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Matrix Science MathematicThis article will begin with the claim that Hamilton spent a great deal of time trying to figure out the three-dimensional complex numbers. He was never able to accomplish that. Complex numbers are in the form a+bi where ‘a’ is a real part and ‘bi’ an imaginary with 𝑖= √−1 The motive behind the claim is that both 𝑖2 and 𝑗2= −1; The failure may also ...
MSc. Ruslan Pozinkevycha
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Colouring lines in projective space
Journal of Combinatorial Theory, Series A, 2006 19 pages; to appear in J.
Ameera Chowdhury +2 more
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The Stereographic Projection in Banach Spaces
Rocky Mountain Journal of Mathematics, 2007 We give a new and direct proof of the fact that, in any infinite dimensional Banach space, the unit sphere minus any one point is homeomorphic to a closed hyperplane. The proof involves L-structures and geometric concepts as, for instance, rotund, smooth and exposed points.
García-Pacheco, Francisco J. +1 more
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Finitistic Spaces with Orbit Space a Product of Projective Spaces
, 2023 Let G = Z2 act freely on a nitistic space X. If the mod 2 cohomology of X is isomorphic to the real projective space RP^{2n+1} (resp. complex projective space CP^{2n+1}) then the mod 2 cohomology of orbit spaces of these free actions are RP1 x CPn (resp. RP2 x HPn) [7]. In this paper, we have discussed converse of these results. We have showed that if
Kumari, Anju, Singh, Hemant Kumar
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Accounts of Chemical Research, 2015 One of the simplest questions that can be asked about molecular diversity is how many organic molecules are possible in total? To answer this question, my research group has computationally enumerated all possible organic molecules up to a certain size to gain an unbiased insight into the entire chemical space. Our latest database, GDB-17, contains 166.
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Matroid Representation of Projective Spaces
European Journal of Combinatorics, 1984 \textit{T. H. Brylawski} and \textit{D. Lucas} have shown [Colloq. Int. Teorie Comb., Roma 1973, Tomo I, 83-104 (1976; Zbl 0392.51007)] that any two representations of the full projective space PG(r,F) of rank r over the field F are projectively equivalent if \(F=GF(p)\).
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On the projective \(LB\)-spaces
, 1992 The main result of the paper is: An LB-space \(Z\) is projective in the category of all LB-spaces (that is: for every LB-space \(X\) every quotient mapping \(q: X\to Z\) has a right inverse) if and only if \(Z\) is isomorphic to the locally convex direct sum of a sequence of \(\ell_ 1(\Gamma)\)-spaces.
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Immersions of real projective spaces into complex projective spaces
Hiroshima Mathematical Journal, 1987 This paper achieves a classification up to regular homotopy of immersions from a real projective space \(P^ n({\mathbb{R}})\) into a complex projective space \(P^ m({\mathbb{C}})\). Calculations with characteristic classes show that, for \(n>m\), any such immersion is nullhomotopic.
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On the Imbedding of a Projectively Connected Space in a Projective Space
On the Imbedding of a Projectively Connected Space in a Projective Spaceapplication/pdf ...
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