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Gradual typing integrates static and dynamic typing by introducing a dynamic type and a consistency relation. A problem of gradual type systems is that dynamic types can easily hide erroneous data flows since consistency relations are not transitive. Therefore, a more rigorous static check is required to reveal these hidden data flows statically. However, in order to preserve the expressiveness of gradually typed languages, static checks for gradually typed languages cannot simply reject programs with potentially erroneous data flows. By contrast, a more reasonable request is to show how these data flows can affect the execution of the program. In this paper, we propose and formalize Static Blame, a framework that can reveal hidden data flows for gradually typed programs and establish the correspondence between static-time data flows and runtime behavior. With this correspondence, we build a classification of potential errors detected from hidden data flows and formally characterize the possible impact of potential errors in each category on program execution, without simply rejecting the whole program. We implemented Static Blame on Grift, an academic gradually typed language, and evaluated the effectiveness of Static Blame by mutation analysis to verify our theoretical results. Our findings revealed that Static Blame exhibits a notable level of precision and recall in detecting type-related bugs. Furthermore, we conducted a manual classification to elucidate the reasons behind instances of failure. We also evaluated the performance of Static Blame, showing a quadratic growth in run time as program size increases.
In the Three Gorges and adjacent areas, there are three planation surfaces and five terraces along the Yangtze River that record the evolution history of the river system. Here, we used diagnostic heavy minerals, U-Pb geochronology, and trace elements of detrital zircons from one planation surface, two terraces, and a modern point bar to reconstruct the evolution history of the upper Yangtze River, specifically the Chuan River in the Sichuan Basin. The sediments in the lowest planation surface had different felsic source rocks derived from east of the Three Gorges, which indicated that before the disintegration of the lowest planation surface (0.75 Ma), there were two paleorivers: the westward-flowing paleo-Chuan River and eastward-flowing paleo-Yangtze River separated by the Huangling Dome. At 0.75–0.73 Ma, the dominant detrital zircons from the Sichuan Basin in the sediments of terrace T5 (the highest terrace) confirmed that the paleo-Yangtze River cut through the Three Gorges and captured the paleo-Chuan River, and the Daliang Mountains became the new drainage divide. Finally, the appearance of materials from the upper Jinsha River in terrace T2 indicated that the paleo-Yangtze River progressively captured the paleo-Jinsha River, and the modern upper Yangtze River formed before 0.05 Ma. These river capture events of the upper Yangtze River confirmed the Quaternary uplift of the SE Tibetan Plateau.
We perform a theoretical investigation of the instability of a helical vortex filament beneath a free surface in a semi-infinite ideal fluid. The focus is on the leading-order free-surface boundary effect upon the equilibrium form and instability of the vortex. This effect is characterised by the Froude number $F_r = U(gh^*)^{-{1}/{2}}$ where $g$ is gravity, and $U = \varGamma /(2{\rm \pi} b^*)$ with $\varGamma$ being the strength, $2{\rm \pi} b^*$ the pitch and $h^*$ the centre submergence of the helical vortex. In the case of $F_r \rightarrow 0$ corresponding to the presence of a rigid boundary, a new approximate equilibrium form is found if the vortex possesses a non-zero rotational velocity. Compared with the infinite fluid case (Widnall, J. Fluid Mech., vol. 54, no. 4, 1972, pp. 641–663), the vortex is destabilised (or stabilised) to relatively short- (or long-)wavelength sub-harmonic perturbations, but remains stable to super-harmonic perturbations. The wall-boundary effect becomes stronger for smaller helix angle and could dominate over the self-induced flow effect depending on the submergence. In the case of $F_r > 0$, we obtain the surface wave solution induced by the vortex in the context of linearised potential-flow theory. The wave elevation is unbounded when the $m$th wave mode becomes resonant as $F_r$ approaches the critical Froude numbers ${\mathcal {F}} (m) = (C_0^*/U)^{-1} (mh^*/b^*)^{-{1}/{2}}$, $m=1, 2, \ldots,$ where $C_0^*$ is the induced wave speed. We find that the new approximate equilibrium of the vortex exists if and only if $F_r < {\mathcal {F}}(1)$. Compared with the infinite fluid and $F_r \rightarrow 0$ cases, the wave effect causes the vortex to be destabilised to super-harmonic and long-wavelength sub-harmonic perturbations with generally faster growth rate for greater $F_r$ and smaller helix angle.
