We prove some zero density theorems for certain families of Dirichlet L-functions. More specifically, the subjects of our interest are the collections of Dirichlet L-functions associated with characters to moduli from certain sparse sets and of certain fixed orders.

Flow transitions are an important fluid-dynamic phenomena for many reasons, including the direct effect on the aerodynamic forces acting on the body. In the present study, two-dimensional (2-D) and three-dimensional (3-D) wake transitions of a NACA0012 airfoil are studied for angles of attack in the range $0^\circ \leq \alpha \leq 20^\circ$ and Reynolds numbers $500 \leq {\textit {Re}} \leq 5000$. The study uses water-channel experiments and 2-D and 3-D numerical simulations based on the nodal spectral-element method, level-set function-based immersed-interface method and Floquet stability analysis. The different wake states are categorised based on the time-instantaneous wake structure, non-dimensional frequency and aerodynamic force coefficients. The wake states and transition boundaries are summarised in a wake regime map. The critical angle of attack and Reynolds number for the supercritical Hopf bifurcation (i.e. steady to periodic wake transition) varies as $\alpha _1 {\sim} {\textit {Re}}^{-0.65}$, while the critical angle of attack for the onset of three dimensionality varies as $\alpha _{3D} {\sim} {\textit {Re}}^{-0.5}$. Over the entire Reynolds number range, the transition to 3-D flow occurs through a mode C (subharmonic) transition. Beyond this initial transition, further instabilities of the 2-D periodic base flow arise and are investigated. For instance, at $ {\textit {Re}}=2000$ and $\alpha _{3D,2}=11.0^\circ$, mode C coexists together with modes related to modes A and QP seen in a stationary circular cylinder wake. In contrast, at $ {\textit {Re}}=5000$ and $\alpha _{3D,2}=8.0^\circ$, the dominant mode C coexists with mode QP. Three-dimensional simulations well beyond critical angles indicate that 2-D vortex-street transitions are approximately maintained in the fully saturated 3-D wakes in a spanwise-averaged sense.

Meat quality is not only influenced by breed but also rearing environment. The aim of this study was to evaluate the influence of different housing environments on growth performance, carcase traits, meat quality, physiological response pre-slaughter and fatty acid composition in two pig breeds. A total of 120 growing pigs at 60-70 days of age were arranged in a 2 × 2 factorial design with the breeds (Duroc × Landrace × Large White [D × L × LW] and Duroc × Landrace × Min pig [D × L × M]) and environmental enrichment (barren concrete floor or enriched with straw bedding) as factors. Each treatment was performed in triplicate with ten pigs per replicate. The pigs housed in the enriched environment exhibited a higher average daily gain, average daily feed intake, saturated fatty acid percentage and backfat depth than the pigs reared in the barren environment. Plasma cortisol levels were lower and growth hormone higher in enriched compared to barren pens. The D × L × M pigs showed lower cooking loss compared with the D × L × LW pigs. Moreover, the D × L × M pigs exhibited poor growth performance but had a better water-holding capacity. Only carcase traits and meat quality interaction effects were observed. We concluded that an enriched environment can reduce preslaughter stress and improve the growth performance of pigs and modulate the fatty acid composition of pork products.

Numerical simulations have been conducted to identify the dominant mechanism responsible for driving secondary flow motions in horizontal particle-laden pipe flows, based on an analysis of the forces acting on each phase. A four-way coupling Euler–Lagrangian approach was employed, using direct numerical simulations for the gas phase and Lagrangian particle tracking to account for the drag, gravitational and lift forces, together with the interactions that occur for both particle–wall and inter-particle collisions. The four different flow regimes, which had been identified previously as depending on various combinations of flow parameters and are characterised by the secondary flow structures of both the fluid and particle phases, were identified via varying the mass loading alone from $\varPhi _m=0.4$ to $\varPhi _m=1.8$. The distribution of the divergence of Reynolds stresses was used to help characterise the classes of the secondary fluid flow. This shows that secondary fluid flows of both the first and second kinds can either exist separately or co-exist in such flows. The forces exerted on the fluid phase by the pressure gradient and fluid–particle interactions were examined qualitatively and quantitatively to identify their contribution to the secondary fluid flow motions. A similar study was also applied to the drag, lift and gravitational forces exerted on the particle phase for the secondary particle flow motions. These were found to explain the secondary flows of both the fluid and particle phases with regard to both the flow direction and magnitude, together with the interaction between the two phases.

