Bergelson and Richter [‘Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions’, Duke Math. J. 171(15) (2022), 3133–3200] established a new dynamical generalisation of the prime number theorem (PNT) and the PNT for arithmetic progressions. Let $h\ge 1, k\ge 2$. Mirsky [‘Note on an asymptotic formula connected with r-free integers’, Quart. J. Math. Oxford Ser. 18 (1947), 178–182] showed that the numbers n such that $n+l_1,\ldots , n+l_h$ are k-free have a natural density for any given nonnegative integers $l_1,\ldots , l_h$. In this note, we show that the Bergelson–Richter theorem holds for the numbers studied by Mirsky.

Objectives: UK policy priority is to support people with dementia (PLwD) to live at home for longer. Initial clinical assessment involves evaluating and managing risk to enable PLwD to live safely and well at home. Risk assessment scales are needed to identify, manage and reduce risk within contemporary dementia practice. The “Islington Dementia Navigator Risk Assessment Tool” (IDNRAT) is used by specialist and non-specialist staff to stratify the level of risk for PLwD and inform a risk management plan and the frequency of follow-up. We assessed whether IDNRAT enables risk detection and whether the risk intervention derived from it is implemented and improves the safety of people living at home with dementia.

Methods: A mixed Methods study to evaluate IDNRAT’s validity, and the feasibility and acceptability of the resulting risk management plan. We investigated the use of the IDNRAT to: (i) detect risk (concurrent validity) and measure the reliability of the tool; (ii) contribute to risk reduction (primary outcome was numbers of decisions implemented); (iii) explore patients’ and carers’ experience of risk stratification.

Results: We found risk stratification scores (n = 119) derived from IDNRAT and compared with gold standard clinical risk assessments showed concordance between clinicians’ ratings. Joint Dementia navigator and researcher interviews (n = 19) showed consistency between the different assessor scores demonstrating IDNRAT has good reliability. Care-plan data showed most participants (n = 275) scored in the low-risk band of IDNRAT (78.9%) at baseline assessment and risk severity ratings (red/amber/green) reduced over the 6–12-month time period. PLwD (n = 19) and family carers (n = 17) had differing perceptions about risk and the PLwD’s susceptibility to risk. Overall, participants found the risk assessment acceptable, were able to identify risks and felt included in decision-making processes.

Conclusions: We found that the IDNRAT used by non-specialist practitioners (dementia navigators) does enable people with dementia to live safely at home in terms of risk- identification, implemented risk enablement decisions and acceptability. IDNRAT is a valid risk assessment tool, which offers a tailored approach to the management of risk, and over 80% of care-plan decisions were implemented. This is consistent with best practice and the tool has potential for wider use.

Timing of food intake is an emerging aspect of nutrition; however, there is a lack of research accurately assessing food timing in the context of the circadian system. The study aimed to investigate the relation between food timing relative to clock time and endogenous circadian timing with adiposity and further explore sex differences in these associations among 151 young adults aged 18–25 years. Participants wore wrist actigraphy and documented sleep and food schedules in real time for 7 consecutive days. Circadian timing was determined by dim-light melatonin onset (DLMO). The duration between last eating occasion and DLMO (last EO-DLMO) was used to calculate the circadian timing of food intake. Adiposity was assessed using bioelectrical impedance analysis. Of the 151 participants, 133 were included in the statistical analysis finally. The results demonstrated that associations of adiposity with food timing relative to circadian timing rather than clock time among young adults living in real-world settings. Sex-stratified analyses revealed that associations between last EO-DLMO and adiposity were significant in females but not males. For females, each hour increase in last EO-DLMO was associated with higher BMI by 0·51 kg/m2 (P = 0·01), higher percent body fat by 1·05 % (P = 0·007), higher fat mass by 0·99 kg (P = 0·01) and higher visceral fat area by 4·75 cm2 (P = 0·02), whereas non-significant associations were present among males. The findings highlight the importance of considering the timing of food intake relative to endogenous circadian timing instead of only as clock time.