Various foods are associated with or protect against type 2 diabetes mellitus (T2DM). This study was to examine the associations of foods and food patterns with the risk of T2DM in South China.
Design:
Case–control study.
Setting:
The dietary patterns were identified by a principal components factor analysis. Univariable and multivariable conditional logistic regression analyses were used to analyse the associations between food groups and dietary patterns and the risk of T2DM.
Participants:
A total of 384 patients with T2DM and 768 controls.
Results:
After adjustment for total energy intake, the standard intake of grains (228·3 ± 71·9 v. 238·8 ± 73·1 g/d, P = 0·025) and fruits (109 ± 90 v. 145 ± 108 g/d, P < 0·001) were lower in T2DM than in controls. Four dietary patterns were identified: (1) high light-coloured vegetables and low grains, (2) high fruits, (3) high red meat and low grains and (4) high dark-coloured vegetable. After adjustment for covariables, multivariable conditional logistic regression analyses showed significant dose-dependent inverse associations between total fruit intake, whole grains intake and the score of the high-fruit dietary pattern (all Pfor trend < 0·001) and the risk of T2DM. The adjusted OR (95 % CI) for T2DM comparing the extreme quartiles were 0·46 (0·29, 0·76) for total fruits, 0·48(0·31, 0·77) for whole grains and 0·42 (0·26, 0·68) for the high-fruit dietary pattern, respectively. Similar associations were observed for all subgroups of fruits (dark-colour and light-colour).
Conclusion:
In South China, a diet rich in fruit and whole grains is associated with lower risk of T2DM.
Few studies have suggested that long-term adherence to low-carbohydrate diets (LCD) may affect maternal glucose metabolism in Western countries. We aimed to investigate the association between LCD during pregnancy and glucose metabolism in a Chinese population. A total of 1018 women in mid-pregnancy were recruited in 2017–2018. Participants underwent a 75 g oral glucose tolerance test (OGTT). Daily dietary intakes over the past month were accessed using a validated FFQ. The overall, animal and vegetable LCD scores which represent adherence to different low-carbohydrate dietary patterns were calculated. Mixed linear regression and generalised linear mixed regression were conducted to evaluate the associations between LCD scores and maternal glucose metabolism. Of the 1018 subjects, 194 (19·1 %) were diagnosed with gestational diabetes mellitus (GDM). The overall LCD score (β: 0·024, se 0·008, PFDR = 0·02) and animal LCD score (β: 0·023, se 0·008, PFDR = 0·02) were positively associated with OGTT 1-h glucose. No significant associations were found between the three different LCD scores with fasting plasma glucose, OGTT 2-h glucose, or insulin resistance, respectively. Compared with the lowest quartile, the crude OR of GDM for the highest quartile were 1·84 (95 % CI 1·14, 2·95) for overall LCD score (Pfor trend = 0·02) and 1·56 (95 % CI 1·00, 2·45) for animal LCD score (Pfor trend = 0·02). However, these associations became non-significant after adjustment for covariates. In conclusion, a low-carbohydrate dietary pattern with high animal protein and fat is associated with higher postprandial 1-h glucose levels in Chinese pregnant women.
Many clinical trials showed favorable effects of high-doses supplemental n-3 polyunsaturated fatty acids (PUFA) on cardio-metabolic risk factors. However, limited studies examined the prospective associations of circulating n-3 PUFA with body fat and its distribution, metabolic syndrome (MS), carotid atherosclerosis, and nonalcoholic fatty liver disease (NAFLD) in subjects with habitual diets containing low levels of n-3 PUFA.
Materials and Methods
This community-based prospective study enrolled 4048 participants (40–75 years) at baseline (2008–2010, 2013) from Guangzhou, China. They were followed-up approximately once every 3 years. Fatty acids in erythrocyte membranes were measured at baseline. We determined metabolic syndrome factors, body fat by DXA scanning, carotid intima-media thickness (IMT) and NAFLD by ultrasound at the visits. General information, anthropometric indices, habitual dietary intake and other covariates were assessed at each visit.
