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

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

Intrinsic Percolative Superconductivity in Heavily Overdoped High Temperature Superconductors

Magnetic measurements on heavily overdoped $La_{2-x}Sr_xCuO_4$, $Tl_2Ba_2CuO_6$, $Bi_2Sr_2CuO_6$ and $Bi_2Sr_2CaCu_2O_8$ 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