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In this article, we study the following Schrödinger equation
\begin{align*}\begin{cases}-\Delta u -\frac{\mu}{|x|^2} u+\lambda u =f(u), &\text{in}~ \mathbb{R}^N\backslash\{0\},\\\int_{\mathbb{R}^{N}}|u|^{2}\mathrm{d} x=a, & u\in H^1(\mathbb{R}^{N}),\end{cases}\end{align*}
where $N\geq 3$, a > 0, and $\mu \lt \frac{(N-2)^2}{4}$. Here $\frac{1}{|x|^2} $ represents the Hardy potential (or ‘inverse-square potential’), λ is a Lagrange multiplier, and the nonlinearity function f satisfies the general Sobolev critical growth condition. Our main goal is to demonstrate the existence of normalized ground state solutions for this equation when $0 \lt \mu \lt \frac{(N-2)^2}{4}$. We also analyse the behaviour of solutions as $\mu\to0^+$ and derive the existence of normalized ground state solutions for the limiting case where µ = 0. Finally, we investigate the existence of normalized solutions when µ < 0 and analyse the asymptotic behaviour of solutions as $\mu\to 0^-$.
In this paper, we study the effect of lateral wall vibrations on the excitation and evolution of non-modal perturbations in hypersonic boundary layers subject to low-frequency freestream vortical disturbances (FSVDs). A novel, high-efficiency numerical approach, combining the harmonic weakly nonlinear Navier–Stokes and nonlinear parabolised stability equation approaches, is developed, which is sufficient to accommodate both the rapid distortion of the perturbation in the leading-edge vicinity and the nonlinear development of finite-amplitude high-order harmonics in the downstream region. The boundary-layer response to low-frequency FSVDs shows a longitudinal streaky structure, for which the temperature perturbation shows much greater magnitude than the streamwise velocity perturbation. The lateral vibration induces a Stokes layer solution for the spanwise velocity perturbation, which interacts with the FSVD-induced perturbations and leads to a suppression of the non-modal perturbation and an enhancement of the downstream modal perturbation. The new perturbations excited by the FSVD–vibration interaction strengthen as the vibration intensifies, and they could become comparable with the FSVD-induced perturbations in downstream locations at a high vibration intensity, indicating a remarkable modification of the streaky structure and its instability property. Secondary instability (SI) analyses based on the streaky base flow indicate that the vibration could enhance or suppress the SI modes, depending on their initial phases over the vibration period. Overall, the average effect is that the low-frequency and high-frequency SI modes are stabilised and destabilised by the vibration, respectively. Since the high-frequency SI modes undergo higher amplifications, the subsequent bypass transition is likely to be promoted by relatively strong vibrations.
The flexible flat cable (FFC) assembly task is a prime challenge in electronic manufacturing. Its characteristics of being prone to deformation under external force, tiny assembly tolerance, and fragility impede the application of robotic assembly in this field. To achieve reliable and stable robotic automation assembly of FFC, an efficient assembly skill acquisition strategy is presented by combining a parallel robot skill learning algorithm with adaptive impedance control. The parallel robot skill learning algorithm is proposed to enhance the efficiency of FFC assembly skill acquisition, which reduces the risk of damaging FFC and tackles the uncertain influence resulting from deformation during the assembly process. Moreover, FFC assembly is also a complex contact-rich manipulation task. An adaptive impedance controller is designed to implement force tracking during the assembly process without precise environment information, and the stability is also analyzed based on the Lyapunov function. Experiments of FFC assembly are conducted to illustrate the efficiency of the proposed method. The experimental results demonstrate that the proposed method is robust and efficient.
The tension distribution problem of cable-driven parallel robots is inevitable in real-time control. Currently, iterative algorithms or geometric algorithms are commonly used to solve this problem. Iterative algorithms are difficult to improve in real-time performance, and the tension obtained by geometric algorithms may not be continuous. In this paper, a novel tension distribution method for four-cable, 3-DOF cable-driven parallel robots is proposed based on the wave equation. The tension calculated by this method is continuous and differentiable, without the need for iterative computation or geometric centroid calculations, thus exhibiting good real-time performance. Furthermore, the feasibility and rationality of this algorithm are theoretically proven. Finally, the real-time performance and continuity of cable tension are analyzed through a specific numerical example.
The discovery that blazars dominate the extra-galactic $\gamma$-ray sky is a triumph in the Fermi era. However, the exact location of $\gamma$-ray emission region still remains in debate. Low-synchrotron-peaked blazars (LSPs) are estimated to produce high-energy radiation through the external Compton process, thus their emission regions are closely related to the external photon fields. We employed the seed factor approach proposed by Georganopoulos et al. It directly matches the observed seed factor of each LSP with the characteristic seed factors of external photon fields to locate the $\gamma$-ray emission region. A sample of 1 138 LSPs with peak frequencies and peak luminosities was adopted to plot a histogram distribution of observed seed factors. We also collected some spectral energy distributions (SEDs) of historical flare states to investigate the variation of $\gamma$-ray emission region. Those SEDs were fitted by both quadratic and cubic functions using the Markov-chain Monte Carlo method. Furthermore, we derived some physical parameters of blazars and compared them with the constraint of internal $\gamma\gamma$-absorption. We find that dusty torus dominates the soft photon fields of LSPs and most $\gamma$-ray emission regions of LSPs are located at 1–10 pc. The soft photon fields could also transition from dusty torus to broad line region and cosmic microwave background in different flare states. Our results suggest that the cubic function is better than the quadratic function to fit the SEDs.
Achieving optimal nutritional status in patients with penetrating Crohn’s disease is crucial in preparing for surgical resection. However, there is a dearth of literature comparing the efficacy of total parenteral nutrition (TPN) v. exclusive enteral nutrition (EEN) in optimising postoperative outcomes. Hence, we conducted a case-matched study to assess the impact of preoperative EEN v. TPN on the incidence of postoperative adverse outcomes, encompassing overall postoperative morbidity and stoma formation, among penetrating Crohn’s disease patients undergoing bowel surgery. From 1 December 2012 to 1 December 2021, a retrospective study was conducted at a tertiary centre to enrol consecutive patients with penetrating Crohn’s disease who underwent surgical resection. Propensity score matching was utilised to compare the incidence of postoperative adverse outcomes. Furthermore, univariate and multivariate logistic regression analyses were conducted to identify the risk factors associated with adverse outcomes. The study included 510 patients meeting the criteria. Among them, 101 patients in the TPN group showed significant improvements in laboratory indicators at the time of surgery compared with pre-optimisation levels. After matching, TPN increased the occurrence of postoperative adverse outcomes (92·2 % v. 64·1 %, P = 0·001) when compared with the EEN group. In the multivariate analysis, TPN showed a significantly higher OR for adverse outcomes than EEN (OR = 4·241; 95 % CI 1·567–11·478; P = 0·004). The study revealed that penetrating Crohn’s disease patients who were able to fulfil their nutritional requirements through EEN exhibited superior nutritional and surgical outcomes in comparison with those who received TPN.
Robots have the capability to perform precise and minimally invasive surgeries. For the robot-assisted teleoperated fracture reduction surgery, the operating accuracy largely depends on visual reference through fluoroscopy. The operator needs to adjust several times according to computed tomography (CT) image. During the robot reduction surgery, there are large muscle forces generated by the numerous muscles surrounding the fractured segments. However, there is no effective reduction force feedback to the master robot. In this paper, in order to improve the operating accuracy of the fracture reduction with teleoperated surgery mode, six-dimensional constraints of the master robot are studied by utilizing the virtual fixture method, which can restrict the position and orientation through the force and visual guidance. The six-dimensional force sensor is used to collect information of the reduction force. For the master robot, a motor stall control method based on the current loop is adopted to provide feedback of the reduction force, which can enhance the surgeon’s sense of operational presence. To verify the effectiveness of virtual fixture and force feedback, the fracture reduction experiments are conducted on the fractured model with simulating lager muscle force. Experimental results show that the reduction errors are within acceptable ranges: $0.03\pm 0.73\textrm{mm}$, $0.54\pm 0.43\textrm{mm}$, $0.46\pm 1.05\textrm{mm}$, $1.05\pm 1.31^{\circ}$, $1.15\pm 1.91^{\circ}$, $1.09\pm 2.61^{\circ}$. The number of fluoroscopy procedures required ranges from 1 to 2 and the average operation time is approximately 170 s. Compared to traditional methods and other teleoperation methods, the fracture reduction accuracy and surgical efficiency of method in this paper are significantly improved.
The fundamental resonance (FR) in the nonlinear phase of the boundary-layer transition to turbulence appears when a dominant planar instability mode reaches a finite amplitude and the low-amplitude oblique travelling modes with the same frequency as the dominant mode, together with the stationary streak modes, undergo the strongest amplification among all the Fourier components. This regime may be the most efficient means to trigger the natural transition in hypersonic boundary layers. In this paper, we aim to reveal the intrinsic mechanism of the FR in the weakly nonlinear framework based on the large-Reynolds-number asymptotic technique. It is found that the FR is, in principle, a triad resonance among a dominant planar fundamental mode, a streak mode and an oblique mode. In the major part of the boundary layer, the nonlinear interaction of the fundamental mode and the streak mode seeds the growth of the oblique mode, whereas the interaction of the oblique mode and the fundamental mode drives the roll components (transverse and lateral velocity) of the streak mode, which leads to a stronger amplification of the streamwise component of the streak mode due to the lift-up mechanism. This asymptotic analysis clearly shows that the dimensionless growth rates of the streak and oblique modes are the same order of magnitude as the dimensionless amplitude of the fundamental mode $(\bar {\epsilon }_{10})$, and the amplitude of the streak mode is $O(\bar {\epsilon }_{10}^{-1})$ greater than that of the oblique mode. The main-layer solution of the streamwise velocity, spanwise velocity and temperature of both the streak and the oblique modes become singular as the wall is approached, and so a viscous wall layer appears underneath. The wall layer produces an outflux velocity to the main-layer solution, inclusion of which leads to an improved asymptotic theory whose accuracy is confirmed by comparing with the calculations of the nonlinear parabolised stability equations (NPSEs) at moderate Reynolds numbers and the secondary instability analysis (SIA) at sufficiently high Reynolds numbers.
In this paper, we present a systematic study of the nonlinear evolution of the travelling Mack modes in a Mach 3 supersonic boundary layer over a rotating cone with a $7^{\circ }$ half-apex angle using the nonlinear parabolic stability equation (NPSE). To quantify the effect of cone rotation, six cases with different rotation rates are considered, and from the same streamwise position, a pair of oblique Mack modes with the same frequency but opposite circumferential wavenumbers are introduced as the initial perturbations for NPSE calculations. As the angular rotation rate $\varOmega$ increases such that $\bar \varOmega$ (defined as the ratio of the rotation speed of the cone to the streamwise velocity at the boundary-layer edge) varies from 0 to $O(1)$, three distinguished nonlinear regimes appear, namely the oblique-mode breakdown, the generalised fundamental resonance and the centrifugal-instability-induced transition. For each regime, the mechanisms for the amplifications of the streak mode and the harmonic travelling waves are explained in detail, and the dominant role of the streak mode in triggering the breakdown of the laminar flow is particularly highlighted. Additionally, from the linear stability theory, the dominant travelling mode undergoes the greatest amplification for a moderate $\varOmega$, which, according to the $e^N$ transition-prediction method, indicates premature transition to turbulence. However, this is in contrast to the NPSE results, in which a delay of the transition onset is observed for a moderate $\varOmega$. Such a disagreement is attributed to the different nonlinear regimes appearing for different rotation rates. Therefore, the traditional transition-prediction method based on the linear instability should be carefully employed if multiple nonlinear regimes may appear.
