Let $L=-\Delta +V$ be a Schrödinger operator in ${\mathbb R}^n$ with $n\geq 3$, where $\Delta $ is the Laplace operator denoted by $\Delta =\sum ^{n}_{i=1}({\partial ^{2}}/{\partial x_{i}^{2}})$ and the nonnegative potential V belongs to the reverse Hölder class $(RH)_{q}$ with $q>n/2$. For $\alpha \in (0,1)$, we define the operator

$$ \begin{align*} T_N^{L^{\alpha}} f(x) =\sum_{j=N_1}^{N_2} v_j(e^{-a_{j+1}L^\alpha} f(x)-e^{-a_{j}L^\alpha} f(x)) \quad \mbox{for all }x\in \mathbb R^n, \end{align*} $$

where $\{e^{-tL^\alpha } \}_{t>0}$ is the fractional heat semigroup of the operator L, $\{v_j\}_{j\in \mathbb Z}$ is a bounded real sequence and $\{a_j\}_{j\in \mathbb Z}$ is an increasing real sequence.

We investigate the boundedness of the operator $T_N^{L^{\alpha }}$ and the related maximal operator $T^*_{L^{\alpha }}f(x):=\sup _N \vert T_N^{L^{\alpha }} f(x)\vert $ on the spaces $L^{p}(\mathbb {R}^{n})$ and $BMO_{L}(\mathbb {R}^{n})$, respectively. As extensions of $L^{p}(\mathbb {R}^{n})$, the boundedness of the operators $T_N^{L^{\alpha }}$ and $T^*_{L^{\alpha }}$ on the Morrey space $L^{\rho ,\theta }_{p,\kappa }(\mathbb {R}^{n})$ and the weak Morrey space $WL^{\rho ,\theta }_{1,\kappa }(\mathbb {R}^{n})$ has also been proved.

This study aimed to understand the potassium voltage-gated channel KQT-like subfamily, member 1 gene polymorphism in a rural elderly population in a county in Guangxi and to explore the possible relationship between its gene polymorphism and blood sugar. The 6 SNP loci of blood DNA samples from 4355 individuals were typed using the imLDRTM Multiple SNP Typing Kit from Shanghai Tianhao Biotechnology Co. The data combining epidemiological information (baseline questionnaire and physical examination results) and genotyping results were statistically analyzed using GMDR0.9 software and SPSS22.0 software. A total of 4355 elderly people aged 60 years and above were surveyed in this survey, and the total abnormal rate of glucose metabolism was 16·11 % (699/4355). Among them, male:female ratio was 1:1·48; the age group of 60–69 years old accounted for the highest proportion, with 2337 people, accounting for 53·66 % (2337/4355). The results of multivariate analysis showed that usually not doing farm work (OR 1·26; 95 % CI 1·06, 1·50), TAG ≥ 1·70 mmol/l (OR 1·19; 95 % CI 1·11, 1·27), hyperuricaemia (OR 1·034; 95 % CI 1·01, 1·66) and BMI ≥ 24 kg/m2 (OR 1·06; 95 % CI 1·03, 1·09) may be risk factors for abnormal glucose metabolism. Among all participants, rs151290 locus AA genotype, A allele carriers (AA+AC) were 0.70 times more likely (0.54 to 0.91) and 0.82 times more likely (0.70 to 0.97) to develop abnormal glucose metabolism than CC genotype carriers, respectively. Carriers of the T allele at the rs2237892 locus (CT+TT) were 0.85 times more likely to have abnormal glucose metabolism than carriers of the CC genotype (0.72 to 0.99); rs2237897 locus CT gene. The possibility of abnormal glucose metabolism in the carriers of CC genotype, TT genotype and T allele (CT + TT) is 0·79 times (0·67–0·94), 0·74 times (0·55–0·99) and 0·78 times (0·66, 0·92). The results of multifactor dimensionality reduction showed that the optimal interaction model was a three-factor model consisting of farm work, TAG and rs2237897. The best model dendrogram found that the interaction between TAG and rs2237897 had the strongest effect on fasting blood glucose in the elderly in rural areas, and they were mutually antagonistic. Environment–gene interaction is an important factor affecting abnormal glucose metabolism in the elderly of a county in Hechi City, Guangxi.

