The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

The hairiness of worsted wool and cashmere yarns and the impact of fiber curvature on hairiness

In this study, a range of carefully selected wool and cashmere yarns as well as their blends were used to examine the effects of fiber curvature and blend ratio on yarn hairiness. The results indicate that yarns spun from wool fibers with a higher curvature have lower yarn hairiness than yarns spun from similar wool of a lower curvature. For blend yarns made from wool and cashmere of similar diameter, yarn hairiness increases with the increase in the cashmere content in the yarn. This is probably due to the presence of increased proportion of the shorter cashmere fibers in the surface regions of the yarn, leading to increased yarn hairiness. A modified hairiness composition model is used to explain these results and the likely origin of leading and trailing hairs. This model highlights the importance of yarn surface composition on yarn hairiness.

Elastic bending of steel-polymer-steel (SPS) laminates to a constant curvature

The shear strain of the interlayer in the elastic regime for a Steel-Polymer-Steel (SPS) laminate material has been studied during bending to a constant curvature. An analytical model is developed and the influence of process parameters are analyzed. The tension in the cover sheets is also determined and, finally, a moment diagram is calculated. The results show that the moment in the SPS laminate is nonuniform along the bent strip even though the curvature is constant because of the tension and compression forces introduced in the cover sheets by the shear reaction force of the interlayer material.

Shear- free perfect fluids with solenoidal magnetic curvature and a γ-law equation of state

We show that shear-free perfect fluids obeying an equation of state p = (γ − 1)μ are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.

Changes in fibre curvature during the processing of wool and alpaca fibres and their blends

This paper studied the wool and alpaca fibre curvature and its variation during the fibre processing. It revealed the effect of wool fibre crimp on the cohesion properties of alpaca and wool blended slivers. Different wool and alpaca tops were blended via a number of gillings, and the role of wool fibre curvature in alpaca/wool blend processing has also been investigated. During the wool fibre processing, fibre curvature tended to diminish gradually from scoured fibre to top. Blending wool with alpaca fibres improved the cohesion properties of the blended sliver, compared with pure alpaca slivers. For a high ratio of alpaca component in the blend, a high-crimp wool should be used to achieve good sliver cohesion.

Short-term and long-term site-specific effects of tennis playing on trabecular and cortical bone at the distal radius

Mechanical loading during growth magnifies the normal increase in bone diameter occurring in long bone shafts, but the response to loading in long bone ends remains unclear. The aim of the study was to investigate the effects of tennis playing during growth at the distal radius, comparing the bone response at trabecular and cortical skeletal sites. The influence of training duration was examined by studying bone response in short-term (children) and long-term (young adults) perspectives. Bone area, bone mineral content (BMC), and bone mineral density (BMD) of the radius were measured by DXA in 28 young (11.6 ± 1.4 years old) and 47 adult tennis players (22.3 ± 2.7 years old), and 70 age-matched controls (12 children, 58 adults) at three sites: the ultradistal region (trabecular), the mid-distal region, and the third-distal region (cortical). At the ultradistal radius, young and adult tennis players displayed similar side-to-side differences, the asymmetry in BMC reaching 16.3% and 13.8%, respectively (P < 0.0001). At the mid- and third-distal radius, the asymmetry was much greater in adults than in children (P < 0.0001) for all the bone parameters (mid-distal radius, +6.6% versus +15.6%; third-distal radius, +6.9% versus +13.3%, for BMC). Epiphyseal bone enduring longitudinal growth showed a great capacity to respond to mechanical loading in children. Prolonging tennis playing into adulthood was associated with further increase in bone mineralization at diaphyseal skeletal sites. These findings illustrate the benefits of practicing impact-loading sports during growth and maintaining physical activity into adulthood to enhance bone mass accrual and prevent fractures later in life.

Experimental evaluation of curl and tensile properties of advanced high strength sheet steels

The response of HSLA steel, 590R, and dual-phase steel, DP-600, to non-uniform deformation imposed in a laboratory Bending-Under-Tension (BUT) test apparatus was evaluated. Samples were deformed with both low and high back tension forces at bend angles of 45 and 90 degrees, and evaluated to determine the ""side-wall curl,"" i.e., the curvature in the sheet section in contact with the die. The results indicate that there are no consistent differences between the two steels, 590R and DP-600. It was found that back tension, tensile strength and sheet thickness were the primary factors affecting curl. The bend angle has an influence on curl, with the curl radius at a 90ø bend angle being greater than the curl radius at a 45\mD bend angle.