In order to solve the problem of the insufficient adaptability of the current small- and medium-sized casting sorting robot gripper, we have designed a casting sorting robot bionic gripper with rigid–flexible coupling structures based on the robot topology theory. The second-order Yeoh model was used to statically model the clamping belt in the gripper to derive the relationship between the external input air pressure and the bending angle of the driving layer, and the feasibility of multiangle bending of the driving layer was verified by finite element analysis. The maximum gripping diameter of the gripper is 140 mm, and in order to test the adaptive gripping ability of the gripper, a prototype of the casting sorting robot gripper is prepared, and the pneumatic control system and human–machine interface of the gripper are designed. After several experimental analyses, the designed casting sorting robot gripper is characterized by strong adaptability and high robustness, with a maximum load capacity of 930 g and a maximum wrap angle of 296°, which can complete the gripping operation within 1 s, and the comprehensive gripping success rate reaches 96.4%. The casting sorting robot gripper designed in the paper can provide a reference for the design and optimization of various types of shaped workpiece gripping manipulators.

The axial offset joint has two rotating axes that do not intersect but have a specific offset in space. It is used widely in parallel manipulators (PMs). The offset-joint workspace can directly affect the PM workspace. This study performed a theoretical derivation and workspace analysis of a class of axial offset joints. First, a theoretical parametric model describing the rotation range of the offset joint is established that considers the interference of the offset joint because of the contact between the upper- and lower-joint brackets during movement. Second, the analytical expressions of the offset-joint workspace are formulated based on the coordinate system transformation. The offset-joint workspace is theoretically calculated in this study using formulations. Then, through a comparative analysis, the superiority of the offset joint compared with the universal joint is verified. The theoretical formulations in this paper can be used to calculate the workspace of a class of axial offset joints. Finally, based on a workspace analysis of three types of PMs using offset, universal, and spherical joints, the offset-joint PM workspace is much larger than those of the other two types.

This paper presents a novel method to improve the working bandwidth and radiation intensity of piezoelectric antenna by using external circuit. This method makes the piezoelectric antenna combined with roles of high radiation intensity and multiple resonant frequencies without changing the structural size of the piezoelectric antenna. The experimental results show that, compared with the original piezoelectric antenna, the tuning range of the resonant frequency of the piezoelectric antenna caused by the series capacitance and inductance is +13.6 and −24%, respectively. The series inductance will produce new resonance frequency, which provides a new method for the multi-band operation of the piezoelectric antenna. The LLC (series and parallel circuit) composite circuit can increase the number of resonant frequencies of the piezoelectric antenna from 1 to 3, and the S11 at the resonant frequencies are all lower than −10 dB, and the radiated magnetic field of the piezoelectric antenna is increased by 42.3% at least. This method makes the piezoelectric antenna have the dual functions of high radiation intensity and multi-band, which has great significance for broadening the application field of piezoelectric antenna.

The knee joint plays a significant role in ground clearness, which is a crucial subtask of normal walking and avoiding falls. While post-stroke survivors are often faced with muscle weakness during walking, which leads to inadequate knee flexion. The lack of ground clearance caused by inadequate knee flexion will severely impede walking, increase metabolic exertion, and increase the risk of falls. A compliant exoskeleton robot possesses more favorable edges than other rigid ones in lightweight, safety, sense of comfort, and so on. We developed a new type of soft exoskeleton robot to assist the knee joint to achieve desired movements with Bowden cable transmitting force and torque. With the agonist–antagonist driving method, like a group of muscles working, we have explored dual-motors structure to realize the knee flexion function. It has built a standard dynamic model to analyze stability and realize the control law. We have conducted simulation and prototype experiments to verify the feasibility and usefulness of our method. The results show that the device can compensate for the lack of the knee joint driving force and realize the reference movement. Finally, we concluded that our method is a desirable way, and the scheme could improve the knee flexion ability and clearing ground.