In this study, we investigated the influence of fiber parameters on stimulated Raman scattering (SRS) and identified a unique pattern of SRS evolution in the counter tandem pumping configuration. Our findings revealed that the SRS threshold in counter-pumping is predominantly determined by the length of the output delivery fiber rather than the gain fiber. By employing the counter tandem pumping scheme and optimizing the fiber parameters, a 10 kW fiber laser was achieved with beam quality M2 of 1.92. No mode instability or severe SRS limitation was observed. To our knowledge, this study achieved the highest beam quality in over 10 kW fiber lasers based on conventional double-clad Yb-doped fiber.

The power scaling on short wavelength (SW) fiber lasers operating around 1 μm are in significant demand for applications in energy, environment and industry. The challenge for performance scalability of high-power SW lasers based on rare-earth-doped fiber primarily lies in the physical limitations, including reabsorption, amplified spontaneous emission and parasitic laser oscillation. Here, we demonstrate an all-fiberized, purely passive SW (1018 nm) random-distributed-feedback Raman fiber laser (RRFL) to validate the capability of achieving high-power output at SWs based on multimode laser diodes (LDs) direct pumping. Directly pumped by multimode LDs, the high-brightness RRFL delivers over 656 W, with an electro-optical efficiency of 20% relative to the power. The slope efficiency is 94%. The beam quality M2 factor is 2.9 (which is ~20 times that of the pump) at the maximum output signal power, achieving the highest brightness enhancement of 14.9 in RRFLs. To the best of our knowledge, this achievement also represents the highest power record of RRFLs utilizing multimode diodes for direct pumping. This work may not only provide a new insight into the realization of high-power, high-brightness RRFLs but also is a promising contender in the power scaling of SWs below 1 μm.

Aspongopus chinensis Dallas 1851, an insect of important economic value, faces challenges in artificial breeding due to mandatory diapause and limited access to wild resources. Heat shock proteins (Hsps) are thought to influence diapause in insects, but little is known about their role in A. chinensis during diapause. This study used genomic methods to identify 25 Hsp genes in A. chinensis, including two Hsp90, 14 Hsp70, four Hsp60 and five small Hsp genes, were located on seven chromosomes, respectively. The gene structures among the same families are relatively conserved. Meanwhile, the motif compositions and secondary structures of A. chinensis Hsps (AcHsps) were predicted. RNA-seq data and fluorescence quantitative PCR analysis showed that there were differences in the expression patterns of AcHsps in diapause and non-diapause stages, and AcHsp70-5 was significantly differentially expressed in both analysis, which was enriched in the pathway of response to hormone. All the results showed that Hsps play an important role in the diapause mechanism of A. chinensis. Our observations highlight the molecular evolution of the Hsp gene and their effect on diapause in A. chinensis.

The late third-millennium BC Longshan period was a crucial time for state formation in central China. During these centuries, long-distance networks expanded and shared material culture and then cultural practices spread across wider areas precipitating social and ideological developments that presaged the rise of states and cities on the Central Plain. In this research, the authors use multiple (strontium, oxygen and carbon) isotope analyses from the dental enamel of 67 individuals buried at the Xiajin cemetery, Shanxi Province. The results indicate significant long-distance migration among females during the Longshan period, which the authors interpret as evidence of exogamous marriage for political alliance-building—a phenomenon found more widely across Eurasia at the start of the Bronze Age.

Dietary antioxidant indices (DAI) may be potentially associated with relative telomere length (RTL) of leucocytes. This study aimed to investigate the relationship between DAI and RTL. A cross-sectional study involving 1656 participants was conducted. A generalised linear regression model and a restricted cubic spline model were used to assess the correlation of DAI and its components with RTL. Generalised linear regression analysis revealed that DAI (β = 0·005, P = 0·002) and the intake of its constituents vitamin C (β = 0·043, P = 0·027), vitamin E (β = 0·088, P < 0·001), Se (β = 0·075, P = 0·003), and Zn (β = 0·075, P = 0·023) were significantly and positively correlated with RTL. Sex-stratified analysis showed that DAI (β = 0·006, P = 0·005) and its constituents vitamin E (β = 0·083, P = 0·012), Se (β = 0·093, P = 0·006), and Zn (β = 0·092, P = 0·034) were significantly and positively correlated with RTL among females. Meanwhile, among males, only vitamin E intake (β = 0·089, P = 0·013) was significantly and positively associated with RTL. Restricted cubic spline analysis revealed linear positive associations between DAI and its constituents’ (vitamin E, Se and Zn) intake and RTL in the total population. Sex-stratified analysis revealed a linear positive correlation between DAI and its constituents’ (vitamin E, Se and Zn) intake and RTL in females. Our study found a significant positive correlation between DAI and RTL, with sex differences.

