Blending Cylinders and Cones using Canal Surfaces

There is reviewed the construction of a rational blending surface between cylinders and cones in some interlocation cases. This surface is constructed as a patch of rolling ball envelope, i.e. as a patch of tangent canal surface of rational-variable radius. This construction defines rational parameterization of a blending surface. The constructed surface is Laguerre invariant

Linear precision for toric surface patches

We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification also includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well-known tensor product patches and B\'ezier triangles, we identify a family of toric patches with trapezoidal shape, each of which has linear precision. B\'ezier triangles and tensor product patches are special cases of trapezoidal patches

Rational rolling ball blending of natural quadrics

We construct a blending surface of two natural quadrics using rational variable rolling ball approach, i.e. as a canal surface with a rational spine curve and a rational radius. All general positions of the given quadric surfaces are considered. The proposed construction is Laguerre invariant. In particular, the blending surface has rational offset of the same degree. Natūralių kvadrikių jungimas racionalaus apriedančio rutuliuko metodu Santrauka Natūralios kvadrikos (sferos, apskritiminiai cilindrai ir kūgiai) dažnai naudojamos geometriniame modeliavime. Šiame darbe siūlomas naujas dvieju natūraliu kvadrikiu glodaus jungimo metodas, naudojant kintamo racionalaus spindulio apriedančio rutuliuko metoda, t.y. jungiamasis paviršius ‐ tai kanalinis paviršius, kuris turi racionalia ašine kreive ir racionalu spinduli. Metodas tinka visiems dvieju kvadrikiu bendru poziciju atvejams. Konstrukcija yra invariantiška Laguerre geometrijos atžvilgiu: pavyzdžiui, jungiamasis paviršius turi to paties laipsnio racionalu ofseta. First Published Online: 14 Oct 201

A Spectral Rotary Analysis of Gravity Waves: An Application During One of the SOUTHTRAC Flights

To understand the main orographic and non-orographic sources of gravity waves (GWs) over South America during an Experiment (Rapp et al., 2021, https://doi.org/10.1175/BAMS-D-20-0034.1), we propose the application of a rotational spectral analysis based on methods originally developed for oceanographic studies. This approach is deployed in a complex scenario of large-amplitude GWs by applying it to reanalysis data. We divide the atmospheric region of interest into two height intervals. The simulations are compared with lidar measurements during one of the flights. From the degree of polarization and the total energy of the GWs, the contribution of the upward and downward wave packets is described as a function of their vertical wavenumbers. At low levels, a larger downward energy flux is observed in a few significant harmonics, suggesting inertial GWs radiated at polar night jet levels, and below, near to a cold front. In contrast, the upward GW energy flux, per unit area, is larger than the downward flux, as expected over mountainous areas. The main sub-regions of upward GW energy flux are located above Patagonia, the Antarctic Peninsula and only some oceanic sectors. Above the sea, there are alternating sub-regions dominated by linearly polarized GWs and sectors of downward GWs. At the upper levels, the total available GW energy per unit mass is higher than at the lower levels. Regions with different degrees of polarization are distributed in elongated bands. A satisfactory comparison is made with an analysis based on the phase difference between temperature and vertical wind disturbances

Blending using ODE swept surfaces with shape control and C1 continuity

Surface blending with tangential continuity is most widely applied in computer aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: 1). exact satisfaction of 1C continuous blending boundary constraints, 2). effective shape control of blending surfaces, 3). high computing efficiency due to explicit mathematical representation of blending surfaces, and 4). ability to blend multiple (more than two) primary surfaces

COI1-dependent jasmonate signalling affects growth, metabolites production and cell wall protein composition in Arabidopsis

Background and Aims: Cultured cell suspensions have been the preferred model to study the apoplast as well as to monitor metabolic and cell cycle-related changes. Previous work showed that methyl jasmonate (MeJA) inhibits leaf growth in a CORONATINE INSENSITIVE 1 (COI1)-dependent manner, with COI1 being the jasmonate (JA) receptor. Here, the effect of COI1 overexpression on the growth of stably transformed arabidopsis cell cultures is described. Methods: Time-course experiments were carried out to analyse gene expression, and protein and metabolite levels. Key Results: Both MeJA treatment and the overexpression of COI1 modify growth, by altering cell proliferation and expansion. DNA content as well as transcript patterns of cell cycle and cell wall remodelling markers were altered. COI1 overexpression also increases the protein levels of OLIGOGALACTURONIDE OXIDASE 1, BETA-GLUCOSIDASE/ENDOGLUCANASES and POLYGALACTURONASE INHIBITING PROTEIN2, reinforcing the role of COI1 in mediating defence responses and highlighting a link between cell wall loosening and growth regulation. Moreover, changes in the levels of the primary metabolites alanine, serine and succinic acid of MeJA-treated Arabidopsis cell cultures were observed. In addition, COI1 overexpression positively affects the availability of metabolites such as β-alanine, threonic acid, putrescine, glucose and myo-inositol, thereby providing a connection between JA-inhibited growth and stress responses. Conclusions: This study contributes to the understanding of the regulation of growth and the production of metabolic resources by JAs and COI1. This will have important implications in dissecting the complex relationships between hormonal and cell wall signalling in plants. The work also provides tools to uncover novel mechanisms co-ordinating cell division and post-mitotic cell expansion in the absence of organ developmental control

Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome