Beyond natural geometry: on the nature of proto-geometry

2019 ◽  
Vol 33 (2) ◽  
pp. 181-205 ◽  
Author(s):  
José Ferreirós ◽  
Manuel J. García-Pérez
Keyword(s):  
Natural Geometry

On the Reaction of 2,5-Dihydroxy-[1,4]-benzoquinone with Diamines – Strain-induced Reactivity Effects

2020 ◽  
Vol 24 ◽  
Author(s):  
Hubert Hettegger ◽  
Andreas Hofinger ◽  
Thomas Rosenau
Keyword(s):  
Nucleophilic Substitution ◽  
Product Structure ◽  
Carbonyl Groups ◽  
Reaction Products ◽  
Double Bonds ◽  
Oh Groups ◽  
Natural Geometry ◽  
Quinoid Structure ◽  
Bond Localization

: The regioselectivity of the reaction of 2,5-dihydroxy-[1,4]-benzoquinone (DHBQ) with diamines could not be explained satisfactorily so far. In general, the reaction products can be derived from the tautomeric ortho-quinoid structure of a hypothetical 4,5-dihydroxy-[1,2]-benzoquinone. However, both aromatic and aliphatic 1,2-diamines form in some cases phenazines, formally by diimine formation on the quinoid carbonyl groups, and in other cases the corresponding 1,2- diamino-[1,2]-benzoquinones, by nucleophilic substitution of the OH groups, the regioselectivity apparently not following any discernible pattern. The reactivity was now explained by an adapted theory of strain-induced bond localization (SIBL). Here, the preservation of the "natural" geometry of the two quinoid C–C double bonds (C3=C4 and C5=C6) as well as the N–N distance of the co-reacting diamine are crucial. A decrease of the annulation angle sum (N–C4–C5 + C4–C5–N) is tolerated well and the 4,5-diamino-ortho-quinones, having relatively short N–N spacings are formed. An increase in the angular sum is energetically unfavorable, so that diamines with a larger N–N distance afford the corresponding ortho-quinone imines. Thus, for the reaction of DHBQ with diamines, exact predictions of the regioselectivity, and the resulting product structure, can be made on the basis of simple computations of bond spacings and product geometries.

The Dioptrique

2017 ◽  
Author(s):  
Walter Ott
Keyword(s):  
Sensory Experience ◽  
The Other ◽  
Brain Image ◽  
Brain Motion ◽  
Natural Geometry ◽  
The Common ◽  
The Brain

Descartes’s treatment of perception in the Optics, though published before the Meditations, contains a distinct account of sensory experience. The end of the chapter suggests some reasons for this oddity, but that the two accounts are distinct is difficult to deny. Descartes in the present work topples the brain image from its throne. In its place, we have two mechanisms, one purely causal, the other inferential. Where the proper sensibles are concerned, the ordination of nature suffices to explain why a given sensation is triggered on the occasion of a given brain motion. The same is true with regard to the common sensibles. But on top of this purely causal story, Descartes re-introduces his doctrine of natural geometry.

Material Selection Based on Finite Element Method in Customized Iliac Implant

2020 ◽  
Vol 1000 ◽  
pp. 82-89
Author(s):  
Dhyah Annur ◽  
Muhammad S. Utomo ◽  
Talitha Asmaria ◽  
Daniel P. Malau ◽  
Sugeng Supriadi ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Selection ◽  
Potential Candidate ◽  
Basic Study ◽  
Common Location ◽  
Weight Support ◽  
Natural Geometry ◽  
Element Method

Osteosarcoma, as the most frequent bone tumor cases, can be found in the pelvis bone. Within the pelvis, the ilium is the most common location for osteosarcoma, followed by the acetabulum and then the ischium. Surgery of pelvis is difficult and the reconstruction is complicated mainly due to the geometry complexity and also the weight support function of the pelvis. Endoprosthesis of the ilium is therefore designed to increase the quality of life of the patient. In this study, the iliac implant is designed based on the natural geometry of the ilium, and the size is modified to fit the morphometry of the Eastern Asian. A finite element method (FEM) is proposed as a basic study in material selection. Titanium and its alloy (Ti-6Al-4V) are studied as the potential candidate for the proposed implant while the finite analysis of the bone was also included. As a preliminary study, in this FEM, only the static load is given, each material is assumed to be isotropic and the contacts were considered bonded. FEM in this study is expected to give a better understanding of the stress distribution, and to optimize the selection of materials.