Achieving an all-fiber ultra-fast system with above kW average power and mJ pulse energy is extremely challenging. This paper demonstrated a picosecond monolithic master oscillator power amplifier system at a 25 MHz repetition frequency with an average power of approximately 1.2 kW, a pulse energy of approximately 48 μJ and a peak power of approximately 0.45 MW. The nonlinear effects were suppressed by adopting a dispersion stretched seed pulse (with a narrow linewidth of 0.052 nm) and a multi-mode master amplifier with an extra-large mode area; then an ultimate narrow bandwidth of 1.32 nm and a moderately broadened pulse of approximately 107 ps were achieved. Meanwhile, the great spatio-temporal stability was verified experimentally, and no sign of transverse mode instability appeared even at the maximum output power. The system has shown great power and energy capability with a sacrificed beam propagation product of 5.28 mm$\cdot$mrad. In addition, further scaling of the peak power and pulse energy can be achieved by employing a lower repetition and a conventional compressor.

In this work, a confined-doped fiber with the core/inner-cladding diameter of 40/250 μm and a relative doping ratio of 0.75 is fabricated through a modified chemical vapor deposition method combined with the chelate gas deposition technique, and subsequently applied in a tandem-pumped fiber amplifier for high-power operation and transverse mode instability (TMI) mitigation. Notably, the impacts of the seed laser power and mode purity are preliminarily investigated through comparative experiments. It is found that the TMI threshold could be significantly affected by the seed laser mode purity. The possible mechanism behind this phenomenon is proposed and revealed through comprehensive comparative experiments and theoretical analysis. Finally, a maximum output power of 7.49 kW is obtained with the beam quality factor of approximately 1.83, which is the highest output power ever reported in a forward tandem-pumped confined-doped fiber amplifier. This work could provide a good reference and practical solution to improve the TMI threshold and realize high-power high-brightness fiber lasers.

We numerically investigated the opposing-buoyancy mixed convection through and around square arrays of $10\times 10$ heated circular cylinders with the solid fraction ($\phi$) ranging from 0.0079 to 0.66 and the Richardson number ($Ri$) varying from 0 to 1 at a fixed Reynolds number ($Re$) of 100. Our simulations revealed that the large mean recirculation in the far wake can be detached from or connected with the vortex pair in the near wake for different combinations of $Ri$ and $\phi$. Also, it was found that the array with relatively small $\phi$ can significantly promote flow instability even at moderate $Ri$. The instability, which is closely related to the fluctuating heat flux, develops from the lateral sides to the downstream side of the array and gives rise to the large mean recirculation in the far wake. The power spectra density of the array-scale force coefficients demonstrates that the flow undergoes different bifurcation behaviours under various parameter combinations, which reflects the interaction between the near-wake and far-wake vortexes. Interestingly, the Strouhal–Richardson number curves can be collapsed onto the same curve when $Ri$ is increased by a $\phi$-dependent factor. Also, for $\phi \leqslant 0.22$, both the mean drag coefficient and the mean Nusselt number of the array were found to decrease linearly with $Ri$ since the buoyancy within the array becomes prominent in this range of $\phi$.

The mid-latitude Westerlies (MLW) are one of the most important atmospheric circulation systems in the Northern Hemisphere, exerting a huge influence on the climate of the region downwind, and thus on vegetation, water resources, and human wellbeing. However, the seasonal variation of the MLW during the Holocene is not yet been fully understood, especially when its contribution is the most important. Here, we used end-member (EM) modeling analysis of the grain-size distributions of a high-altitude aeolian sedimentary sequence (4452 m a.s.l.) from the Yarlung Zangbo River valley in the southern Tibetan Plateau to reveal variations in the winter MLW during the Holocene. Analysis of seasonal differences in modern atmospheric circulation suggests that the southern Tibetan Plateau was heavily influenced by the mid-latitude Westerlies at the 400, 500, and 600 hPa levels in winter, while it was seldom influenced at these levels in summer. Four grain-size end-members are identified, representing distinct aerodynamic environments, of which EM1 (modal grain size 8.1 μm) can be used as a proxy of the winter MLW. A reconstruction of the variation of the winter MLW during the Holocene based on EM1 revealed that a weaker winter MLW occurred during the Early to Middle Holocene, and a stronger winter MLW during the Middle to Late Holocene. Overall, we suggest that this change in the winter MLW was closely related to the insolation/temperature/pressure gradient between low and high latitudes in the Northern Hemisphere.

