Numerical Strategies of Computing the Luminosity Distance

We propose two efficient numerical methods of evaluating the luminosity distance in the spatially flat {\Lambda}CDM universe. The first method is based on the Carlson symmetric form of elliptic integrals, which is highly accurate and can replace numerical quadratures. The second method, using a modified version of Hermite interpolation, is less accurate but involves only basic numerical operations and can be easily implemented. We compare our methods with other numerical approximation schemes and explore their respective features and limitations. Possible extensions of these methods to other cosmological models are also discussed.Comment: 4 pages, 2 figures. v2: A minor error in the last equation has been corrected (conclusions are not affected). v3: Accepted by MNRA

A Robust Quantum Random Access Memory

A "bucket brigade" architecture for a quantum random memory of $N=2^n$ memory cells needs $n(n+5)/2$ times of quantum manipulation on control circuit nodes per memory call. Here we propose a scheme, in which only average $n/2$ times manipulation is required to accomplish a memory call. This scheme may significantly decrease the time spent on a memory call and the average overall error rate per memory call. A physical implementation scheme for storing an arbitrary state in a selected memory cell followed by reading it out is discussed.Comment: 5 pages, 3 figure

A Counter-Example to the Nichtnegativstellensatz

Klep and Schweighofer asked whether the Nirgendsnegativsemidefinitheitsstellensatz holds for a symmetric noncommutative polynomial whose evaluations at bounded self-adjoint operators on any nontrivial Hilbert space are not negative semidefinite. We provide a counter-example to this open problem

Design and Synthesis of Novel Anticancer Peptide Nanoparticles

Cancer has now become a common disease affecting human health. Existing cancer treatment drugs can no longer meet the growing needs of cancer patients, and the emergence of anticancer drug resistance has exacerbated this phenomenon. By designing and synthesizing new anticancer peptide nanoparticles and studying their anticancer effects, new strategies for cancer treatment may be obtained. Novel anticancer peptides are synthesized by adding basic amino acids and solid-phase synthesis technology, and their structural information is determined by mass spectrometry. Nanoparticles of anticancer peptide were synthesized by nano-self-assembly technology. Two novel anticancer peptides exhibited anticancer activity, one of which was assembled into nanoparticles. The theoretical isoelectric points of the modified SZG3 and SZG5 are all greater than physiological pH, and will be positively charged under physiological conditions. The estimated half-life of SZG3 and SZG5 is significantly extended (30h), which is beneficial to increase the efficacy and reduce toxic and side effects. SZG3 and SZG5 have a good inhibitory effect on tumor cells and have low toxicity to normal cells. Keywords: anticancer peptide, study, design, cancer, nanoparticles&nbsp