The relationship of a diet low in fibre with mortality has not been evaluated. This study aims to assess the burden of non-communicable chronic diseases (NCD) attributable to a diet low in fibre globally from 1990 to 2019.
Design:
All data were from the Global Burden of Disease (GBD) Study 2019, in which the mortality, disability-adjusted life-years (DALY) and years lived with disability (YLD) were estimated with Bayesian geospatial regression using data at global, regional and country level acquired from an extensively systematic review.
Setting:
All data sourced from the GBD Study 2019.
Participants:
All age groups for both sexes.
Results:
The age-standardised mortality rates (ASMR) declined in most GBD regions; however, in Southern sub-Saharan Africa, the ASMR increased from 4·07 (95 % uncertainty interval (UI) (2·08, 6·34)) to 4·60 (95 % UI (2·59, 6·90)), and in Central sub-Saharan Africa, the ASMR increased from 7·46 (95 % UI (3·64, 11·90)) to 9·34 (95 % UI (4·69, 15·25)). Uptrends were observed in the age-standardised YLD rates attributable to a diet low in fibre in a number of GBD regions. The burden caused by diabetes mellitus increased in Central Asia, Southern sub-Saharan Africa and Eastern Europe.
Conclusions:
The burdens of disease attributable to a diet low in fibre in Southern sub-Saharan Africa and Central sub-Saharan Africa and the age-standardised YLD rates in a number of GBD regions increased from 1990 to 2019. Therefore, greater efforts are needed to reduce the disease burden caused by a diet low in fibre.
Insulin-like growth factor 1 receptor (IGF1R) is a cell surface receptor, belonging to the tyrosine kinase receptor superfamily. IGF1R plays a role not only in normal cell development but also in malignant transformation, which has become a candidate therapeutic target for the treatment of human cancer. This study aimed to explore insertions and deletions (indels) in IGF1R gene and investigate their association with growth traits in four Chinese cattle breeds (Xianan cattle, Jinnan cattle, Qinchuan cattle and Nanyang cattle). The current paper identified a 28-bp indel by polymerase chain reaction within IGF1R gene. The analysis showed that there was a significant correlation between the locus and the hucklebone width of Nanyang cattle in four periods, in which it was highly correlated at 6, 12 and 18 months. At the age of 6 months, it was also significantly correlated with body height, body weight and body length. Association analysis showed that the locus in Jinnan cattle was extremely significantly correlated with body slanting length and body weight, and significantly correlated with chest circumference. There was no significant correlation between this locus and growth traits of Xianan cattle and Qinchuan cattle. The detected indel in the IGF1R gene was significantly associated with growth traits in Jinnan and Nanyang cattle, and could be used as a molecular marker for growth trait selection.
With the increase of crewed space missions and the rise of space microbiology, the research of microbes grown under microgravity environment has been attracting more attention. The research scope in space microbiology has been extended beyond pathogens directly related to spaceflight. Y. pestis, the causative agent of plague, is also of interest to researchers. After being cultivated for 40 consecutive passages in either simulated microgravity (SMG) or normal gravity (NG) conditions, the Y. pestis strain 201 cultures were analysed regarding their phenotypic features. By using crystal violet staining assays, increased biofilm amount was detected in Y. pestis grown under SMG condition. Besides that, the damage degrees of Hela cell caused by SMG-grown Y. pestis were found diminished in comparison to those under NG condition. Consistent with this observation, the death course was delayed in mice infected with SMG-grown Y. pestis, suggesting that microgravity condition can contribute the attenuated virulence. RNA-seq-based transcriptomics analysis showed that a total of 218 genes were differentially regulated, of which 91 upregulated and 127 downregulated. We found that dozens of virulence-associated genes were downregulated, which partially explained the reduced virulence of Y. pestis under SMG condition. Our study demonstrated that long-term exposure to SMG influences the pathogenesis and biofilm formation ability of Y. pestis, which provides a novel avenue to study the mechanism of physiology and virulence of this pathogen. Microgravity enhanced the ability of biofilm formation and reduced the virulence and cytotoxicity of Y. pestis. Many virulence-associated genes of Y. pestis were differentially regulated in response to the stimulated microgravity. However, there is no molecular evidence to explain the enhanced biofilm formation ability, which requires further research. Taken together, the phenotype changes of Y. pestis under SMG conditions can provide us a new research direction of its potential pathogenesis.