Representing complex flows by evolving vortex structures is an important principle in many investigations of wall-bounded turbulence. The practice of this principle benefits from the bi-directional transformation between the velocity field and the corresponding vortex field. While the velocity-to-vortex transformation could be implemented by various vortex identification criteria, few efforts have been devoted to the inverse process. This work develops a linear reconstruction method, which allows an effective reconstruction for the velocity field of wall turbulence based on a given vortex field. The vortex field is defined as a vector field by combining the swirl strength and the real eigenvector of the velocity gradient tensor. The reconstructed velocity fields are calculated by convolution operations on the vortex fields, with the kernel functions derived by the field-based linear stochastic estimation. The method can effectively recover the turbulent motions in a large scale range, showing clear advantages over the Biot–Savart formula in the near-wall region. The method is also employed to investigate the inducing effects of vortices at different heights. The wall-bounding effect on the induced motions is observed from the contribution spectra of vortices. The higher-order moments of the reconstructed streamwise velocity component present larger deviations from the original data, which is discussed and explained reasonably. At last, the vortex fields filtered by prescribed thresholds are employed to reconstruct the velocity fields. It is found that the strongest vortex components occupying 5 % of the total volume can reasonably recover the main flow features including both the near-wall streaks and the large-scale motions.

The eastern margin of the Tibetan Plateau, a global biodiversity hotspot, is threatened by habitat degradation. Conservation actions are required in this region, but limited knowledge of large and medium-sized mammals is hampering conservation planning. Using 149 camera traps, we surveyed large and medium-sized mammals in Xionglongxi Provincial Nature Reserve and adjacent areas, on the eastern margin of the Tibetan Plateau, during September 2016–May 2017. We obtained 5,752 independent captures of 29 large and medium-sized mammal species, including 13 that are globally threatened and 22 that are nationally threatened in China. Carnivores were especially diverse, with 16 species recorded. Of particular significance was our detection of seven felid species, including the leopard Panthera pardus and the snow leopard Panthera uncia. Our record of the Chinese mountain cat Felis bieti extends the known range of this species. We documented new upper elevation limits for eight species. There was elevational overlap between the leopard and the snow leopard, suggesting potential competition between the two species. The grey wolf Canis lupus and the leopard were the dominant predators, and the woolly hare Lepus oiostolus and several species of ungulates were the most frequently photographed prey species. The study area maintains a significant community of large and medium-sized mammals, which is more diverse than in other areas on the eastern edge of the Tibetan Plateau. We recommend the establishment of a larger nature reserve of national protection status in the region of the Xionglongxi Provincial Nature Reserve, to protect the unique subalpine and alpine ecosystems in this area.

The Shuangjianzishan vein-type Ag-Pb-Zn deposit in the southern Great Xing’an Range (GXR), NE China, is hosted in the slate of the Lower Permian Dashizhai Formation intruded by granite porphyry. In this paper, U–Pb zircon ages and bulk-rock and isotope (Sr, Nd, Pb and Hf) compositions are reported to investigate the derivation, evolution and geodynamic setting of this granite porphyry. It is closely associated with Pb-Zn-Ag mineralization in the southern GXR and contains important geological information relating to regional tectonic evolution. Laser ablation – inductively coupled plasma – mass spectrometry (LA-ICP-MS) zircon U–Pb dating yields an emplacement age of 131 ± 1 Ma for the granite porphyry. Bulk-rock analyses show that the Shuangjianzishan granite porphyry is characterized by high Si, Na and K contents but low Mg and Fe contents, and that the enrichment of Zr, Y and Ga suggests an A-type granite affinity. Most of the studied samples have relatively low 87Sr/86Sr values (0.70549–0.70558), with positive ϵNd(t) (0.71–0.88) and ϵHf(t) (4.9–6.9) values. The Sr–Nd isotope modelling results, in combination with the young TDM2 ages of Nd and Hf (850–864 and 668–778 Ma, respectively), reveal that the Shuangjianzishan granite porphyry may be derived from the melting of mantle-derived juvenile component, with minor lower crustal components; this finding is also supported by Pb isotopic compositions. Considering the widespread presence of granitoids with coeval volcanic rocks and regional geology data, we propose that the Shuangjianzishan granite porphyry formed in a post-orogenic extensional environment related to the upwelling of asthenospheric mantle following the closure of the Mongol–Okhotsk Ocean.

