scholarly journals Big bang maps and color charge force

2021 ◽  
Vol 12 (2) ◽  
pp. 164-172
Author(s):  
Gudrun Kalmbach H.E.
Keyword(s):  
Hilbert Space ◽  
Gravity Field ◽  
Fiber Bundle ◽  
Big Bang ◽  
Color Charge ◽  
Orthogonal Projections ◽  
3 Dimensional ◽  
Projective Duality ◽  
S Factor ◽  
Hopf Map

The Planck and other natural numbers are used for units of forces. They arise also as weights of Gleason operators, defined by 3-dimensional spin-like base triples GF and their weigths. The spin lengths are the spin GF weights for instance. The measuring GF operator triples arise by projective duality from 1-dimensional force vectors in projective to R5 extended Hilbert space H4. Color charges are set as a separate force, using a G-compass (figure 2). For the universes evolution after a big bang several maps are introduced, mostly belonging to the gravity field quantum rgb-graviton. It presents the neutral color charge of nucleons. Orthogonal projections of H4, also in spiralic and angular form, central or stereographic projective maps belong to them. They project also the S³ factor of the strong interation geometry S³xS5 down to the SU(2) geometry S³ of the Hopf map. Fiber bundle maps are added also to S5 with the same fiber S1 to the base space CP² for nucleons and atomic kernels. In octonian coordinates, listed by indices, 01234567, there are three projections from the energy space 123456 of SI to complex quaternionic 2x2-matrix presentations of spacetime 1234, of CP² as 3456 and of GR with mass and rgb-gravitons 1256. GR and CP² are projected into 1234 as the universes spacetime, observable as bubbles for atoms and matter 3456 and GR potentials and actions about and for mass carrying systems 1256.

scholarly journals Asymptotic normalization coefficient for α+d →6Li from the peripheral direct capture d(α,γ)6 reaction and the astrophysical S factor at Big Bang energies

2020 ◽  
Vol 227 ◽  
pp. 02016
Author(s):  
K.I. Tursunmakhatov ◽  
R. Yarmukhamedov ◽  
S.B. Igamov
Keyword(s):  
Big Bang ◽  
Asymptotic Normalization ◽  
Direct Capture ◽  
Asymptotic Normalization Coefficient ◽  
S Factor ◽  
Low Energies

The results of the analysis of the new experimental astrophysical S factors Sexp24(E) [D. Trezzi, et al., Astropart. Phys. 89, 57 (2017)] and those measured earlier [R. G. Robertson, et al., Phys. Rev. Lett. 47, 1867 (1981)] for the nuclear-astrophysical d(α,γ)6Li reaction directly measured at extremely low energies E, are presented. New estimates and their uncertainties have been obtained for values of the asymptotic normalization coefficient for α + γ → 6Li and for the direct astrophysical S factors at Big Bang energies.

scholarly journals Determination of the asymptotic normalization coefficient (nuclear vertex constant) for α + d →6Li from the new direct measured d(α,γ)6Li data and its implication for extrapolating the d(α,γ)6Li astrophysical S factor at Big Bang energies

2019 ◽  
Vol 49 ◽  
pp. 1960017
Author(s):  
K. I. Tursunmakhatov ◽  
R. Yarmukhamedov
Keyword(s):  
Potential Method ◽  
Big Bang ◽  
Asymptotic Normalization ◽  
Vertex Constant ◽  
Asymptotic Normalization Coefficient ◽  
S Factor ◽  
Low Energies ◽  
Body Potential

The results of the analysis of the new experimental astrophysical S factors [Formula: see text] [D. Trezzi et al., Astropart. Phys. 89, 57 (2017)] and those measured earlier [R. G. Robertson et al., Phys. Rev. Lett. 47, 1867 (1981)] for the nuclear-astrophysical [Formula: see text] reaction directly measured at extremely low energies [Formula: see text], which is derived within the modified two-body potential method, are presented. New estimates and their uncertainties have been obtained for values of the asymptotic normalization coefficient for [Formula: see text] and for the direct astrophysical [Formula: see text] factors at Big Bang energies.

