Search results for "Geometry"

Geometry of the projectivization of ideals and applications to problems of birationality

2018

In this thesis, we interpret geometrically the torsion of the symmetric algebra of the ideal sheaf I_Z of a scheme Z defined by n+1 equations in an n-dimensional variety. This is equivalent to study the geometry of the projectivization of I_Z. The applications of this point of view concern, in particular, the topic of birational maps of the projective space of dimension 3 for which we construct explicit birational maps that have the same algebraic degree as their inverse, free and nearly-free curves for which we generalise a characterization of free curves by extending the notion of Milnor and Tjurina numbers. We tackle also the topic of homaloidal hypersurfaces, our original motivation, fo…

Lawvere–Tierney sheaves in Algebraic Set Theory

2009

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

Sequential formula translation

1983

The syntax of an algorithmic language such as ALGOL is conveniently described as a sequence of states indicated by an element called cellar. Transitions are controlled by admissible state- s ymbol pairs which may be represented by a transition matrix. This description of syntax furnishes at the same time an extremely simple rule for translating into machine programs statements in the algorithmic language. Sequential treatment, however, is not feasible in the case of certain optimizing processes such as recursive address calculation.

Influence of Joint Geometry on Micro and Macro Mechanical Properties of Friction Stir Spot Welded Joints

2014

AbstractSpot welding can be considered a very common joining technique in automotive and transportation industries as it permits to obtain effective lap-joints with short process times and what is more it is easily developed through robots and automated systems. Recently, Friction Stir Spot Welding (FSSW) has been proposed as a natural evolution of the already known Friction Stir Welding (FSW) process, allowing to obtain sound spot joints that do not suffer from the insurgence of typical welding defects due to the melting of the base material. Similarly to FSW, both geometrical and technological parameters must be considered as they affect the material flow and the heat flux generated durin…

Detection of Amyloid-β Fibrils Using Track-Etched Nanopores: Effect of Geometry and Crowding

2021

Several neurodegenerative diseases have been linked to proteins or peptides that are prone to aggregate in different brain regions. Aggregation of amyloid-β (Aβ) peptides is recognized as the main cause of Alzheimer's disease (AD) progression, leading to the formation of toxic Aβ oligomers and amyloid fibrils. The molecular mechanism of Aβ aggregation is complex and still not fully understood. Nanopore technology provides a new way to obtain kinetic and morphological aspects of Aβ aggregation at a single-molecule scale without labeling by detecting the electrochemical signal of the peptides when they pass through the hole. Here, we investigate the influence of nanoscale geometry (conical an…

In vitro evaluation of the ability of three apex locators to determine the working length during retreatment.

2005

The purpose of this in vitro study was to evaluate the accuracy of three apex locators in determining the working length during the retreatment process. Twenty extracted single-rooted human teeth with mature apices were used in this study. The root canal length of each tooth was measured placing a #15 file until the tip was visible at the apical foramen. The direct visual measurement was reduced by 0.5 mm and recorded. The root canals were instrumented and filled to the direct visual measurement using lateral compaction technique. After 7 days the teeth were retreated using three apex locators: ProPex, NovApex, and Root ZX, for determining the retreatment working length. Afterward, comparis…

Relationship between particle size and dissolution rate of bulk powders and sieving characterized fractions of two qualities of orthoboric acid

1996

Drug Dev. Ind. Pharm. ISI Document Delivery No.: VN279 Times Cited: 1 Cited Reference Count: 22 Tromelin, A Habillon, S Andres, C Pourcelot, Y Chaillot, B; International audience; We have carried out a study of the particle size distribution and aqueous dissolution rate of two commercially available qualities of orthoboric acid, labeled ''crystal'' (ABC) and ''powder'' (ABP). In a previous work, we have shown that the two commercial qualities of orthoboric acid chosen as model compound (''powder'' and ''crystal'') are related to the same crystal network in spite of their different names. However, these two qualities have very different size particle distributions, as previously determined b…

The Transfer Function of Non-Stationary Indoor Channels and its Relationship to System Functions of LFMCW Radars

2021

This paper studies the relationship between the time-variant (TV) channel transfer function (CTF) of non-stationary indoor channels and the system functions of linear frequency modulated continuous waves (LFMCW) radars. To do so, we consider a moving person/object in indoor environments, which is modelled by a cluster of moving point scatterers. It is shown that the TVCTF can be obtained from the beat signal of LFMCW radar systems. Analytical expressions are derived for the TV demodulated radar response, the complex channel gain, and the TV Doppler-delay profile. A relationship between the presented results and existing non-stationary indoor channel models assuming pulsed wave systems is al…

Analytische Geometrie nach Prof. Dr. F. Schur

1892

Quantum state engineering using one-dimensional discrete-time quantum walks

2017

Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin, and providing …