Results
Among the total 4048 subjects, 3075 and 2671 subjects had erythrocyte n-3 PUFA data and completed the first and second follow-ups. Generally, erythrocyte n-3 PUFA were favorably associated with body fat (particularly at abdomen) and its changes, and with the presence and incidence of MS, type 2 diabetes, carotid IMT thickening. The participants with the highest (vs lowest) quartile of n-3 PUFA were associated with -5.81% fat mass (p < 0.001) and -2.11% of fat mass change at the abdomen (Android) area. The adjusted hazards ratios (95% CI) for the highest (vs. lowest) group were 0.74 (0.61, 0.89) (total n-3 PUFA), 0.71 (0.59, 0.86) (docosahexaenoic acid, DHA), 0.78 (0.65, 0.95) (docosapentaenoic acid, DPA), 1.96 (1.60, 2.40) (gamma-linolenic acid, GLA) for MS; 0.70(0.55, 0.90) (total n-3 PUFA), 0.67(0.52,0.87) (DHA) and 0.73(0.57,0.93) (DPA) for bifurcation IMT thickening, 0.57(0.38, 0.86) (eicosapentaenoic acid, EPA) and 0.63 (0.41, 0.95) (DPA) for type 2 diabetes, and 1.18 (1.09, 1.33) (DHA) for alleviated NAFLD. Both higher levels of total and individual marine n-3 PUFAs (DHA, EPA and DPA) were associated with lower blood pressure at baseline and lower changes in diastolic and systolic blood pressure over the follow-up period. Plant n-3 PUFA (α-linolenic acid, ALA) largely had less significant association with the above-mentioned indices as compared with marine n-3 PUFAs.
Discussion
Higher proportions of erythrocyte n-3 PUFA (particularly marine sources) was associated with lower body fat, blood pressure and their changes, and lower risks of MS, type 2 diabetes and bifurcation IMT thickening, but higher chance of alleviated NAFLD in middle-aged and older adults.
In December, 2019, an infectious outbreak of unknown cause occurred in Wuhan, which attracted intense attention. Shortly after the virus was identified as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the epidemic of coronavirus disease 2019 (COVID-19) broke out, and an information storm occurred. At that time, 2 important aspects, that is, the stages of spread and the components of the epidemic, were unclear. Answers to the questions (1) what are the sources, (2) how do infections occur, and (3) who will be affected should be clarified as the outbreak continues to evolve. Furthermore, components of the epidemic and the stages of spread should be explored and discussed. Based on information of SARS, Middle East respiratory syndrome (MERS), and COVID-19, the components of the epidemic (the sources, the routes of infection, and the susceptible population) will be discussed, as well as the role of natural and social factors involved. Epidemiologic characteristics of patients will be traced based on current information.
To suppress the interface gap between the cell walls of wood and filled epoxy resin, a green and universal H2O2 or H2O2/HAc steam-modified delignification approach is developed to remove more lignin, thereby generating more pores to be more conveniently backfilled by epoxy resin for highly transparent wood composites. Utilizing the excellent penetration ability of steam, not only different wood species, such as basswood and pine, with different cutting directions but also the thickest (40 mm) and largest (210 × 190 mm) wood samples can be successfully delignified. Compared with the 1.9% lignin content (which is the normal content of delignified wood prepared by solution-based methods) of delignified wood, the as-prepared delignified wood has the lowest lignin content of 0.84% to date. After the infiltration of epoxy resin, not only did the mechanical strength of the 5-mm transparent wood composite increase from 12.5 to 20.6 MPa, but the transmittance (the wavelength was 550 nm) also increased from 80 to 87% due to the lower absorbance of visible light by lignin and the suppression of the interface debonding gap between the cell walls and the backfilled epoxy resin.
The U genome of Aegilops umbellulata is an important basic genome of genus Aegilops. Direct gene transfer from Ae. umbellulata into wheat is feasible but not easy. Triticum turgidum–Ae. umbellulata amphidiploids can act as bridges to circumvent obstacles involving direct gene transfer. Seven T. turgidum–Ae. umbellulata amphidiploids were produced via unreduced gametes for spontaneous doubling of chromosomes of triploid T. turgidum–Ae. umbellulata F1 hybrid plants. Seven pairs of U chromosomes of Ae. umbellulata were distinguished by fluorescence in situ hybridization (FISH) probes pSc119.2/(AAC)5 and pTa71. Polymorphic FISH signals were detected in three (1U, 6U and 7U) of seven U chromosomes of four Ae. umbellulata accessions. The chromosomes of the tetraploid wheat parents could be differentiated by probes pSc119.2 and pTa535, and identical FISH signals were observed among the three accessions. All the parental chromosomes of the amphidiploids could be precisely identified by probe combinations pSc119.2/pTa535 and pTa71/(AAC)5. The T. turgidum–Ae. umbellulata amphidiploids possess valuable traits for wheat improvement, such as strong tillering ability, stripe rust resistance and seed size-related traits. These materials can be used as media in gene transfers from Ae. umbellulata into wheat.