We present a decomposition of the streamwise fluid force for in-line vortex-induced vibration (VIV) to provide insight into how the wake drag acts as a driving force in fluid–structure interaction. This force decomposition is an extension of that proposed in the recent work of Konstantinidis et al. (J. Fluid Mech., vol. 907, 2021, p. A34), and is applied to and validated by our experiments examining a circular cylinder freely vibrating in line with the free stream. It is revealed from the decomposition and linear analysis that two regimes of significant vibration are in phase synchronisation, while they are separated by a desynchronised regime marked by competition between non-stationary frequency responses of the cylinder vibration and the vortex shedding. Of interest, such a near-resonance desynchronisation regime is not seen in the transverse vibration case.

The incidence of scarlet fever has increased dramatically in recent years in Chongqing, China, but there has no effective method to forecast it. This study aimed to develop a forecasting model of the incidence of scarlet fever using a seasonal autoregressive integrated moving average (SARIMA) model. Monthly scarlet fever data between 2011 and 2019 in Chongqing, China were retrieved from the Notifiable Infectious Disease Surveillance System. From 2011 to 2019, a total of 5073 scarlet fever cases were reported in Chongqing, the male-to-female ratio was 1.44:1, children aged 3–9 years old accounted for 81.86% of the cases, while 42.70 and 42.58% of the reported cases were students and kindergarten children, respectively. The data from 2011 to 2018 were used to fit a SARIMA model and data in 2019 were used to validate the model. The normalised Bayesian information criterion (BIC), the coefficient of determination (R2) and the root mean squared error (RMSE) were used to evaluate the goodness-of-fit of the fitted model. The optimal SARIMA model was identified as (3, 1, 3) (3, 1, 0)12. The RMSE and mean absolute per cent error (MAPE) were used to assess the accuracy of the model. The RMSE and MAPE of the predicted values were 19.40 and 0.25 respectively, indicating that the predicted values matched the observed values reasonably well. Taken together, the SARIMA model could be employed to forecast scarlet fever incidence trend, providing support for scarlet fever control and prevention.

Understanding the size of oil droplets released from a jet in crossflow is crucial for estimating the trajectory of hydrocarbons and the rates of oil biodegradation/dissolution in the water column. We present experimental results of an oil jet with a jet-to-crossflow velocity ratio of 9.3. The oil was released from a vertical pipe 25 mm in diameter with a Reynolds number of 25 000. We measured the size of oil droplets near the top and bottom boundaries of the plume using shadowgraph cameras and we also filmed the whole plume. In parallel, we developed a multifluid large eddy simulation model to simulate the plume and coupled it with our VDROP population balance model to compute the local droplet size. We accounted for the slip velocity of oil droplets in the momentum equation and in the volume fraction equation of oil through the local, mass-weighted average droplet rise velocity. The top and bottom boundaries of the plume were captured well in the simulation. Larger droplets shaped the upper boundary of the plume, and the mean droplet size increased with elevation across the plume, most likely due to the individual rise velocity of droplets. At the same elevation across the plume, the droplet size was smaller at the centre axis as compared with the side boundaries of the plume due to the formation of the counter-rotating vortex pair, which induced upward velocity at the centre axis and downward velocity near the sides of the plume.

Calculi with disjoint intersection types support a symmetric merge operator with subtyping. The merge operator generalizes record concatenation to any type, enabling expressive forms of object composition, and simple solutions to hard modularity problems. Unfortunately, recent calculi with disjoint intersection types and the merge operator lack a (direct) operational semantics with expected properties such as determinism and subject reduction, and only account for terminating programs. This paper proposes a type-directed operational semantics (TDOS) for calculi with intersection types and a merge operator. We study two variants of calculi in the literature. The first calculus, called λi, is a variant of a calculus presented by Oliveira et al. (2016) and closely related to another calculus by Dunfield (2014). Although Dunfield proposes a direct small-step semantics for her calculus, her semantics lacks both determinism and subject reduction. Using our TDOS, we obtain a direct semantics for λi that has both properties. The second calculus, called λi+, employs the well-known subtyping relation of Barendregt, Coppo and Dezani-Ciancaglini (BCD). Therefore, λi+ extends the more basic subtyping relation of λi, and also adds support for record types and nested composition (which enables recursive composition of merged components). To fully obtain determinism, both λi and λi+ employ a disjointness restriction proposed in the original λi calculus. As an added benefit the TDOS approach deals with recursion in a straightforward way, unlike previous calculi with disjoint intersection types where recursion is problematic. We relate the static and dynamic semantics of λi to the original version of the calculus and the calculus by Dunfield. Furthermore, for λi+, we show a novel formulation of BCD subtyping, which is algorithmic, has a very simple proof of transitivity and allows for the modular addition of distributivity rules (i.e. without affecting other rules of subtyping). All results have been fully formalized in the Coq theorem prover.

