Oval Domes: History, Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals. The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building. Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building. The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design

Au/Si(111): Analysis of the (√3 × √3 )R30° and 6×6 structures by in-plane x-ray diffraction

In-plane, fractional-order diffraction-data sets from thin Au layers on Si(111) with (√3 × √3 )R30° and 6×6 structures were measured at the wiggler beamline W1 at the Hamburg synchrotron radiation laboratory. For the √3 × √3 structure the trimer model is confirmed with an Au-Au distance of 2.8 Å. In the √3 × √3 unit cell, two additional sites beside the Au trimer were found which can be identified with distorted substrate layers or additional partially occupied Au sites. The 6×6 structure is a sixfold twinned structure. The observed Patterson function clearly indicates the main features of the structural units. Each consists of three trimer clusters of Au atoms, forming a nearly equilateral triangle. The local structure of each trimer is either the original √3 × √3 structure or a twin structure where the Au trimers are rotated by 60°. Three of these structural units form the 6×6 unit cell. Model calculations with incoherent superposition of twin domains lead to Patterson maps very similar to the one observed

Properties of tomato powders as additives for food fortification and stabilization

The antioxidant activities of two freeze-dried tomato powders as additives for food fortification and stabilization were studied. The two tomato powders were obtained from the whole fruit and from the pulp after \u201cserum\u201d separation, respectively. The antioxidant activity was studied by measuring (a) the inhibition of the singlet oxygen-catalyzed oxidation of alpha-linolenic acid, in the presence or absence of copper ions, as a model of the oxidative processes occurring in foods, and (b) the inhibition of xanthine oxidase (XOD)- and myeloperoxidase (MPO)-catalyzed reactions and copper-induced lipid peroxidation. The partial separation of \u201cserum\u201d decreased the freeze-drying time by 50%. The partially fractionated tomato powder had a 60% lower phenolic content and an 11-fold higher lycopene content than the whole tomato powder, on a dry weight basis. Ascorbic acid was almost completely removed by fractionation. Both the powder obtained from the whole tomato and that obtained from the partially fractionated tomato had antioxidant activity in all the model systems used. Based on these results, we conclude that tomato powders have multifunctional properties, which could address the prevention of oxidative degradations both in foods and in vivo. Therefore, tomato can be regarded as source of food additives for fortification and stabilization, even if it is submitted to technological processes that can cause the loss of the more labile hydrophilic antioxidants

Adjuvant Radiation in Resectable Node-Positive Merkel Cell Carcinoma in the Immunotherapy Era: Implications for Future and Ongoing Trials

Merkel cell carcinoma (MCC) is a cutaneous malignancy often treated with surgical resection followed by adjuvant radiation therapy (RT). In the node-positive setting, adjuvant RT reduces the risk of locoregional recurrence, but historical data suggest that distant failure is a persistent issue and often fatal. This has prompted new efforts to intensify treatment in these patients with the addition of neoadjuvant or adjuvant immune checkpoint inhibitor therapy. However, newer diagnostic techniques have led to stage migration in patients with previously subclinical metastatic disease; consequently, preventing locoregional recurrence may be a higher priority in node-positive MCC patients than was previously believed. Recent trials in node-positive MCC, such as ADMEC-O, have had lower rates of adjuvant RT utilization in treatment versus control arms, which may have attenuated the observed effect of adjuvant immunotherapy. The low utilization of adjuvant RT may have also resulted in a higher recurrence rate in patients who did not have a complete response to neoadjuvant immunotherapy in the CHECKMATE 358 trial. Altogether, these are important considerations for ongoing and future immunotherapy trials in MCC and may affect the interpretation of their results. Ongoing clinical trials may determine which patients are at low risk of recurrence when treated with immunotherapy and whether adjuvant RT could be omitted in select patients