153,487 research outputs found
An octonion algebra originating in combinatorics
C.H. Yang discovered a polynomial version of the classical Lagrange identity
expressing the product of two sums of four squares as another sum of four
squares. He used it to give short proofs of some important theorems on
composition of delta-codes (now known as T-sequences). We investigate the
possible new versions of his polynomial Lagrange identity. Our main result
shows that all such identities are equivalent to each other.Comment: 11 pages, A simpler proof of the main theorem, due to Alberto
Elduque, is inserted. The paper will appear in the Proc. Amer. Math. So
Extracting Functional Modules from Biological Pathways
It has been proposed that functional modules are the fundamental units of cellular function. Methods to identify these modules have thus far relied on gene expression data or protein-protein interaction (PPI) data, but have a few limitations. We propose a new method, using biological pathway data to identify functional modules, that can potentially overcome these limitations. We also construct a network of these modules using functionally relevant PPI data. This network displays the flow and integration of information between modules and can be used to map cellular function
Evidence for very strong electron-phonon coupling in YBa_{2}Cu_{3}O_{6}
From the observed oxygen-isotope shift of the mid-infrared two-magnon
absorption peak of YBaCuO, we evaluate the oxygen-isotope
effect on the in-plane antiferromagnetic exchange energy . The exchange
energy in YBaCuO is found to decrease by about 0.9% upon
replacing O by O, which is slightly larger than that (0.6%) in
LaCuO. From the oxygen-isotope effects, we determine the lower
limit of the polaron binding energy, which is about 1.7 eV for
YBaCuO and 1.5 eV for LaCuO, in quantitative
agreement with angle-resolved photoemission data, optical conductivity data,
and the parameter-free theoretical estimate. The large polaron binding energies
in the insulating parent compounds suggest that electron-phonon coupling should
also be strong in doped superconducting cuprates and may play an essential role
in high-temperature superconductivity.Comment: 4 pages, 1 figur
General response theory of topologically stable Fermi points and its implications for disordered cases
We develop a general response theory of gapless Fermi points with nontrivial
topological charges for gauge and nonlinear sigma fields, which asserts that
the topological character of the Fermi points is embodied as the terms with
discrete coefficients proportional to the corresponding topological charges.
Applying the theory to the effective non-linear sigma models for topological
Fermi points with disorders in the framework of replica approach, we derive
rigorously the Wess-Zumino terms with the topological charges being their
levels in the two complex symmetry classes of A and AIII. Intriguingly, two
nontrivial examples of quadratic Fermi points with the topological charge `2'
are respectively illustrated for the classes A and AIII. We also address a
qualitative connection of topological charges of Fermi points in the real
symmetry classes to the topological terms in the non-linear sigma models, based
on the one-to-one classification correspondence.Comment: 8 pages and 2 figures, revised version with appendi
Genetic algorithm and neural network hybrid approach for job-shop scheduling
Copyright @ 1998 ACTA PressThis paper proposes a genetic algorithm (GA) and constraint satisfaction adaptive neural network (CSANN) hybrid approach for job-shop scheduling problems. In the hybrid approach, GA is used to iterate for searching optimal solutions, CSANN is used to obtain feasible solutions during the iteration of genetic algorithm. Simulations have shown the valid performance of the proposed hybrid approach for job-shop scheduling with respect to the quality of solutions and the speed of calculation.This research is supported by the National Nature Science Foundation and National High
-Tech Program of P. R. China
A cellular automata modelling of dendritic crystal growth based on Moore and von Neumann neighbourhood
An important step in understanding crystal growth patterns involves simulation of the growth processes using mathematical models. In this paper some commonly used models in this area are reviewed, and a new simulation model of dendritic crystal growth based on the Moore and von Neumann neighbourhoods in cellular automata models are introduced. Simulation examples are employed to find ap-
propriate parameter configurations to generate dendritic crystal growth patterns. Based on these new modelling results the relationship between tip growth speed
and the parameters of the model are investigated
Topological Classification and Stability of Fermi Surfaces
In the framework of the Cartan classification of Hamiltonians, a kind of
topological classification of Fermi surfaces is established in terms of
topological charges. The topological charge of a Fermi surface depends on its
codimension and the class to which its Hamiltonian belongs. It is revealed that
six types of topological charges exist, and they form two groups with respect
to the chiral symmetry, with each group consisting of one original charge and
two descendants. It is these nontrivial topological charges which lead to the
robust topological protection of the corresponding Fermi surfaces against
perturbations that preserve discrete symmetries.Comment: 5 pages, published version in PR
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