70,056 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
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
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
Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
A topology-intrinsic connection between the stabilities of Fermi surfaces
(FSs) and topological insulators/superconductors (TIs/TSCs) is revealed. In
particular, a one-to-one relation between the topological types of FSs and
TIs/TSCs is rigorously derived; combining it with a well-established
topological theory of FSs, we produce a complete table illustrating precisely
topological types of all TIs/TSCs, while a valid part of it was postulated
before. Moreover, we propose and prove a general index theorem that relates the
topological charge of FSs on the natural boundary of a strong TI/TSC to its
bulk topological number. Implications of the general index theorem on the
boundary quasi-particles are also addressed.Comment: 5 pages with Supplemental Material, more content is adde
Intrinsic Percolative Superconductivity in Heavily Overdoped High Temperature Superconductors
Magnetic measurements on heavily overdoped ,
, and single crystals reveal
a new type magnetization hysteresis loops characterized by the vanishing of
usual central peak near zero field. Since this effect has been observed in
various systems with very different structural details, it reflects probably a
generic behavior for all high temperature superconductors. This easy
penetration of magnetic flux can be understood in the picture of percolative
superconductivity due to the inhomogeneous electronic state in heavily
overdoped regime.Comment: 4 pages, 5 figure
Effect of carrot puree edible films on quality preservation of fresh-cut carrots
peer-reviewedFinancial support from the high level talent fund of Henan University of Technology Science and Technology (No. 2012BS024) is gratefully acknowledged.The effect of edible films based on carrot puree, chitosan, corn starch, gelatin, glycerol and cinnamaldehyde on fresh-cut carrots was studied during storage. Several parameters, such as firmness, colour, weight loss, total carotenoids, total phenols, polyphenol oxidase (PPO) activity and peroxidase (POD) activity in coated carrots were determined at regular intervals and then compared with the uncoated carrots throughout the storage period. Significant and expected changes were observed in all carrot samples that were compared. The coating treatment significantly (P < 0.05) delayed the senescence, reduced the deterioration of exterior quality and retained total carotenoids well compared with control (P < 0.05). In addition, significant inhibition of PPO activity (P < 0.05) and POD activity (P < 0.05) as well as reduced accumulation of polyphenols (P < 0.05) were observed for all coated samples. All of these favourable responses induced by coating treatment on minimally processed fresh-cut carrots showed beneficial physiological effects, which would give some useful references to the fresh-cut fruit and vegetable processing industry and satisfy people’s requirements allowing for extending product shelf life without negatively affecting the sensory quality or acceptability.Henan University of Technology Science and Technolog
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