The Tensor Rank of the Tripartite State ∣W⟩⊗n\ket{W}^{\otimes n}}

Tensor rank refers to the number of product states needed to express a given multipartite quantum state. Its non-additivity as an entanglement measure has recently been observed. In this note, we estimate the tensor rank of multiple copies of the tripartite state $\ket{W}=\tfrac{1}{\sqrt{3}}(\ket{100}+\ket{010}+\ket{001})$. Both an upper bound and a lower bound of this rank are derived. In particular, it is proven that the tensor rank of $\ket{W}^{\otimes 2}$ is seven, thus resolving a previously open problem. Some implications of this result are discussed in terms of transformation rates between $\ket{W}^{\otimes n}$ and multiple copies of the state $\ket{GHZ}=\tfrac{1}{\sqrt{2}}(\ket{000}+\ket{111})$.Comment: Comments: 3 pages (Revtex 4). Minor corrections to Theorem 1. Presentation refined. Main results unchanged. Comments are welcom

Application of RNA silencing to plant disease resistance

To reduce the losses caused by plant pathogens, plant biologists have adopted numerous methods to engineer resistant plants. Among them, RNA silencing-based resistance has been a powerful tool that has been used to engineer resistant crops during the last two decades. Based on this mechanism, diverse approaches were developed. In this review, we focus on the application of RNA silencing to produce plants that are resistant to plant viruses such as RNA and DNA viruses, viroids, insects, and the recent expansion to fungal pathogens

Triple-product asymmetry in the radiative two-pion tau decay

In this work, we perform a detailed study of the $\tau^-\to\pi^-\pi^0\gamma\nu$ decay process within the resonance chiral theory. We pay special attention to the triple-product asymmetry in the $\tau^-\to\pi^-\pi^0\gamma\nu$ process. The minimal resonance chiral Lagrangian and the odd-intrinsic parity resonance operators are simultaneously included to calculate the decay amplitudes. Various invariant-mass distributions in the $\pi^-\pi^0$, $\pi^-\gamma$ and $\pi^0\gamma$ systems are studied and they reveal different resonance dynamics. We further predict the intriguing nonzero triple-product asymmetry distributions, which may provide useful guidelines for future experimental measurements conducted at the Belle-II and super tau-charm facilities.Comment: 32 pages, 9 figures. To match the published versio

Revisit of tensor-meson nonet in resonance chiral theory

We study the properties of the lowest multiplet of light-flavor tensor meson resonances, i.e. $f_2(1270)$, $a_2(1320)$, $K_2^*(1430)$, and $f_2'(1525)$, within the resonance chiral theory approach. The higher-order resonance chiral operators, including the light-quark mass and $1/N_C$ corrections, are simultaneously incorporated in our study. The use of resonance chiral expressions allows us to analyze not only the relevant experimental data but also in the meantime the lattice results at unphysical quark masses, including the masses of the lowest multiplet of tensor resonances and their decay widths into two pseudoscalar mesons. In addition, the radiative decays of the tensor resonances into one photon plus one pseudoscalar meson and two photons are also studied.Comment: 18 pages, 3 tables, 3 figures. To match the published versio

2-Cyclo­hexyl-4-[(3,5-dimethyl­piperidin-1-yl)meth­yl]-5-methyl­phenol

The title compound, C21H33NO, crystallizes with three independent mol­ecules in the asymmetric unit. The cyclo­hexane and piperidine rings adopt chair conformations. The crystal packing is stabilized by inter­molecular O—H⋯N and C—H⋯O hydrogen bonds, and by weak π–π stacking inter­actions [centroid–centroid distance = 3.876 (2) Å]

Sedentary Behavior Is Independently Related to Fat Mass among Children and Adolescents in South China

We aim to explore the independent associations of sedentary behaviors (SB) with body mass distribution among Chinese children. Data on the screen-based sedentary time (television viewing and computer use) and doing homework, physical activities and dietary intake of 1586 Chinese children (50.3% girls) aged 7–15 years were obtained through validated questionnaires. Skin-fold thickness, body height, and weight were measured to calculate percent body fat (%BF), fat mass index (FMI), and fat-free mass index (FFMI). Parental characteristics were collected by questionnaires. Among girls, time of SB (screen time or doing homework) was positively related to %BF, FMI, and FFMI (p < 0.03) after adjusting for maternal overweight, the average annual income of family, moderate-to-vigorous physical activity energy expenditure, and energy intake: Girls in the highest tertile of screen time/homework had 16.7%/23.3% higher relative FMI and 2.9%/2.9% higher relative FFMI than girls in the lowest tertile. Among boys, screen time was positively associated with FFMI (p 0.09), while time of doing homework was positively related to %BF and FMI (p = 0.03). Sedentary behaviors might be positively and independently related to fat mass among Chinese children, and were more pronounced in girls