12,144 research outputs found
A hierarchical research by large-scale and ab initio electronic structure theories -- Si and Ge cleavage and stepped (111)-2x1 surfaces --
The ab initio calculation with the density functional theory and plane-wave
bases is carried out for stepped Si(111)-2x1 surfaces that were predicted in a
cleavage simulation by the large-scale (order-N) electronic structure theory
(T. Hoshi, Y. Iguchi and T. Fujiwara, Phys. Rev. B72 (2005) 075323). The
present ab initio calculation confirms the predicted stepped structure and its
bias-dependent STM image. Moreover, two (meta)stable step-edge structures are
found and compared. The investigation is carried out also for Ge(111)-2x1
surfaces, so as to construct a common understanding among elements. The present
study demonstrates the general importance of the hierarchical research between
large-scale and ab initio electronic structure theories.Comment: 5 pages, 4 figures, to appear in Physica
On the simplest sextic fields and related Thue equations
We consider the parametric family of sextic Thue equations where
is an integer and is a divisor of . We
show that the only solutions to the equations are the trivial ones with
.Comment: 12 pages, 2 table
Accuracy control in ultra-large-scale electronic structure calculation
Numerical aspects are investigated in ultra-large-scale electronic structure
calculation. Accuracy control methods in process (molecular-dynamics)
calculation are focused. Flexible control methods are proposed so as to control
variational freedoms, automatically at each time step, within the framework of
generalized Wannier state theory. The method is demonstrated in silicon
cleavage simulation with 10^2-10^5 atoms. The idea is of general importance
among process calculations and is also used in Krylov subspace theory, another
large-scale-calculation theory.Comment: 8 pages, 3 figures. To appear in J.Phys. Condens. Matter. A preprint
PDF file in better graphics is available at
http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htm
Birational classification of fields of invariants for groups of order
Let be a finite group acting on the rational function field
by -automorphisms for
any . Noether's problem asks whether the invariant field
is rational (i.e. purely transcendental) over
. Saltman and Bogomolov, respectively, showed that for any prime
there exist groups of order and of order such that
is not rational over by showing the non-vanishing
of the unramified Brauer group: . For , Chu,
Hu, Kang and Prokhorov proved that if is a 2-group of order , then
is rational over . Chu, Hu, Kang and Kunyavskii
showed that if is of order 64, then is rational over
except for the groups belonging to the two isoclinism families
and . Bogomolov and B\"ohning's theorem claims that if
and belong to the same isoclinism family, then
and are stably -isomorphic. We investigate the
birational classification of for groups of order 128 with
. Moravec showed that there exist exactly 220
groups of order 128 with forming 11
isoclinism families . We show that if and belong to
or (resp. or ), then and
are stably -isomorphic with
. Explicit structures of non-rational
fields are given for each cases including also the case
with .Comment: 31 page
Large-scale electronic-structure theory and nanoscale defects formed in cleavage process of silicon
Several methods are constructed for large-scale electronic structure
calculations. Test calculations are carried out with up to 10^7 atoms. As an
application, cleavage process of silicon is investigated by molecular dynamics
simulation with 10-nm-scale systems. As well as the elementary formation
process of the (111)-(2 x 1) surface, we obtain nanoscale defects, that is,
step formation and bending of cleavage path into favorite (experimentally
observed) planes. These results are consistent to experiments. Moreover, the
simulation result predicts an explicit step structure on the cleaved surface,
which shows a bias-dependent STM image.Comment: 4 page 4 figures. A PDF file with better graphics is available at
http://fujimac.t.u-tokyo.ac.jp/lses
What Happened to Japanese Banks?
This paper argues that the slow and incomplete deregulation of the financial system in the 1980s was the most important factor behind the Japanese banking troubles in the 1990s. The regression analysis of Japanese banks shows that the cross-sectional variation of bad loans ratios is best explained by the variation in the growth of loans to the real estate industry. The variation of growth of real estate lending, in turn, is explained by the varied experience of losing existing customers to capital markets. The rapid appreciation of land prices in the late 1980s also fueled the growth of real estate lending.
Rationality problem for algebraic tori
We give the complete stably rational classification of algebraic tori of
dimensions and over a field . In particular, the stably rational
classification of norm one tori whose Chevalley modules are of rank and
is given. We show that there exist exactly (resp. , resp. )
stably rational (resp. not stably but retract rational, resp. not retract
rational) algebraic tori of dimension , and there exist exactly
(resp. , resp. ) stably rational (resp. not stably but retract
rational, resp. not retract rational) algebraic tori of dimension . We make
a procedure to compute a flabby resolution of a -lattice effectively by
using the computer algebra system GAP. Some algorithms may determine whether
the flabby class of a -lattice is invertible (resp. zero) or not. Using the
algorithms, we determine all the flabby and coflabby -lattices of rank up to
and verify that they are stably permutation. We also show that the
Krull-Schmidt theorem for -lattices holds when the rank , and fails
when the rank is . Indeed, there exist exactly (resp. )
-lattices of rank (resp. ) which are decomposable into two different
ranks. Moreover, when the rank is , there exist exactly -lattices
which are decomposable into the same ranks but the direct summands are not
isomorphic. We confirm that for any Bravais group of dimension
where is the flabby class of the corresponding -lattice of
rank . In particular, for any maximal finite subgroup where . As an application of the methods
developed, some examples of not retract (stably) rational fields over are
given.Comment: To appear in Mem. Amer. Math. Soc., 147 pages, minor typos are
correcte
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