Further Results on the Distinctness of Decimations of l-sequences

Let $\underline{a}$ be an \textit{l}-sequence generated by a feedback-with-carry shift register with connection integer $q=p^{e}$, where $p$ is an odd prime and $e\geq 1$. Goresky and Klapper conjectured that when $p^{e}\notin \{5,9,11,13\}$, all decimations of $\underline{a}$ are cyclically distinct. When $e=1$ and $p>13$, they showed that the set of distinct decimations is large and, in some cases, all deciamtions are distinct. In this article, we further show that when $e\geq 2$ and$p^{e}\neq 9$, all decimations of $\underline{a}$ are also cyclically distinct.Comment: submitted to IEEE-I

Price Determination in the Bottled Water Industry: A Case Study of Poland Spring

This paper analyzes the price of a single brand in the bottled water industry. We find that the brand's price is negatively related to its own share. We also find that price is positively related to the four firm concentration ratio in the carbonated segment, but unrelated in the noncarbonated segment.Demand and Price Analysis,

Gauge Independence of Magnetic Moment and Vanishing Charge of Dirac Neutrinos: an Exact One-loop Demonstration

The magnetic moment and vanishing charge of a Dirac neutrino are physically observable quantities and must not depend on the choice of gauge in a consistent quantum field theory. We verify this statement explicitly at the one loop level in both R_xi and unitary gauges of the minimally extended standard model. We accomplish this by manipulating directly the integrands of loop integrals and employing simple algebraic identities and integral relations. Our result generally applies for any masses of the relevant particles and unitary neutrino mixing.Comment: 14 pages, 2 figure