A Cubic Pure Half-Spinor Approach to High Performance Photon-Counting Computerized X-ray Tomography – Transcendence of the Brauer Mirror Symmetry Functor –
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2024-09-30 |
| Journal | Complex Analysis and Operator Theory |
| Authors | Walter Schempp |
Abstract
Section titled “Abstract”Abstract The goal of this paper is to present a spectral theory of advanced photon-counting computerized X-ray tomography, which is a promising microelectronical semiconductor wafer X-ray technique on the verge of becoming clinically feasible and has the potential to dramatically alter the clinical application of computer-aided medical diagnosis in the upcoming decades. In analogy to the deep fact that any real division algebra has dimension 1, 2, 4 or 8, the isogeneous third Galois cohomological, mirror symmetrical approach to high spatial resolution spectral photon-counting computerized tomography establishes that the exceptional Lie group $$\textrm{Spin}(8,\mathbb {R})$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mtext>Spin</mml:mtext> <mml:mo>(</mml:mo> <mml:mn>8</mml:mn> <mml:mo>,</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is the only one of the spin group spectrum $${\textrm{Spin}(n,\mathbb {R})\mid n \ge 1}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mo>{</mml:mo> <mml:mtext>Spin</mml:mtext> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> <mml:mo>∣</mml:mo> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> to admit a triality automorphism. It is the exceptional phenomenon of triality which is able to produce by the spin representation theory of the exceptional Lie group of octonions $$\mathbb {O}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mi>O</mml:mi> </mml:math> the spectral shaped digital signals of spectral photon-counting computerized X-ray tomography. Similarly to spin echo magnetic resonance tomography, the mathematical approach to spectral high performance computerized tomography is based on the isogeneously invariant, projectively weighted, symplectic coadjoint orbit picture $$\mathfrak {Lie}(\mathcal {N})^*/\textrm{CoAd}(\mathcal {N})$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mi>Lie</mml:mi> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>/</mml:mo> <mml:mtext>CoAd</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> of the real 3-dimensional Heisenberg unipotent Lie group $$\mathcal {N}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mi>N</mml:mi> </mml:math> of type $$\textrm{GL}(3,\mathbb {R})$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mtext>GL</mml:mtext> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and its solvable diamond toric Lie group extension.
Tech Support
Section titled “Tech Support”Original Source
Section titled “Original Source”References
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