We study theoretically and numerically the nonlinear seakeeping problem of a submerged or floating body translating with constant forward speed $U$ parallel to the undisturbed free surface while at the same time undergoing a small oscillatory motion and/or encountering small-amplitude waves at frequency $\unicode[STIX]{x1D714}$. It is known that at the critical frequency corresponding to $\unicode[STIX]{x1D70F}\equiv \unicode[STIX]{x1D714}U/g=1/4$, where $g$ is the gravitational acceleration, the classical linear solution is unbounded for a single point source, and the inclusion of third-order free-surface nonlinearity due to cubic self-interactions of waves is necessary to remove the associated singularity. Although it has been shown that the linear solution is in fact bounded for a body with full geometry rather than a point source, the solution still varies sharply near the critical frequency. In this work, we show theoretically that for a submerged body, the nonlinear correction to the linear solution due to cubic self-interactions of resonant waves in the neighbourhood of $\unicode[STIX]{x1D70F}=1/4$ is of first order in the wave steepness (or body motion amplitude), which is the same order as the linear solution. With the inclusion of nonlinear effects in the dispersion relation, the wavenumbers of resonant waves become complex-valued and the resonant waves become evanescent, with their amplitudes vanishing with the distance away from the body. To assist in understanding the theory, we derive the analytic nonlinear solution for the case of a submerged two-dimensional circular cylinder in the neighbourhood of $\unicode[STIX]{x1D70F}=1/4$. Independent numerical simulations confirm the analytic solution for the submerged circular cylinder. Finally, we also demonstrate by numerical simulations that similar significant nonlinear effects for a surface-piercing body exist in the neighbourhood of $\unicode[STIX]{x1D70F}=1/4$.
We investigated the effects of dietary l-arginine level and feeding duration on the intestinal damage of broilers induced by Clostridium perfringens (CP) in vivo, and the antimicrobial effect of its metabolite nitric oxide (NO) in vitro. The in vivo experiment was designed as a factorial arrangement of three dietary treatments×two challenge statuses. Broilers were fed a basal diet (CON) or a high-arginine diet (ARG) containing 1·87 % l-arginine, or CON for the first 8 d and ARG from days 9 to 28 (CON/ARG). Birds were co-infected with or without Eimeria and CP (EM/CP). EM/CP challenge led to intestinal injury, as evidenced by lower plasma d-xylose concentration (P<0·01), higher paracellular permeability in the ileum (P<0·05) and higher numbers of Escherichia coli (P<0·05) and CP (P<0·001) in caecal digesta; however, this situation could be alleviated by l-arginine supplementation (P<0·05). The intestinal claudin-1 and occludin mRNA expression levels were decreased (P<0·05) following EM/CP challenge; this was reversed by l-arginine supplementation (P<0·05). Moreover, EM/CP challenge up-regulated (P<0·05) claudin-2, interferon-γ (IFN-γ), toll-like receptor 2 and nucleotide-binding oligomerisation domain 1 (NOD1) mRNA expression, and l-arginine supplementation elevated (P<0·05) IFN-γ, IL-10 and NOD1 mRNA expression. In vitro study showed that NO had bacteriostatic activity against CP (P<0·001). In conclusion, l-arginine supplementation could inhibit CP overgrowth and alleviate intestinal mucosal injury by modulating innate immune responses, enhancing barrier function and producing NO.