Wood vinegar, a product of pyrolysis, can induce phytotoxicity on plants when applied at an adequate rate and concentration. The objective of this research was to investigate wood vinegar obtained from the pyrolysis of apple tree branches for weed control in dormant zoysiagrass. In environment-controlled growth chambers, white clover visual injury and shoot mass reduction were evaluated and compared to the nontreated control after wood vinegar application at 1,000, 2,000, or 4,000 L ha−1 under 10 C or 30 C temperature conditions. Averaged across rates, wood vinegar rapidly desiccated white clover and caused 83% and 71% visual injury at 10 C and 30 C, respectively, at 1 d after treatment (DAT). Averaged across temperatures, wood vinegar at 1,000, 2,000, and 4,000 L ha−1 reduced white clover shoot mass by 56%, 81%, and 98% from the nontreated control at 10 DAT, respectively. In field experiments, weed control increased as wood vinegar rates increased from 1,000 to 5,000 L ha−1 in dormant zoysiagrass. The effective application dose of wood vinegar required to provide 90% control (ED90) of annual fleabane, Persian speedwell, and white clover was determined to be 2,450, 2,300, and 4,020 L ha−1, respectively, at 2 wk after treatment. Turf quality did not differ among the wood vinegar treatments and the nontreated control when zoysiagrass completely recovered from dormancy. Overall, results illustrate that wood vinegar resulting from the pyrolysis of apple tree branches can be used as a nonselective herbicide in dormant turfgrass, offering a new nonsynthetic herbicide option for weed control in managed turf.

In late December 2019, patients of atypical pneumonia due to an unidentified microbial agent were reported in Wuhan, Hubei Province, China. Subsequently, a novel coronavirus was identified as the causative pathogen which was named SARS-CoV-2. As of 12 February 2020, more than 44 000 cases of SARS-CoV-2 infection have been confirmed in China and continue to expand. Provinces, municipalities and autonomous regions of China have launched first-level response to major public health emergencies one after another from 23 January 2020, which means restricting movement of people among provinces, municipalities and autonomous regions. The aim of this study was to explore the correlation between the migration scale index and the number of confirmed coronavirus disease 2019 (COVID-19) cases and to depict the effect of restricting population movement. In this study, Excel 2010 was used to demonstrate the temporal distribution at the day level and SPSS 23.0 was used to analyse the correlation between the migration scale index and the number of confirmed COVID-19 cases. We found that since 23 January 2020, Wuhan migration scale index has dropped significantly and since 26 January 2020, Hubei province migration scale index has dropped significantly. New confirmed COVID-19 cases per day in China except for Wuhan gradually increased since 24 January 2020, and showed a downward trend from 6 February 2020. New confirmed COVID-19 cases per day in China except for Hubei province gradually increased since 24 January 2020, and maintained at a high level from 24 January 2020 to 4 February 2020, then showed a downward trend. Wuhan migration scale index from 9 January to 22 January, 10 January to 23 January and 11 January to 24 January was correlated with the number of new confirmed COVID-19 cases per day in China except for Wuhan from 22 January to 4 February. Hubei province migration scale index from 10 January to 23 January and 11 January to 24 January was correlated with the number of new confirmed COVID-19 cases per day in China except for Hubei province from 22 January to 4 February. Our findings suggested that people who left Wuhan from 9 January to 22 January, and those who left Hubei province from 10 January to 24 January, led to the outbreak in the rest of China. The ‘Wuhan lockdown’ and the launching of the first-level response to this major public health emergency may have had a good effect on controlling the COVID-19 epidemic. Although new COVID-19 cases continued to be confirmed in China outside Wuhan and Hubei provinces, in our opinion, these are second-generation cases.

Energy chirp compensation of the electron bunch (e-bunch) in a laser wakefield accelerator, which is caused by the phase space rotation in the gradient wakefield, has been applied in many schemes for low energy spread e-bunch generation. We report the experimental observation of energy chirp compensation of the e-bunch in a nonlinear laser wakefield accelerator with a negligible beam loading effect. By adjusting the acceleration length using a wedge-roof block, the chirp compensation of the accelerated e-bunch was observed via an electron spectrometer. Apart from this, some significant parameters for the compensation process, such as the longitudinal dispersion and wakefield slope at the bunch position, were also estimated. A detailed comparison between experiment and simulation shows good agreement of the wakefield and bunch parameters. These results give a clear demonstration of the longitudinal characteristics of the wakefield in a plasma and the bunch dynamics, which are important for better control of a compact laser wakefield accelerator.