This article addresses recent advances in liquid phase transmission electron microscopy (LPTEM) for studying nanoscale synthetic processes of carbon-based materials that are independent of the electron beam—those driven by nonradiolytic chemical or thermal reactions. In particular, we focus on chemical/physical formations and the assembly of nanostructures composed of organic monomers/polymers, peptides/DNA, and biominerals. The synthesis of carbon-based nanomaterials generally only occurs at specific conditions, which cannot be mimicked by aqueous solution radiolysis. Carbon-based structures themselves are also acutely sensitive to the damaging effects of the irradiating beam, which make studying their synthesis using LPTEM a unique challenge that is possible when beam effects can be quantified and mitigated. With new direct sensing, high frame-rate cameras, and advances in liquid cell holder designs, combined with a growing understanding of irradiation effects and proper experimental controls, microscopists have been able to make strides in observing traditionally problematic carbon-based materials under conditions where synthesis can be controlled, and imaged free from beam effects, or with beam effects quantified and accounted for. These materials systems and LPTEM experimental techniques are discussed, focusing on nonradiolytic chemical and physical transformations relevant to materials synthesis.

Renal fibrosis is common especially in the elderly population. Recently, we found that vitamin D deficiency caused prostatic hyperplasia. This study aimed to investigate whether vitamin D deficiency promotes renal fibrosis and functional impairment. All mice except controls were fed with vitamin D-deficient (VDD) diets, beginning from their early life. The absolute and relative kidney weights on postnatal week 20 were decreased in VDD diet-fed male pups but not in female pups. A mild pathological damage was observed in VDD diet-fed male pups but not in females. Further analysis showed that VDD-induced pathological damage was aggravated, accompanied by renal dysfunction in 40-week-old male pups. An obvious collagen deposition was observed in VDD diet-fed 40-week-old male pups. Moreover, renal α-smooth muscle actin (α-SMA), a marker of epithelial–mesenchymal transition (EMT), and Tgf-β mRNA were up-regulated. The in vitro experiment showed that 1,25-dihydroxyvitamin D3 alleviated transforming growth factor-β1 (TGF-β1)-mediated down-regulation of E-cadherin and inhibited TGF-β1-evoked up-regulation of N-cadherin, vimentin and α-SMA in renal epithelial HK-2 cells. Moreover, 1,25-dihydroxyvitamin D3 suppressed TGF-β1-evoked Smad2/3 phosphorylation in HK-2 cells. These results provide experimental evidence that long-term vitamin D deficiency promotes renal fibrosis and functional impairment, at least partially, through aggravating TGF-β/Smad2/3-mediated EMT in middle-aged male mice.

The limit behavior of partial sums for short range dependent stationary sequences (with summable autocovariances) and for long range dependent sequences (with autocovariances summing up to infinity) differs in various aspects. We prove central limit theorems for partial sums of subordinated linear processes of arbitrary power rank which are at the border of short and long range dependence.

During recent stratigraphical and micropaleontological investigations of the Gulupu section in Tüna, Yadong, of the Eocene Zhepure Formation, numerous holoplanktonic mollusks (pteropods) were recovered. Four species, assignable to two genera of pteropods (including Limacina yadongensis new species) were systematically described and illustrated, and a gastropod-bivalve biofacies was identified. This is the first report of Eocene (Ypresian) pteropods in southern Tibet; the same stratum also yields many other neritic faunas. The data presented in this study suggest that a semi-closed restricted gulf in the Tüna area existed and the occurrence of pteropods in Tüna may indicate transport from more open, deep water by oceanic currents during early Eocene. Based on the analysis of paleogeographical distribution of pteropods, it indicates that a Tethys seaway existed during the early Eocene (Ypresian).

UUID: http://zoobank.org/7eb6f8dd-a973-4834-986a-310008476eb0

Outbreaks of norovirus-associated gastroenteritis have been reported in schools in recent decades in China. For early warning and response to infectious disease outbreaks, the Shanghai Infectious Diseases Bud Event Surveillance System (IDBESS) was established in 2016. Bud event is a term used for the early sign of a potential infectious disease outbreak in public settings when the first few cases appear. This study aimed to describe the epidemiological characteristics of Norovirus-associated gastroenteritis bud events from June 2016 to December 2017 and to understand factors influencing the severity of events. Data were extracted from the IDBESS, supplemented by field investigations and school absence surveillance. In total, 189 bud events of Norovirus-associated gastroenteritis were reported in schools and kindergartens, affecting 3827 individuals and 52.38% happened in primary schools. The attack rate of Norovirus-associated gastroenteritis was 3.82% on average in students in the affected schools. In each event, case numbers varied between 5 and 148, with a median of 16. The duration of bud events lasted for 2 days on average. School absence happened in 47.93% (1797/3749) of affected students and the average duration of absence was 3.07 days. It was found that a longer delay before reporting was associated with a longer-lasting duration of bud event (OR = 2.25, 95% CI: 1.65, 3.07). In conclusion, ascribed to the sensitive threshold for alerting and the timely field investigation, the surveillance of bud events of Norovirus-associated gastroenteritis is effective in the control of Norovirus infection among preschool children and students in Shanghai.

The association between milk consumption and the metabolic syndrome remains inconclusive, and data from Chinese populations are scarce. We conducted a cross-sectional study to investigate the association between milk consumption and the metabolic syndrome and its components among the residents of Suzhou Industrial Park, Suzhou, China. A total of 5149 participants were included in the final analysis. A logistic regression model was applied to estimate the OR and 95 % CI for the prevalence of the metabolic syndrome and its components according to milk consumption. In addition, the results of our study were further meta-analysed with other published observational studies to quantify the association between the highest v. lowest categories of milk consumption and the metabolic syndrome and its components. There was no significant difference in the odds of having the metabolic syndrome between milk consumers and non-milk consumers (OR 0·86, 95 % CI 0·73, 1·01). However, milk consumers had lower odds of having elevated waist circumference (OR 0·78, 95 % CI 0·67, 0·92), elevated TAG (OR 0·83, 95 % CI 0·70, 0·99) and elevated blood pressure (OR 0·85, 95 % CI 0·73, 0·99). When the results were pooled together with other published studies, higher milk consumption was inversely associated with the risk of the metabolic syndrome (relative risk 0·80, 95 % CI 0·72, 0·88) and its components (except elevated fasting blood glucose); however, these results should be treated with caution as high heterogeneity was observed. In summary, the currently available evidence from observational studies suggests that higher milk consumption may be inversely associated with the metabolic syndrome.

Vortex structures are very popular research objects in turbulent boundary layers (TBLs) because of their prime importance in turbulence modelling. This work performs a tomographic particle image velocimetry measurement on the near-wall region ($y<0.1\unicode[STIX]{x1D6FF}$) of TBLs at three Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=1238$, 2286 and 3081. The main attention is paid to the wall-normal evolution of the vortex geometries and topologies. The vortex is identified with swirl strength ($\unicode[STIX]{x1D706}_{ci}$), and its orientation is recognized by using the real eigenvector of the velocity gradient tensor. The vortex inclination angles in the streamwise–wall-normal plane and in the streamwise–spanwise plane as functions of wall-normal positions are investigated, which provide useful information to speculate on the three-dimensional shape of the vortex tubes in a TBL. The difference between the orientations of vorticity and swirl is discussed and their inherent relationship is revealed based on the governing equation of vorticity. Linear stochastic estimation (LSE) is further deployed to directly extract three-dimensional vortex models. The LSE velocity fields for ejection events happening at different wall-normal positions shed light on the evolution of the topologies for the vortices dominating ejection events. LSE based on a centred prograde spanwise vortex provides a typical packet model, which indicates that the population density of the packets in a TBL is large enough to leave footprints in conditionally averaged flow fields. This work should help to settle the severe debate on the existence of packet structures and also lays some foundation for the TBL model theory.

Post-irradiation plastic strain spreading in ferritic grains is investigated by means of three-dimensional dislocation dynamics simulations, whereby dislocation-mediated plasticity mechanisms are analyzed in the presence of various disperse defect populations, for different grain size and orientation cases. Each simulated irradiation condition is then characterized by a specific “defect-induced apparent straining temperature shift” (ΔDIAT) magnitude, reflecting the statistical evolutions of dislocation mobility. It is found that the calculated ΔDIAT level closely matches the ductile-to-brittle transition temperature shift (ΔDBTT) associated with a given defect dispersion, characterized by the (average) defect size D and defect number density N. The noted ΔDIAT/ΔDBTT correlation can be explained based on plastic strain spreading arguments and applicable to many different ferritic alloy compositions, at least within the range of simulation conditions examined herein. This systematic study represents one essential step toward the development of a fully predictive, dose-dependent fracture model, adapted to polycrystalline ferritic materials.