real geometry
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Author(s):  
José F. Fernando

AbstractA classical problem in real geometry concerns the representation of positive semidefinite elements of a ring A as sums of squares of elements of A. If A is an excellent ring of dimension $$\ge 3$$ ≥ 3 , it is already known that it contains positive semidefinite elements that cannot be represented as sums of squares in A. The one dimensional local case has been afforded by Scheiderer (mainly when its residue field is real closed). In this work we focus on the 2-dimensional case and determine (under some mild conditions) which local excellent henselian rings A of embedding dimension 3 have the property that every positive semidefinite element of A is a sum of squares of elements of A.


2021 ◽  
Vol 2127 (1) ◽  
pp. 012013
Author(s):  
V Kravchenko ◽  
O A Azarova ◽  
T A Lapushkina

Abstract A partially automatic method of digital processing images (photographs, shadow and Schlieren pictures) for the analysis of experimental data is proposed. The method is utilized to investigate the effect of the region of ionization instability created by a glow gas discharge on the front of an initially flat shock wave. The proposed method is based on a composition of simple image processing operations and makes it possible to perform simulations taking into account the real geometry of the ionization strata and the shape of the front of a shock wave based on the obtained experimental images. First, as a result of digital processing the geometry of experimental objects is extracted from the images. This information is then embedded in the Navier-Stokes code for conducting simulations. New results for the real geometry of ionization strata of different scales are presented which confirmed the previous ones obtained for the density homogeneously stratified source model.


2021 ◽  
Vol 2081 (1) ◽  
pp. 012023
Author(s):  
V V Kassandrov ◽  
N V Markova

Abstract The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures naturally arise in the framework of biquaternionic analysis. Both together, algebraic and twistor structures impose rigid restriction on the transport of singular points of biquaternion-valued fields identified with particle-like formations.


Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2548
Author(s):  
Tomás Recio ◽  
Rafael Losada ◽  
Zoltán Kovács ◽  
Carlos Ueno

Recently developed GeoGebra tools for the automated deduction and discovery of geometric statements combine in a unique way computational (real and complex) algebraic geometry algorithms and graphic features for the introduction and visualization of geometric statements. In our paper we will explore the capabilities and limitations of these new tools, through the case study of a classic geometric inequality, showing how to overcome, by means of a double approach, the difficulties that might arise attempting to ‘discover’ it automatically. On the one hand, through the introduction of the dynamic color scanning method, which allows to visualize on GeoGebra the set of real solutions of a given equation and to shed light on its geometry. On the other hand, via a symbolic computation approach which currently requires the (tricky) use of a variety of real geometry concepts (determining the real roots of a bivariate polynomial p(x,y) by reducing it to a univariate case through discriminants and Sturm sequences, etc.), which leads to a complete resolution of the initial problem. As the algorithmic basis for both instruments (scanning, real solving) are already internally available in GeoGebra (e.g., via the Tarski package), we conclude proposing the development and merging of such features in the future progress of GeoGebra automated reasoning tools.


2021 ◽  
Author(s):  
Sotiris Sofias
Keyword(s):  
The Real ◽  

An analytical Geometrical calculation of the Pyramids of Giza using the ultimate applications such as Auto Cad and Google Earth base maps. The correlation with the Orion Constellation is not mathematically correct.


Lubricants ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 83
Author(s):  
Franco Concli ◽  
Augusto Della Torre

Additive Manufacturing (AM) is becoming a more and more widespread technology. Its capability to produce complex geometries opens new design possibilities. Despite the big efforts made by the scientific community for improving the AM processes, this technology still has some limitations, mainly related to the achievable surface quality. It is known that AM technologies promote the formation of LACKS of fusion inside the material. In some cases, the external surfaces are finished with traditional machining. This is the case of AM-produced gears. While the grinding operation aims to reduce the surface roughness, the presence of porosities just below the surface of the wrought component, could lead, after grinding, to the exposure of those porosities leading to a pitted surface. This phenomenon is surely not beneficial in terms of structural resistance, but can help the lubrication promoting the clinging of the lubricant to the surface. The aim of this paper is to study this effect. Micro-Computer-Tomography (μ-CT) analyses were performed on a 17-4 PH Stainless Steel (SS) produced via Selective Laser Melting (SLM). The real geometry of the pores was reproduced virtually and analyzed by means of multiphase CFD analyses in the presence of centrifugal effects.


2021 ◽  
Vol 2 ◽  
pp. 100007
Author(s):  
Sunil Raghavendra ◽  
Alberto Molinari ◽  
Michele Dallago ◽  
Gianluca Zappini ◽  
Filippo Zanini ◽  
...  

2021 ◽  
Author(s):  
Carmelo Mineo ◽  
Donatella Cerniglia ◽  
Vito Ricotta ◽  
Bernhard Reitinger

Abstract Many industrial sectors face increasing production demands and need to reduce costs, without compromising the quality. Whereas mass production relies on well-established protocols, small production facilities with small lot sizes struggle to update their highly changeable production at reasonable costs. The use of robotics and automation has grown significantly in recent years, but extremely versatile robotic manipulators are still not commonly used in small factories. Beside of the investments required to enable efficient and profitable use of robot technology, the efforts needed to program robots are only economically viable in case of large lot sizes. Generating robot programs for specific manufacturing tasks still relies on programming trajectory waypoints by hand. The use of virtual simulation software and the availability of the specimen digital models can facilitate robot programming. Nevertheless, in many cases, the virtual models are not available or there are unavoidable differences between virtual and real setups, leading to inaccurate robot programs and time-consuming manual corrections. This could be avoided by measuring the real-geometry and the position of the specimen, which creates the paradox of having to plan robot paths for surface mapping purposes, before the originally intended robot task can be approached. Previous works have demonstrated the use of robotically manipulated optical sensors to map the geometry of samples. However, the use of simple user-defined robot paths, which are not optimized to the part geometry, typically causes some areas of the samples to not be mapped with the required level of accuracy or to not be sampled at all by the optical sensor. This work presents an autonomous framework to enable adaptive surface mapping, without any previous knowledge of the part geometry being transferred to the system. The article gives an overview of the related work in the field, a detailed description of the proposed framework and a proof of its functionality through both simulated and experimental evidences.


2021 ◽  
Vol 51 (1) ◽  
pp. 63-81
Author(s):  
Ivan ZVARA ◽  
Roman PAŠTEKA ◽  
Roland KARCOL

Interpretation and inversion of microgravity anomalies belong to important tasks of near-surface geophysics, mostly in cavities detection in engineering, environmental and archaeological applications. One of the mostly used concepts of inversion in applied gravimetry is based on the approximation of the model space by means of 2D or 3D elementary sources with the aim to estimate their densities by means of the solution of a corresponding linear equation system. There were published several approaches trying to obtain correct and realistic results, which describe real parameters of the sources. In the proposed contribution we analyse the properties of two additional functionals, which describe additional properties of the searched solution – namely so-called L2-smoothing and minimum support focusing stabilizers. For the inversion itself, we have used the regularized conjugate gradient method. We have studied properties of these two stabilizers in the case of one synthetic model and one real-world dataset (microgravity data from St. Nicholas church in Trnava). Results have shown that proposed algorithm with the minimum support stabilizer can generate satisfactory model results, from which we can describe real geometry, dimensions and physical properties of interpreted cavities.


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