The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem

2015 ◽  
Vol 2015 (708) ◽  
pp. 1-15 ◽  
Author(s):  
Konstantin A. Makarov ◽  
Albrecht Seelmann
Keyword(s):  
Hilbert Space ◽  
Orthogonal Projections ◽  
Bounded Linear ◽  
Length Space ◽  
Metric Properties ◽  
Perturbation Problem ◽  
Subspace Perturbation Problem ◽  
Adjoint Operators ◽  
Spectral Subspaces ◽  
Operator Angle

AbstractWe consider the problem of variation of spectral subspaces for bounded linear self-adjoint operators in a Hilbert space. Using metric properties of the set of orthogonal projections as a length space, we obtain a new estimate on the norm of the operator angle associated with two spectral subspaces for isolated parts of the spectrum of the perturbed and unperturbed operators, respectively. In particular, recent results by Kostrykin, Makarov and Motovilov from [Proc. Amer. Math. Soc. 131, 3469–3476] and [Trans. Amer. Math. Soc. 359, 77–89] are strengthened.

scholarly journals The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
J. A. Helayël-Neto ◽  
Alireza Sepehri ◽  
Tooraj Ghaffary
Keyword(s):  
Modified Gravity ◽  
Dimensional Space ◽  
Main Idea ◽  
Big Bang ◽  
Space Time ◽  
Dimensional Manifold ◽  
3 Dimensional ◽  
Dimensional Space Time ◽  
The Big Bang ◽  
Chern Simons

It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.

scholarly journals α+d→Li6+γ astrophysical S factor and its implications for Big Bang nucleosynthesis

2017 ◽  
Vol 96 (4) ◽  
Author(s):  
A. Grassi ◽  
G. Mangano ◽  
L. E. Marcucci ◽  
O. Pisanti
Keyword(s):  
Big Bang ◽  
Big Bang Nucleosynthesis ◽  
S Factor

scholarly journals On the closure of the sum of closed subspaces

2001 ◽  
Vol 26 (5) ◽  
pp. 257-267 ◽  
Author(s):  
Irwin E. Schochetman ◽  
Robert L. Smith ◽  
Sze-Kai Tsui
Keyword(s):  
Hilbert Space ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
The Other ◽  
Quadratic Programming Problem ◽  
Orthogonal Projections ◽  
The Cost ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for the sum of closed subspaces of a Hilbert space to be closed. Specifically, we show that the sum will be closed if and only if the angle between the subspaces is not zero, or if and only if the projection of either space into the orthogonal complement of the other is closed. We also give sufficient conditions for the sum to be closed in terms of the relevant orthogonal projections. As a consequence, we obtain sufficient conditions for the existence of an optimal solution to an abstract quadratic programming problem in terms of the kernels of the cost and constraint operators.

A functional-analytic framework for the study of elliptic equations on variable domains

1990 ◽  
Vol 116 (3-4) ◽  
pp. 367-380 ◽  
Author(s):  
José M. Vegas
Keyword(s):  
Boundary Condition ◽  
Hilbert Space ◽  
Elliptic Equations ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Analytic Framework ◽  
Orthogonal Projections ◽  
Variable Domains

SynopsisGiven a decreasing sequence of domains Ωn converging in measure to some domain Ω0, a sequence of subspaces V of a Hilbert space V is constructed in such a way that the convergence of the solutions of u −Δu = f on Ωn with Neumann Boundary Condition is given in terms of the convergence of the orthogonal projections Pn on Vn. Under dissipative assumptions, we can obtain continuation results for equations like u −Δu = f(x,u ∇u).

scholarly journals HOPF MAP AND QUANTIZATION ON SPHERE

1999 ◽  
Vol 14 (38) ◽  
pp. 2649-2655 ◽  
Author(s):  
HITOSHI IKEMORI ◽  
SHINSAKU KITAKADO ◽  
HIDEHARU OTSU ◽  
TOSHIRO SATO
Keyword(s):  
Fiber Bundle ◽  
Square Root ◽  
Hopf Map ◽  
Bundle Structure

Quantization of a system constrained to move on a sphere is considered by taking a square root of the "on sphere condition". We arrive at the fiber bundle structure of the Hopf map in S2 and S4. This leads to more geometrical understanding of monopole and instanton gauge structures that emerge in the course of quantization.

scholarly journals Construction of Schauder decomposition on banach spaces of periodic functions

1998 ◽  
Vol 41 (1) ◽  
pp. 61-91 ◽  
Author(s):  
Say Song Goh ◽  
S. L. Lee ◽  
Zuowei Shen ◽  
W. S. Tang
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Banach Spaces ◽  
Biorthogonal System ◽  
The Other ◽  
Projection Operators ◽  
Reconstruction Algorithms ◽  
Periodic Functions ◽  
Orthogonal Projections ◽  
Wavelet Decompositions

This paper deals with Schauder decompositions of Banach spaces X2π of 2π-periodic functions by projection operators Pk onto the subspaces Vk, k = 0,1,…, which form a multiresolution of X2π,. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space on one hand and by interpolatory projections in the Banach space C2π on the other. The approach, using “orthogonal splines”, is constructive and leads to the construction of a Schauder decomposition of X2π and a biorthogonal system for X2π, and its dual X2π. Decomposition and reconstruction algorithms are derived from the construction.

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