The Shape of Space: The Beginning of Non-Euclidean Geometry
V .7 :Non – Euclidean geometry in modern mathematics
... Euclidean models of the hyperbolic plane. In all the preceding models, it was necessary to introduce a special definition of distance in order to make everything work right. It would be very satisfying if we could ...
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The Moulds, for Euclidean Geometry Quantization , and Relativity
... createdthe Non-Euclid geometries which deviated GR in Space-time confinement, so ,not conceiving the beyond Planck`s existence, not explaining the WHY speed of light is constant, and thus the whole ...
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Misconceptions of Universe Expansion, Accelerated Universe Expansion, and Their Sources Virtual Reality of Inflationary Cosmology
... Lobachevskian geometry of a non-expanding Universe is provided for ex- perimental data acquired in the Supernova Project, showing an excellent agreement between experimental data and our theoretical ...deep ...
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Special geometry, black holes and Euclidean supersymmetry
... the geometry of space-time and the geometry of the target manifold of the scalar ...case, space-time is Euclidean, but, as we will see, the scalar manifold is pseudo- Riemannian with ...
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Michael Beaney (ed.), The Oxford Handbook of the History of Analytic Philosophy
... of space and time and of categories through some key de- velopments in nineteenth-century German philosophy of science to a variety of approaches typical of analytic ...of space and time, is a ‘structural ...
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On the metric triangle inequality
... extrametric space, providing an interesting geometric model that illustrates the existence of the hyperbolic non-Euclidean geometry on the place where the triangle inequality is ...
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After Non-Euclidean Geometry: Intuition, Truth and the Autonomy of Mathematics
... the Euclidean system as true. For example, Frege regards thinking about non-Euclidean geometries as using “still the same old intuition of Euclidean space, the only one whose structures ...
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Orientation Maps in V1 and Non-Euclidean Geometry
... to Euclidean geometry but have a meaning on every “symmetric enough” space, and we thus saw how a unique Gaussian random field providing V1-like maps can be associated to each irreducible “factor” in ...
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Exploring concepts and applications of taxicab geometry
... in Euclidean geometry for the last 2000 years, came possible by the use of taxicab ...geometry. Euclidean geometry measures distance "as the crow flies", but this rarely ...
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Brief Note on a Scalar Quantum Field with Finite Lifetime in a Lorentz Invariant Non Rectangular Euclidean Space
... the geometry of Minkowski space (MS) may not be appropriate for the calculation of the high energy range of momentum ...invariant, geometry is constructed. It turns out that a non-rectangular ...
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The Issues of the Judicial System and the Jurisdiction of the Courts of the First Instance in the Republic of Austria
... Fifthly, according to §13 of the code individually judges also consider criminal cases as a court of the first instance. Let’s make clarifying that these judges can hear cases of crimes that are not within the ...
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Influence of the cross-section shape in the capillaries on the wetting properties demonstrated by the calculated wetting angles
... A b s t r a c t. Earlier results had shown that the contracting force of water films between parallel solid surfaces increased when they were deformed to give longer menisci by subdividing the water volume. Since ...
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Efficient Shape Optimization of Space Trusses
... In all the cases, for the supporting arch and the double-layer truss, the solution procedure was stable. As shown, a gradient-based algorithm can perform the optimization very efficiently. However, in shape-design ...
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Primordial germ cell biology at the beginning of the XXI Century
... the beginning of the 1980s, our understanding of the biology of mammalian PGCs was limited to the morphological description of their origin in the gonads, and their migration and differentiation within the gonadal ...
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I : Vector algebra and Euclidean geometry
... As noted before, in a completely analytic treatment of Euclidean geometry, it would be necessary to verify explicitly that the interpretations for “undefined concepts” satisfy the synthetic axioms. We shall ...
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Constructing Curvature: The Iterative Design of a Computer-Based Microworld for Non-Euclidean Geometry
... The aim of this chapter is to develop a model of a context in which to teach and learn non-euclidean geometry. §2.1 reviews the definition of models and modelling and discusses their c[r] ...
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Constraints Influencing the Design of Forming Shoulders and the Use of Exact Geometry
... the geometry o f the shoulder is considered and means fo r defining its complex form discussed, together with the design issues related to the performance o f the machine in terms o f web tension and its ability ...
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Consideration of the contribution of chemical (non-enzymatic) conversion of substrate in the general mechanism of enzyme reaction
... influence of the chemical (non-catalytic) reaction during the investigation of the catalytic reaction, in experimental studies, in particular enzyme-cata- lyzed reactions, the contribution of the ...
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Quaternions applied to physics in non euclidean space 1 The mathematical methods
... Tlie terms "similarly directed" and 'oppoand site " give different meanings for the two axes except when the centre or axis of symmetry is given the terms ought not to be used in ellipti[r] ...
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Registration of Diffusion Tensor Images in Log-Euclidean and Euclidean Space
... This additional freedom allows for the registration of images across patients, where the size and geometry of the captured structures may vary to some degree. Furthermore, from a computational point of view, ...
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