Further refinements of the Heinz inequality

The celebrated Heinz inequality asserts that $2|||A^{1/2}XB^{1/2}|||\leq |||A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}|||\leq |||AX+XB|||$ for $X \in \mathbb{B}(\mathscr{H})$, A,B\in \+, every unitarily invariant norm $|||\cdot|||$ and $\nu \in [0,1]$. In this paper, we present several improvement of the Heinz inequality by using the convexity of the function $F(\nu)=|||A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}|||$, some integration techniques and various refinements of the Hermite--Hadamard inequality. In the setting of matrices we prove that \begin{eqnarray*} &&\hspace{-0.5cm}\left|\left|\left|A^{\frac{\alpha+\beta}{2}}XB^{1-\frac{\alpha+\beta}{2}}+A^{1-\frac{\alpha+\beta}{2}}XB^{\frac{\alpha+\beta}{2}}\right|\right|\right|\leq\frac{1}{|\beta-\alpha|} \left|\left|\left|\int_{\alpha}^{\beta}\left(A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}\right)d\nu\right|\right|\right|\nonumber\\ &&\qquad\qquad\leq \frac{1}{2}\left|\left|\left|A^{\alpha}XB^{1-\alpha}+A^{1-\alpha}XB^{\alpha}+A^{\beta}XB^{1-\beta}+A^{1-\beta}XB^{\beta}\right|\right|\right|\,, \end{eqnarray*} for real numbers $\alpha, \beta$.Comment: 15 pages, to appear in Linear Algebra Appl. (LAA

Knowlesi malaria in Vietnam

The simian malaria parasite Plasmodium knowlesi is transmitted in the forests of Southeast Asia. Symptomatic zoonotic knowlesi malaria in humans is widespread in the region and is associated with a history of spending time in the jungle. However, there are many settings where knowlesi transmission to humans would be expected but is not found. A recent report on the Ra-glai population of southern central Vietnam is taken as an example to help explain why this may be so

Constraints on millicharged particles with low threshold germanium detectors at Kuo-Sheng Reactor Neutrino Laboratory

Relativistic millicharged particles ($\chi_q$) have been proposed in various extensions to the Standard Model of particle physics. We consider the scenarios where they are produced at nuclear reactor core and via interactions of cosmic-rays with the earth's atmosphere. Millicharged particles could also be candidates for dark matter, and become relativistic through acceleration by supernova explosion shock waves. The atomic ionization cross section of $\chi_q$ with matter are derived with the equivalent photon approximation. Smoking-gun signatures with significant enhancement in the differential cross section are identified. New limits on the mass and charge of $\chi_q$ are derived, using data taken with a point-contact germanium detector with 500g mass functioning at an energy threshold of 300~eV at the Kuo-Sheng Reactor Neutrino Laboratory.Comment: 8 pages, 7 figure