Variation of fibre diameter coefficient of variation and fibre curvature across mohair fleeces: Implications for animal selection, genetic selection and fleece evaluation

The presentwork aimed to determine howthe average fibre diameter coefficient of variation (CVD) and fibre curvature (FC) differences between nine sampling sites vary between sex and flock, to identify differences in variability between sampling sites as a result of between animal and between sire variability and to determine correlations between sampling sites in between animal and between sire variability. Australian Angoras (n = 313) from two farms in southern Australia were sampled at 12 and 18 months of age at nine sites (mid side, belly, brisket, hind flank, hip, hock, mid back, neck, shoulder). Staples were taken prior to shearing at skin level and CVD and FC determined. For each shearing, differences in CVD and FC between sampling sites, how these differences were affected by farm, sex, and sire, and the covariance between sites for sire and individual animal effects were investigated by restricted maximum likelihood (REML) analyses. The median mid side CVD at 12 and 18 months of age ranged from 23.6 to 25.1% but the actual range was 16.8–34.2%. The median mid side FC at 12 and 18 months of age ranged from 14.4 to 18.6◦/mm but the actual range was 10.5–26.3◦/mm. The general pattern for CVDwas for the mid back, hip and neck sites to have similar CVD, the brisket, hind flank and hock sites to have larger CVD and the belly to have smaller CVD than the mid side site. The between animal variation for CVD was lowest at the mid back site. This implies that the mid back would be the most effective site for between animal selection for CVD. Heritabilities for CVD (range at 18 months 0.18–0.30) were only about half the heritabilities for mean fibre diameter in the same study. There was a marked anterior–posterior increase in FC at both farms and with both ages. The results give no clear indication of the best site for between animal selection for FC, other than that the hock should be avoided. Heritabilities for FC are moderate to high (range at 18 months 0.44–0.77) and the genetic correlations are high except for the hock. Thus genetic selection for FC at any site, other than the hock, should be effective for changing FC over the entire fleece. There was more variability between animals than between sites and sires. These results are put into context with associated research on variation in mean fibre diameter and staple length.

Comparison of pQCT parameters between ulna and radius in retired elite gymnasts : the skeletal benefits associated with long-term gymnastics are bone- and site-specific

Objectives: To compare the skeletal benefits associated with gymnastics between ulna and radius.
Methods: 19 retired artistic gymnasts, aged 18-36 years, were compared to 24 sedentary women. Bone mineral content (BMC), total and cortical bone area (ToA, CoA), trabecular and cortical volumetric density (TrD, CoD) and cortical thickness (CoTh) were measured by pQCT at the 4% and 66% forearm.
Results: At the 4% site, BMC and ToA were more than twice greater at the radius than ulna whereas at the 66% site, BMC, ToA, CoA, CoTh and SSIpol were 20 to 51% greater at the ulna than radius in both groups (p<0.0001). At the 4% site, the skeletal benefits in BMC of the retired gymnasts over the non-gymnasts were 1.9 times greater at the radius than ulna (p<0.001), with enlarged bone size at the distal radius only. In contrast, the skeletal benefits at the 66% site were twice greater at the ulna than radius for BMC and CoA (p<0.01).
Conclusion: Whereas the skeletal benefits associated with long-term gymnastics were greater at the radius than ulna in the distal forearm, the reverse was found in the proximal forearm, suggesting both bones should be analysed when investigating forearm strength.

Variation in the softness and fibre curvature of cashmere, alpaca, mohair and other rare animal fibres

Softness of apparel textiles is a major attribute sought by consumers. There is surprisingly little objective information on the softness properties of rare animal fibres, particularly cashmere, alpaca and mohair. Samples of these and other rare animal fibres from different origins of production and processors were objectively measured for fibre diameter, fibre curvature (FC, crimp) and resistance to compression (softness). While there were curvilinear responses of resistance to compression to FC and to mean fibre diameter, FC accounted for much more of the variance in resistance to compression. Fibre type was an important determinant of resistance to compression. The softest fibres were alpaca, mohair and cashgora and all of the fibres measured were softer than most Merino wool. Quivet, llama, camel, guanaco, vicuña, yak wool, bison wool, dehaired cow down and Angora rabbit were also differentiated from alpaca, mohair and cashmere. There were important differences in the softness and FC of cashmere from different origins with cashmere from newer origins of production (Australia, New Zealand and USA) having lower resistance to compression than cashmere from traditional sources of China and Iran. Cashmere from different origins was differentiated on the basis of resistance to compression, FC and fibre diameter. Cashgora was differentiated from cashmere by having a lower FC and lower resistance to compression. There were minority effects of colour and fibre diameter variation on resistance to compression of cashmere. The implications of these findings for the identification and use of softer raw materials are discussed.