The Middle Miocene Climatic Optimum is known for abrupt events during the global cooling trend of the past 20 Ma. Its identification in the Tibetan Plateau can help explain the cause of the critical Middle Miocene climate transition in Central Asia. In this study, fine-grained mixed sediments widely distributed in the Miocene Qaidam Lake in the northern Tibetan Plateau were used as a sensitive indicator for palaeoclimate. Their geochemical characteristics were investigated, together with an analysis of 2600 m long successive gamma-ray logging data from the whole JS2 drillcore, to understand the mid-Miocene climate transition in the Tibetan Plateau. By comparing the gamma-ray curve of the mixed sediments with global temperature, the Middle Miocene Climatic Optimum event can be easily identified. Further, the detailed petrological features and geochemical data of lacustrine fine-grained mixed sediments from a 400 m drillcore show oxidizing, high-sedimentation rate and brackish-saline water conditions in a semi-arid climate during the Middle Miocene period, demonstrating a dryer climate in the Qaidam Basin than in the monsoon-sensitive regions in Central Asia. These fine-grained mixed sediments have recorded climate drying before 15.3 Ma that represents a climatic transition within the Middle Miocene Climatic Optimum; increasing carbonate-rich mixed sediments, decreasing algal limestone layers and decreasing lacustrine organic matter are indicators of this transition. Regional tectonic events include the retreat of the Paratethys from Central Asia at ∼15 Ma and the synchronous tectonic reorganization of the Altyn-Tagh fault system and the northeastern Tibetan Plateau. We find that global climate change is the primary factor affecting the overall characteristics and changes of the Neogene climate in the Qaidam Basin, including the occurrence of the Middle Miocene Climatic Optimum and the cooling and drying tendency, while the regional events are a secondary factor.
Increased intake of vegetables and fruits has been associated with reduced risk of tuberculosis infection. Vegetables and fruits exert immunoregulatory effects; however, it is not clear whether vegetables and fruits have an adjuvant treatment effect on tuberculosis. Between 2009 and 2013, a hospital-based cohort study was conducted in Linyi, Shandong Province, China. Treatment outcome was ascertained by sputum smear and chest computerised tomography, and dietary intake was assessed by a semi-quantitative FFQ. The dietary questionnaire was conducted at the end of month 2 of treatment initiation. Participants recalled their dietary intake of the previous 2 months. A total of 2309 patients were enrolled in this study. After 6 months of treatment, 2099 patients were successfully treated and 210 were uncured. In multivariate models, higher intake of total vegetables and fruits (OR 0·70; 95 % CI 0·49, 0·99), total vegetables (OR 0·68; 95 % CI 0·48, 0·97), dark-coloured vegetables (OR 0·61; 95 % CI 0·43, 0·86) and light-coloured vegetables (OR 0·67; 95 % CI 0·48, 0·95) were associated with reduced failure rate of tuberculosis treatment. No association was found between total fruit intake and reduced failure rate of tuberculosis treatment (OR 0·98; 95 % CI 0·70, 1·37). High intake of total vegetables and fruits, especially vegetables, is associated with lower risk of failure of tuberculosis treatment in pulmonary tuberculosis patients. The results provide important information for dietary guidelines during tuberculosis treatment.