La3+ doped yttrium iron garnet films have been grown on (111) oriented gadolinium gallium garnet substrates via Liquid phase epitaxy technique as a basic material for ISHE device fabrication. Pt as a material with a large spin hall angle was used as a spin detection layer. We investigated the dependence of the spin pumping effect on the power and frequency of the excitation microwaves in La:YIG/Pt bilayers by measuring the ISHE voltage. We demonstrated that the area under the ISHE curve(SISHE) across a wide power range had a nearly linear correlation with the input microwave power (Pin). The parameter SISHE can be used to describe the spin current energy in a Pt layer which can be a useful parameter for a microwave rectifier.

In this study, we investigate a new simple scheme using a planar undulator (PU) together with a properly dispersed electron beam ($e$ beam) with a large energy spread (${\sim}1\%$) to enhance the free-electron laser (FEL) gain. For a dispersed $e$ beam in a PU, the resonant condition is satisfied for the center electrons, while the frequency detuning increases for the off-center electrons, inhibiting the growth of the radiation. The PU can act as a filter for selecting the electrons near the beam center to achieve the radiation. Although only the center electrons contribute, the radiation can be enhanced significantly owing to the high-peak current of the beam. Theoretical analysis and simulation results indicate that this method can be used for the improvement of the radiation performance, which has great significance for short-wavelength FEL applications.

Background: Parkinson’s disease (PD) is a degenerative disorder of the central nervous system mainly affecting the motor system. Presently, there is no effective and safe drug to treat patients with PD. Ginkgo biloba extract (GBE), obtained from leaves of the Ginkgo biloba tree, is a complex mixture of ingredients primarily containing two active components: flavonoids and terpenoids. In this study, we investigated the effects of GBE on A53T α-synuclein transgenic mice, a PD model that has better simulated the progression of PD patients than other models such as the 1-methyl-4-phenyl-1,2,3,6 tetrahydropyridine–induced PD model. Methods: Fifty α-synuclein A53T transgenic mice were fed and treated with GBE, and locomotor activity was detected by pole test, forced swim test, and wire-hang test. The expression of tyrosine hydroxylase and dopamine transporters was detected using immunohistochemistry. Superoxide dismutase activity, glutathione peroxidase activity, and malondialdehyde expression were detected using an assay kit. Results: Our results show that GBE treatment improved locomotor activity and that superoxide dismutase and glutathione peroxidase inhibited the expression of methane dicarboxylic aldehyde and recovered the expression of tyrosine hydroxylase and dopamine transporters. Conclusions: The GBE treatment improved locomotor activity and inhibited the development of PD in the A53T α-synuclein transgenic mice, which may be partly responsible for decreased oxidative damage and maintain the normal dopamine homeostasis.

The purpose of this study was to investigate the joint associations of dietary pattern and television viewing with risk factors of CVD among urban adults in China. A community-based cross-sectional study was conducted among urban adults in Nanjing, China. Five dietary patterns were identified based on a FFQ. Television time was obtained from a standard questionnaire and further classified into two categories (≤7, >7 h/week). Multiple logistic regression was used to calculate the OR and 95 % CI for the separate and joint associations of dietary patterns and television viewing with CVD risk factors. Compared with other dietary patterns, participants who followed the healthy traditional pattern had a lower likelihood of abdominal obesity (AO) (OR 0·52; 95 % CI 0·41, 0·67). Participants watching television no more than 7 h/week presented a 19 and 21 % lower likelihood for hypertension (HT) and elevated total cholesterol (ETC) than those with television time >7 h/week. Individuals who had less television time and a healthy dietary pattern had a lower OR for the presence of AO (OR 0·48; 95 % CI 0·36, 0·65), HT (OR 0·71; 95 % CI 0·66, 0·77), ETC (OR 0·72; 95 % CI 0·57, 0·91) and elevated TAG (OR 0·76; 95 % CI 0·61, 0·95), compared with those who followed other dietary patterns and television time >7 h/week. In conclusion, both healthy traditional pattern and less television time are jointly associated with reduced levels of CVD risk factors. It has important public health implications regarding the precision prevention of CVD at population level.