The effects of live yeast (LY) and mannan-oligosaccharide (MOS) supplementation on intestinal disruption induced by Escherichia coli in broilers were investigated. The experimental design was a 3×2 factorial arrangement with three dietary treatments (control, 0·5 g/kg LY (Saccharomyces cerevisiae, 1·0×1010 colony-forming units/g), 0·5 g/kg MOS) and two immune treatments (with or without E. coli challenge from 7 to 11 d of age). Samples were collected at 14 d of age. The results showed that E. coli challenge impaired (P<0·05) growth performance during the grower period (1–21 d) and the overall period (1–35 d) of broilers, increased (P<0·05) serum endotoxin and diamine oxidase levels coupled with ileal myeloperoxidase and lysozyme activities, whereas reduced (P<0·05) maltase activity, and compromised the morphological structure of the ileum. Besides, it increased (P<0·05) the mRNA expressions of several inflammatory genes and reduced occludin expression in the ileum. Dietary treatment with both LY and MOS reduced (P<0·05) serum diamine oxidase and ileal myeloperoxidase levels, but elevated villus height (P<0·10) and the ratio of villus height:crypt depth (P<0·05) of the ileum. It also alleviated (P<0·05) E. coli-induced increases (P<0·05) in ileal Toll-like receptor 4, NF-κB and IL-1β expressions. Moreover, LY supplementation reduced (P<0·05) feed conversion ratio of birds during the grower period and enhanced (P<0·05) the community diversity (Shannon and Simpson indices) of ileal microbiota, whereas MOS addition counteracted (P<0·05) the decreased ileal IL-10 and occludin expressions in challenged birds. In conclusion, both LY and MOS supplementation could attenuate E. coli-induced intestinal disruption by alleviating intestinal inflammation and barrier dysfunction in broilers. Moreover, LY addition could improve intestinal microbial community structure and feed efficiency of broilers.
Narrow gap submerged arc welding method accompanied with multilayer and multipass technology was used to manufacture advanced 9Cr and CrMoV dissimilarly welded joint used as a newly developed turbine rotor. The aim of this investigation was to evaluate the high cycle fatigue (HCF) behavior of the welded joint at room temperature. Uniaxial-stress controlled HCF tests at stress ratio R = −1 were performed with specimens chipped from the welded joint of mockup and the S–N curve up to 1.0 × 108 cycle lifetime was obtained. It was found that the fracture location transferred from heat affected zone (HAZ) of CrMoV side to weld metal (WM) with decreasing stress amplitude. The microstructure of the welded joint was characterized and microstructure diversity was found to be responsible for the failure locations both in the CrMoV–HAZ and WM. Fracture morphology of failure samples were also investigated by a scanning electron microscope. It is detected that the stress amplitude required to drive the inclusion to be the crack initiation of the CrMoV–HAZ lies behind the transition. With decreasing stress amplitudes, void in the WM more easily tends to be the initiation of a fatigue crack than inclusion.
A series of zeolite–zeolite composites were prepared by a two-step hydrothermal crystallization procedure in which the mixture of presynthesized ZSM-5 zeolite acts as nutrients for the growth of postsynthesized Y zeolite, and the as-synthesized products are denoted as MFI–FAU. The structural, crystalline, and textural properties of the as-synthesized materials, as well as the references Y, ZSM-5, and a corresponding physical mixture composed of Y and ZSM-5 zeolite, were characterized by x-ray powder diffraction (XRD), Fourier transform infrared spectrum (FTIR), temperature-programmed desorption of ammonia, N2 adsorption–desorption, scanning electron microscopy, energy-dispersive spectrometry, and Thermogravimetry. The results show that the ratio of Y to ZSM-5 in the composite can be adjusted by controlling the hydrothermal treatment time of the second-step synthesis. Steric hindrance provoked by the concurrently growing crystals offers the postsynthesized Y zeolite phase, a relatively smaller size. A hierarchical pores system, which results from the extraction of silicon species from ZSM-5 and the polycrystalline accumulation of Y zeolite, has been created in the zeolite–zeolite composite. Catalytic performances of the zeolite–zeolite composite catalysts as well as the references catalysts were investigated during the catalytic cracking of isopropylbenzene. As compared with the corresponding physical mixture, the composite catalysts display the excellent catalytic performances with a higher conversion of isopropylbenzene as well as a longer catalytic life because of the introduced hierarchical pores system and the formation of special composite structure.
As Earth-based radio tracking navigation is severely limited because of communications constraints and low relative navigation accuracy, autonomous optical navigation capabilities are essential for both robotic and manned deep-space exploration missions. Image processing is considered one of the key technologies for autonomous optical navigation to extract high-precision navigation observables from a raw image. New image processing algorithms for deep-space autonomous optical navigation are developed in this paper. First, multiple image pre-processing and the Canny edge detection algorithm are adopted to identify the edges of target celestial bodies and simultaneously remove the potential false edges. Secondly, two new limb profile fitting algorithms are proposed based on the Least Squares method and the Levenberg-Marquardt algorithm, respectively, with the assumption that the perspective projection of a target celestial body on the image plane will form an ellipse. Next, the line-of-sight (LOS) vector from the spacecraft to the centroid of the observed object is obtained. This is taken as the navigation measurement observable and input to the navigation filter algorithm. Finally, the image processing algorithms developed in this paper are validated using both synthetic simulated images and real flight images from the MESSENGER mission.
