies with respect to the valence band edge. In contrast to the ternary materials, only three levels, at Ec − 2.1 eV, Ev + 0.3 eV, and 0.6 eV, were observed for the ZnO control sample in this systematically grown series of samples. Substantially higher concentrations of the deep levels at Ev + 0.3 eV and Ec − 2.1 eV were observed in ZnO compared to the Mg alloyed samples. Moreover, there is a general invariance of trap concentration of the Ev + 0.3 eV and 0.6 eV levels on Mg content, while at least and order of magnitude dependency of the Ec − 1.4 eV and Ec − 2.6 eV levels in Mg alloyed samples
Quantum groups and double quiver algebras
For a finite dimensional semisimple Lie algebra and a root
of unity in a field we associate to these data a double quiver
It is shown that a restricted version of the quantized
enveloping algebras is a quotient of the double quiver algebra
Comment: 15 page
Notes on two-parameter quantum groups, (I)
A simpler definition for a class of two-parameter quantum groups associated
to semisimple Lie algebras is given in terms of Euler form. Their positive
parts turn out to be 2-cocycle deformations of each other under some
conditions. An operator realization of the positive part is given.Comment: 11 page
Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time
Thomassen characterized some 1-plane embedding as the forbidden configuration
such that a given 1-plane embedding of a graph is drawable in straight-lines if
and only if it does not contain the configuration [C. Thomassen, Rectilinear
drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988].
In this paper, we characterize some 1-plane embedding as the forbidden
configuration such that a given 1-plane embedding of a graph can be re-embedded
into a straight-line drawable 1-plane embedding of the same graph if and only
if it does not contain the configuration. Re-embedding of a 1-plane embedding
preserves the same set of pairs of crossing edges.
We give a linear-time algorithm for finding a straight-line drawable 1-plane
re-embedding or the forbidden configuration.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016). This is an extended
abstract. For a full version of this paper, see Hong S-H, Nagamochi H.:
Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time,
Technical Report TR 2016-002, Department of Applied Mathematics and Physics,
Kyoto University (2016
Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
We study the following classes of beyond-planar graphs: 1-planar, IC-planar,
and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar,
and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every
edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs
of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two
pairs of crossing edges share two vertices. We study the relations of these
beyond-planar graph classes (beyond-planar graphs is a collective term for the
primary attempts to generalize the planar graphs) to right-angle crossing (RAC)
graphs that admit compact drawings on the grid with few bends. We present four
drawing algorithms that preserve the given embeddings. First, we show that
every -vertex NIC-planar graph admits a NIC-planar RAC drawing with at most
one bend per edge on a grid of size . Then, we show that
every -vertex 1-planar graph admits a 1-planar RAC drawing with at most two
bends per edge on a grid of size . Finally, we make two
known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at
most one bend per edge and for drawing IC-planar RAC graphs straight-line
Exploring complex networks via topological embedding on surfaces
We demonstrate that graphs embedded on surfaces are a powerful and practical
tool to generate, characterize and simulate networks with a broad range of
properties. Remarkably, the study of topologically embedded graphs is
non-restrictive because any network can be embedded on a surface with
sufficiently high genus. The local properties of the network are affected by
the surface genus which, for example, produces significant changes in the
degree distribution and in the clustering coefficient. The global properties of
the graph are also strongly affected by the surface genus which is constraining
the degree of interwoveness, changing the scaling properties from
large-world-kind (small genus) to small- and ultra-small-world-kind (large
genus). Two elementary moves allow the exploration of all networks embeddable
on a given surface and naturally introduce a tool to develop a statistical
mechanics description. Within such a framework, we study the properties of
topologically-embedded graphs at high and low `temperatures' observing the
formation of increasingly regular structures by cooling the system. We show
that the cooling dynamics is strongly affected by the surface genus with the
manifestation of a glassy-like freezing transitions occurring when the amount
of topological disorder is low.Comment: 18 pages, 7 figure
Stability conditions and Stokes factors
Let A be the category of modules over a complex, finite-dimensional algebra.
We show that the space of stability conditions on A parametrises an
isomonodromic family of irregular connections on P^1 with values in the Hall
algebra of A. The residues of these connections are given by the holomorphic
generating function for counting invariants in A constructed by D. Joyce.Comment: Very minor changes. Final version. To appear in Inventione
Molecular basis of RNA polymerase III transcription repression by Maf1
RNA polymerase III (Pol III) transcribes short RNAs required for cell growth. Under stress conditions, the conserved protein Maf1 rapidly represses Pol III transcription. We report the crystal structure of Maf1 and cryo-electron microscopic structures of Pol III, an active Pol III-DNA-RNA complex, and a repressive Pol III-Maf1 complex. Binding of DNA and RNA causes ordering of the Pol III-specific subcomplex C82/34/31 that is required for transcription initiation. Maf1 binds the Pol III clamp and rearranges C82/34/31 at the rim of the active center cleft. This impairs recruitment of Pol III to a complex of promoter DNA with the initiation factors Brf1 and TBP and thus prevents closed complex formation. Maf1 does however not impair binding of a DNA-RNA scaffold and RNA synthesis. These results explain how Maf1 specifically represses transcription initiation from Pol III promoters and indicate that Maf1 also prevents reinitiation by binding Pol III during transcription elongation
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