A class of gcd-graphs having Perfect State Transfer

Let $G$ be a graph with adjacency matrix $A$. The transition matrix corresponding to $G$ is defined by $H(t):=\exp{\left(itA\right)}$, t\in\Rl. The graph $G$ is said to have perfect state transfer (PST) from a vertex $u$ to another vertex $v$, if there exist \tau\in\Rl such that the $uv$-th entry of $H(\tau)$ has unit modulus. The graph $G$ is said to be periodic at \tau\in\Rl if there exist \gamma\in\Cl with $|\gamma|=1$ such that $H(\tau)=\gamma I$, where $I$ is the identity matrix. A $\mathit{gcd}$-graph is a Cayley graph over a finite abelian group defined by greatest common divisors. In this paper, we construct classes of $\mathit{gcd}$-graphs having periodicity and perfect state transfer

Attempts Towards Total synthesis of (±) Spirooliganone-A

The group has recently reported a novel protocol of oxidative dearomatization of napthols using phenyl selenium bromide (PhSeBr). The progress through this process towards the natural product synthesis especially the Spiroliganone system in the different conditions are the main goal for this work. Target was mainly the synthesis of oxa-spirane core through oxidative de- aromatization of the phenolic ring

How can economic schemes curtail the increasing sex ratio at birth in China?

Fertility decline, driven by the one-child policy, and son preference have contributed to an alarming difference in the number of live male and female births in China. We present a quantitative model where people choose to sex-select because they perceive that married sons are more valuable than married daughters. Due to the predominant patrilocal kinship system in China, daughters-in-law provide valuable emotional and financial support, enhancing the perceived present value of married sons. We argue that inter-generational transfer data will help ascertain the extent to which economic schemes (such as pension plans for families with no sons) can curtail the increasing sex ratio at birth.sex ratio at birth, sex-selection, sex-selective potency, son preference, value of child