To compare the differences in hyperlipidaemia prevalence and its risk factors between the Guangxi Bai Ku Yao and Han populations.
Design
Cross-sectional study of hyperlipidaemia.
Setting
Both populations were from Lihu and Baxu villages in Nandan County, Guangxi Zhuang Autonomous Region, People’s Republic of China.
Subjects
A total of 1170 healthy subjects of Bai Ku Yao and 1173 participants of Han Chinese aged 15–89 years were surveyed by a stratified randomized cluster sampling. Information on demographic, dietary and lifestyle characteristics was collected by standard questionnaires. Blood pressure, height, weight, waist circumference, serum lipids and apolipoproteins were measured, and BMI (kg/m2) was calculated as weight divided by the square of height.
Results
The prevalence rates of hypercholesterolaemia, hypertriacylglycerolaemia and hyperlipidaemia in Bai Ku Yao and Han were 12·4 % v. 26·2 % (P < 0·001), 15·0 % v. 14·8 % (P > 0·05) and 24·4 % v. 33·9 % (P < 0·001), respectively. Hyperlipidaemia was positively correlated with BMI, waist circumference, total energy and total fat intakes, and negatively associated with physical activity and total dietary fibre intake in Bai Ku Yao (P < 0·05 to 0·001). Hyperlipidaemia was positively associated with age, alcohol consumption, BMI, waist circumference, total energy and total fat intakes, and inversely correlated with physical activity and total dietary fibre intake in Han (P < 0·05 to 0·001).
Conclusions
The prevalence of hypercholesterolaemia and hyperlipidaemia was significantly lower in the Bai Ku Yao than in the Han population, which might result from different dietary habits, lifestyle choices and physical activity level, as well as genetic factors between the two ethnic groups.
The optical emission spectra of the plasma generated by a
1.06-μm Nd:YAG laser irradiation of Al target in air was
recorded and analyzed in a spatially resolved manner. Electron
temperatures and densities in the plasma were obtained using
the relative emission intensities and the Stark-broadened
linewidths of Al(I) emission lines, respectively. The dependence
of the electron density and temperature on the distance from
the target surface and on the laser irradiance were manifested.
We also discussed how the air takes part in the plasma evolution
process and confirmed that the ignition of the air plasma was
by the collisions between the energetic electrons and the nitrogen
atoms through a cascade avalanche process.
When skim milk at pH 6·55 was heated (75 to 100 °C for up to 60 min), the casein micelle size, as monitored by photon correlation spectroscopy, was found to increase during the initial stages of heating and tended to plateau on prolonged heating. At any particular temperature, the casein micelle size increased with longer holding times, and, at any particular holding time, the casein micelle size increased with increasing temperature. The maximum increase in casein micelle size was about 30–35 nm. The changes in casein micelle size were poorly correlated with the level of whey protein denaturation. However, the changes in casein micelle size were highly correlated with the levels of denatured whey proteins that were associated with the casein micelles. The rate of association of the denatured whey proteins with the casein micelles was considerably slower than the rate of denaturation of the whey proteins. Removal of the whey proteins from the skim milk resulted in only small changes in casein micelle size during heating. Re-addition of β-lactoglobulin to the whey-protein-depleted milk caused the casein micelle size to increase markedly on heat treatment. The changes in casein micelle size induced by the heat treatment of skim milk may be a consequence of the whey proteins associating with the casein micelles. However, these associated whey proteins would need to occlude a large amount of serum to account for the particle size changes. Separate experiments showed that the viscosity changes of heated milk and the estimated volume fraction changes were consistent with the particle size changes observed. Further studies are needed to determine whether the changes in size are due to the specific association of whey proteins with the micelles or whether a low level of aggregation of the casein micelles accompanies this association behaviour. Preliminary studies indicated lower levels of denatured whey proteins associated with the casein micelles and smaller changes in casein micelle size occurred as the pH of the milk was increased from pH 6·5 to pH 6·7.
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