Proposed percutaneous aortic valve prosthesis made of cryogel

2019 ◽  
Vol 233 (5) ◽  
pp. 515-524 ◽  
Author(s):  
Hadi Mohammadi ◽  
Dylan Goode ◽  
Guy Fradet ◽  
Kibret Mequanint
Keyword(s):  
Aortic Valve ◽  
Heart Valves ◽  
Kidney Injury ◽  
Blood Stream ◽  
Valve Prosthesis ◽  
Element Analysis ◽  
Novel Approach ◽  
Natural Geometry ◽  
Myocardial Infraction ◽  
Aortic Valve Prosthesis

Transcatheter heart valves are promising for high-risk patients. Generally, their leaflets are made of pericardium stented in a Nitinol basket. Despite their relative success, they are associated with significant complications such as valve migration, implantation risks, stroke, coronary obstruction, myocardial infraction, acute kidney injury (which all are due to the release of detached solid calcific pieces in to the blood stream) and expected issues existing with tissue valves such as leaflet calcification. This study is an attempt to fabricate the first ever polymeric percutaneous valves made of cryogel following the geometry and mechanical properties of porcine aortic valve to address some of the above-mentioned shortcomings. A novel, one-piece, tricuspid percutaneous valve, consisting of leaflets made entirely from the hydrogel, polyvinyl alcohol cryogel reinforced by bacterial cellulose natural nanocomposite, attached to a Nitinol basket was developed and demonstrated. Following the natural geometry of the valve, a novel approach was applied based on the revolution about an axis of a hyperboloid shape. The geometry was modified based on avoiding sharp warpage of leaflets and removal of the central opening orifice area of the valve when valve is fully closed using the finite element analysis. The modified geometry was replaced by a cloud of (control) points and was essentially converted to Bezier surfaces for further adjustment. A cavity mold was then designed and fabricated to form the valve. The fabricated valve was sewn into the Nitinol basket which is covered by Dacron cloth. The models presented in this study merit further development and revisions for both aortic and mitral positions.

CLASSES MINIMALES DE RÉSEAUX ET RÉTRACTIONS GÉOMÉTRIQUES ÉQUIVARIANTES DANS LES ESPACES SYMÉTRIQUES

2001 ◽  
Vol 64 (2) ◽  
pp. 275-286 ◽  
Author(s):  
CHRISTOPHE BAVARD
Keyword(s):  
Finite Group ◽  
Euclidean Space ◽  
Symmetric Space ◽  
Group Action ◽  
Symmetric Spaces ◽  
Classification Problem ◽  
Finite Group Action ◽  
Natural Geometry ◽  
A Finite Group

Equivariant and cocompact retractions of certain symmetric spaces are constructed. These retractions are defined using the natural geometry of symmetric spaces and in relation to the theory of lattices of euclidean space. The following cases are considered: the symmetric space corresponding to lattices endowed with a finite group action, from which is obtained some information relating to the classification problem of these lattices, and the Siegel space Sp2g(R)/Ug, for which a natural Sp2g(Z)-equivariant cocompact retract of codimension 1 is obtained.

The Cartesians

2017 ◽  
Author(s):  
Walter Ott
Keyword(s):  
Direct Realism ◽  
Brain Image ◽  
Natural Geometry ◽  
The Mind ◽  
Antoine Arnauld ◽  
Sensible Qualities ◽  
The Brain ◽  
Independent Existence ◽  
Extended Bodies

This chapter examines the crisis of perception as it figures in the work of four of Descartes’s immediate successors: Louis de la Forge, Robert Desgabets, Pierre-Sylvain Régis, and Antoine Arnauld. La Forge opts for a version of Descartes’s last view, which has no place for natural geometry. Desgabets defends a version of Descartes’s earliest view, which requires the mind to turn to the brain image. Régis thinks we sense colors and sounds and the rest and then use these to imagine extension. Arnauld’s case is especially problematic, since he rejects the mind-independent existence of sensible qualities but seems committed to some version of direct realism. He is then left with the question how the mind projects these illusory states on to extended bodies, a question for which he has no answer.

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