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full two-dimensional (2D) image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields, and other sample-dependent properties. However, extracting this information requires complex analysis pipelines that include data wrangling, calibration, analysis, and visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open-source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail and present results from several experimental datasets. We also implement a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open-source HDF5 standard. We hope this tool will benefit the research community and help improve the standards for data and computational methods in electron microscopy, and we invite the community to contribute to this ongoing project.

Student's t test is valid for statistical inference under the normality assumption or asymptotically. By contrast, although the bootstrap t test was proposed in 1993, it is seldom adopted in medical research. We aim to demonstrate that the bootstrap t test outperforms Student's t test under normality in data. Using random data samples from normal distributions, we evaluated the testing performance, in terms of true-positive rate (TPR) and false-positive rate and diagnostic abilities, in terms of the area under the curve (AUC), of the bootstrap t test and Student's t test. We explore the AUC of both tests with varying sample size and coefficient of variation. We compare the testing outcomes using the COVID-19 serial interval (SI) data in Shenzhen and Hong Kong, China, for demonstration. With fixed TPR, the bootstrap t test maintained the equivalent accuracy in TPR, but significantly improved the true-negative rate from the Student's t test. With varying TPR, the diagnostic ability of bootstrap t test outperformed or equivalently performed as Student's t test in terms of the AUC. The equivalent performances are possible but rarely occur in practice. We find that the bootstrap t test outperforms by successfully detecting the difference in COVID-19 SI, which is defined as the time interval between consecutive transmission generations, due to sex and non-pharmaceutical interventions against the Student's t test. We demonstrated that the bootstrap t test outperforms Student's t test, and it is recommended to replace Student's t test in medical data analysis regardless of sample size.

We present 63 new multi-site radial velocity (RV) measurements of the K1III giant HD 76920, which was recently reported to host the most eccentric planet known to orbit an evolved star. We focused our observational efforts on the time around the predicted periastron passage and achieved near-continuous phase coverage of the corresponding RV peak. By combining our RV measurements from four different instruments with previously published ones, we confirm the highly eccentric nature of the system and find an even higher eccentricity of $e=0.8782 \pm 0.0025$ , an orbital period of $415.891^{+0.043}_{-0.039}\,\textrm{d}$ , and a minimum mass of $3.13^{+0.41}_{-0.43}\,\textrm{M}_{\textrm{J}}$ for the planet. The uncertainties in the orbital elements are greatly reduced, especially for the period and eccentricity. We also performed a detailed spectroscopic analysis to derive atmospheric stellar parameters, and thus the fundamental stellar parameters ( $M_*, R_*, L_*$ ), taking into account the parallax from Gaia DR2, and independently determined the stellar mass and radius using asteroseismology. Intriguingly, at periastron, the planet comes to within 2.4 stellar radii of its host star’s surface. However, we find that the planet is not currently experiencing any significant orbital decay and will not be engulfed by the stellar envelope for at least another 50–80 Myr. Finally, while we calculate a relatively high transit probability of 16%, we did not detect a transit in the TESS photometry.

An explainable, efficient, and lightweight method for texture generation, called TGHop (an acronym of Texture Generation PixelHop), is proposed in this work. Although synthesis of visually pleasant texture can be achieved by deep neural networks, the associated models are large in size, difficult to explain in theory, and computationally expensive in training. In contrast, TGHop is small in its model size, mathematically transparent, efficient in training and inference, and able to generate high-quality texture. Given an exemplary texture, TGHop first crops many sample patches out of it to form a collection of sample patches called the source. Then, it analyzes pixel statistics of samples from the source and obtains a sequence of fine-to-coarse subspaces for these patches by using the PixelHop++ framework. To generate texture patches with TGHop, we begin with the coarsest subspace, which is called the core, and attempt to generate samples in each subspace by following the distribution of real samples. Finally, texture patches are stitched to form texture images of a large size. It is demonstrated by experimental results that TGHop can generate texture images of superior quality with a small model size and at a fast speed.