The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

Correlating Charge-Carrier Dynamics with Efficiency in Quantum-Dot Solar Cells: Can Excitonics Lead to Highly Efficient Devices?

The photovoltaic performance of quantum-dot solar cells strongly depends on the charge-carrier relaxation and recombination processes, which need to be modulated in a favorable way to obtain maximum efficiency. Recently, significant efforts have been devoted to investigate the carrier dynamics of nanocrystal sensitizers, both in solution and deposited on TiO₂ photoanodes, with the aim to correlate the excitonics with solar-energy conversion efficiency. This Minireview summarizes some proof of the concepts that efficiency can be directly correlated to the exciton dynamics of quantum-dot solar cells. The presented findings are based on CdSeS alloy, CdSe/CdS core/shell, Au/CdSe nanohybrids, and Mn-doped CdZnSSe nanocrystals, where the favourable excitonic processes are optimized to enhance the efficiency. Future prospects and limitations are addressed as well.     

Oxidative dehydrogenation of n-octane over a vanadium–magnesium oxide catalyst: Influence of the gas hourly space velocity

Oxidative dehydrogenation (ODH) of n-octane was carried out over a vanadium–magnesium oxide catalyst in a continuous flow fixed bed reactor. The catalyst was characterized by ICP–OES, powder XRD and SEM. The catalytic tests were carried out at different gas hourly space velocities (GHSVs), viz. 4000, 6000, 8000, and 10,000 h^?1. The best selectivity for octenes was obtained at the GHSV of 8000 h^?1, while that for C8 aromatics was attained at the GHSV of 6000 h^?1 at high temperatures (500 and 550 °C). The catalytic testing at the GHSV of 10,000 h^?1 showed the lowest activity, while that at the GHSV of 4000 h^?1 consistently showed the lowest ODH selectivity. Generally, the best ODH performance was obtained by the catalytic testing at the GHSVs of 6000 and 8000 h^?1. No phasic changes were observed after the catalytic testing.     

New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Liquid chromatography‐tandem mass spectrometry assay for the simultaneous determination of three major flavonoids and their glucuronidated metabolites in rats after oral administration of Artemisia annua L. extract at a therapeutic ultra‐low dose

The traditional antimalarial herb Artemisia annua L., from which artemisinin is isolated, is widely used in endemic regions. It has been suggested that artemisinin activity can be enhanced by flavonoids in A. annua; however, how fast and how long the flavonoids are present in the body remains unknown. In the present study, a rapid and sensitive liquid chromatography with tandem mass spectrometry method was developed and validated for the simultaneous determination of three major flavonoids components, i.e. chrysosplenol D, chrysoplenetin, and artemetin and their glucuronidated metabolites in rats after oral administrations of A. annua extracts at a therapeutic ultra‐low dose. The concentration of the intact form was determined directly, and the concentration of the glucuronidated form was assayed in the form of flavonoids aglycones, after treatment with β‐glucuronidase/sulfatase. The method was linear in the range of 0.5–300.0 ng/mL for chrysoplenetin and artemetin, and 2–600 ng/mL for chrysosplenol D. All the validation data conformed to the acceptance requirements. The study revealed a significantly higher exposure of the flavonoid constituents in conjugated forms in rats, with only trace intact from. Multiple oral doses of A. annua extracts led to a decreased plasma concentration levels for three flavonoids.     

Preparation,structure elucidation,and antioxidant activity of new bis(thiosemicarbazone) derivatives

Schiff-base–bearing new bis(thiosemicarbazone) derivatives were prepared from terephthalaldehyde and various thiosemicarbazides. FT–IR, ¹H NMR, ¹³C NMR, and UV–Vis spectroscopic methods and elemental analysis were used to elucidate the identification of the synthesized molecules. The in vitro antioxidant activity of the synthesized compounds was analysed with the 1,1-diphenyl-2-picryl hydrazyl free-radical–trapping process. The synthesized compounds exhibited lower antioxidant activity than the standard ascorbic acid. IC₅₀ values of the synthesized molecules measured from 3.81 ± 0.01 to 29.05 ± 0.11 μM. Among the synthesized compounds, compound 3 had the best antioxidant activity. Moreover, this study explained the structure–activity relationship of the synthesized molecules with different substituents in radical trapping reactions.     

Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.     

小直径棒材超声横波检测仿真分析

采用超声水浸聚焦斜入射方式进行小棒材表面、近表缺陷检测时,声波在水/棒和棒/缺陷界面会发生反射、折射、散射、衍射及波形转换等一系列物理变换。此时缺陷可检性对声波入射条件十分敏感,常出现由于检测条件设置不当而导致缺陷漏检、误检的情况。为解决这一问题,本文针对小棒材超声斜入射检测中的主要参数——入射角和水距,开展声场及缺陷声响应仿真,研究检测参数对不同部位缺陷检测能力的影响,并对仿真结果进行试验验证。通过研究得到了检测水距、入射角度对缺陷检测能力的影响,并得到最优检测条件。试验验证结果表明研究制定的检测方案可有效检测出表面、近表面裂纹缺陷。