Exterior splashes and linear sets of rank 3

In \PG(2,q^3), let $\pi$ be a subplane of order $q$ that is exterior to \li. The exterior splash of $\pi$ is defined to be the set of $q^2+q+1$ points on \li that lie on a line of $\pi$. This article investigates properties of an exterior \orsp\ and its exterior splash. We show that the following objects are projectively equivalent: exterior splashes, covers of the circle geometry $CG(3,q)$, Sherk surfaces of size $q^2+q+1$, and \GF(q)-linear sets of rank 3 and size $q^2+q+1$. We compare our construction of exterior splashes with the projection construction of a linear set. We give a geometric construction of the two different families of sublines in an exterior splash, and compare them to the known families of sublines in a scattered linear set of rank 3

The tangent splash in \PG(6,q)

Let B be a subplane of PG(2,q^3) of order q that is tangent to $\ell_\infty$. Then the tangent splash of B is defined to be the set of q^2+1 points of $\ell_\infty$ that lie on a line of B. In the Bruck-Bose representation of PG(2,q^3) in PG(6,q), we investigate the interaction between the ruled surface corresponding to B and the planes corresponding to the tangent splash of B. We then give a geometric construction of the unique order-$q$-subplane determined by a given tangent splash and a fixed order-$q$-subline.Comment: arXiv admin note: substantial text overlap with arXiv:1303.550

Spin-Selective Transport of Electron in DNA Double Helix

The experiment that the high spin selectivity and the length-dependent spin polarization are observed in double-stranded DNA [Science ${\bf 331}$, 894 (2011)], is elucidated by considering the combination of the spin-orbit coupling, the environment-induced dephasing, and the helical symmetry. We show that the spin polarization in double-stranded DNA is significant even in the case of weak spin-orbit coupling, while no spin polarization appears in single-stranded DNA. Furthermore, the underlying physical mechanism and the parameters-dependence of the spin polarization are studied.Comment: 5 pages; 4 figure

Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization

We study Andreev bound states (ABS) and resulting charge transport of Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures is sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode similar to that in spinless chiral p-wave pairing in topological phase (TP). We clarify that two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether ABS exists at QCP or not. In the former type, ABS has a energy gap and does not cross at zero energy in non-topological phase (NTP). These complex properties can be detected by tunneling conductance between normal metal / RSC junctions.Comment: 5 pages, 6 figure

Factors Influencing the Purchase of Live Seafood in the North Central Region of the United States

This study assesses the preferences of shoppers of live seafood products in the North Central Region of the US accounting for heterogeneity in their preferences. The results suggest that quality assurance considerations and high incomes are factors that would increase the probability of higher expenditures on live fish/shellfish. The purchase of saltwater fish and shellfish also increased the probability of higher expenditures. The North Central Region produces freshwater seafood, and maintaining fish quality through the production process is important to this niche market. Shoppers also purchased live seafood frequently, signifying the importance of availability.Live fish, preferences, random parameters ordered probit, Consumer/Household Economics, Food Consumption/Nutrition/Food Safety, Institutional and Behavioral Economics, Public Economics, Q11, Q21, Q22,