A series of xLiMn0.5Fe0.5PO4–yLi3V2(PO4)3/C (x:y= 4:1, 3:1, 2:1, 1:1, 1:2, and 1:3) composite cathode materials for lithium-ion batteries are successfully prepared by the rheological phase reaction method. The structures, morphologies, and electrochemical properties of these composite materials are studied. The results indicate that xLiMn0.5Fe0.5PO4–yLi3V2(PO4)3/C composites are composed of LiMn0.5Fe0.5PO4 and Li3V2(PO4)3 phases and mutual doping exists. The initial discharge capacities, initial Coulombic efficiencies, and capacity retentions of composites increase but then decline with the increase of Li3V2(PO4)3 content. All the composites show higher capacity retentions than LiMn0.5Fe0.5PO4/C and Li3V2(PO4)3/C single phases except LMFP–3LVP/C. The composite material of x:y= 1:1 exhibits remarkably superior electrochemical performance than the single phases and other composites both in discharge capacity and cycle performance, delivering the initial discharge capacity of 148.2 mA h/g (2.0–4.5 V) and 170.1 mA h/g (2.0–4.8 V) at 0.1 C. And the corresponding capacity retentions are 98.0 and 90.4% after 100 cycles, respectively.
The oriental armyworm, Mythimna separata is an important crop pest in eastern Asia. Nocturnal insects, including nocturnal moths, have phototactic behavior to an artificial light source. Phototactic behavior in insects is species-specific in response to different wavelengths of light sources. Our previous study showed that green (520 nm) light emitting diode (LED) light resulted in a significantly higher phototactic behavior in M. separata moths compared to the other wavelength LED lights. The goal of the present study is to investigate the influence of green light illumination on biological characteristics of different developmental stages in M. separata. Our results revealed that when different developmental stages of M. separata were exposed to the green light illumination in a dark period, several biological characteristics in all developmental stages except for egg stage were positively changed, but those of F1 generation M. separata which are next generation of the adults exposed to the green light did not significantly change compared with the control level. These findings suggest that green light illumination at night (or dark period) has a positive effect on the development and longevity of M. separata.
AlMgB14–TiB2 ceramic was successfully brazed to TC4 alloy with inactive AgCu filler alloy. X-ray diffractometer, SEM, and energy-dispersive spectrometer were used to study interfacial microstructure and shear strength of the joints under different brazing temperatures. The results indicated that the typical microstructure of the TC4/AlMgB14–TiB2 joint was TC4/Ti(s.s) + Ti2Cu/Ti2Cu/TiCu/TiCu2Al/Ag(s.s) + Cu(s.s)/TiB whiskers/TiB2 reaction layer/AMBT. By increasing the brazing temperature, the thickness of the TC4 diffusion layer was improved, whereas that of the brazing seam decreased remarkably. When the brazing temperature was increased to 880 °C, the brazing seam was composed of Ti–Cu intermetallic Ag(s.s) with a few Cu(s.s), TiCu2Al distributed. Meanwhile, the formation of a continuous TiB2 reaction layer at the interface of the AMBT and brazing filler facilitated the improvement of joint shear strength. The joint with the maximum shear strength of 46.7 MPa was obtained while brazing at 880 °C for 10 min.
Obesity and insulin resistance play important roles in the pathogenesis of non-alcoholic fatty liver disease (NAFLD). Mg intake is linked to a reduced risk of metabolic syndrome and insulin resistance; people with NAFLD or alcoholic liver disease are at high risk of Mg deficiency. The present study aimed to investigate whether Mg and Ca intakes were associated with risk of fatty liver disease and prediabetes by alcohol drinking status.
Design
We analysed the association between Ca or Mg intake and fatty liver disease, prediabetes or both prediabetes and fatty liver disease in cross-sectional analyses.
Setting
Third National Health and Nutrition Examination Survey (NHANES III) follow-up cohort of US adults.
Subjects
Nationally representative sample of US adults in NHANES (n 13 489).
Results
After adjusting for potential confounders, Mg intake was associated with approximately 30 % reduced odds of fatty liver disease and prediabetes, comparing the highest intake quartile v. the lowest. Mg intake may only be related to reduced odds of fatty liver disease and prediabetes in those whose Ca intake is less than 1200 mg/d. Mg intake may also only be associated with reduced odds of fatty liver disease among alcohol drinkers.
Conclusions
The study suggests that high intake of Mg may be associated with reduced risks of fatty liver disease and prediabetes. Further large studies, particularly prospective cohort studies, are warranted to confirm the findings.