Papers by Dr. Klaus Braun
Supporting mathematics of a Krein space based mechanical and dynamical quanta energy field model
A Bessel function based proof is provided that the Euler-Mascheroni constant 𝜸 is irrational
The proposed Unified Field Theory (UFT) provides an all-encompassing theory, where physical model... more The proposed Unified Field Theory (UFT) provides an all-encompassing theory, where physical models of different physical areas are no longer decoupled and differently scaled according to their different levels of granularity. The proposed UFT supports the aspiration of A. Unzicker's book "Mathematical Reality", to form a consistent picture of reality by observing nature from the cosmos to elementary particles, (UnA2); it also support the theme of his book, “The Liquid (metallic hydrogen) Sun, A Coming Revolution In Astro-Physics, (UnA4), (RoP), (JeJ).
The mathematical modelling framework of the UFT is based on the Hilbert-Krein space theory and the concept of a Krein space intrinsic self-adjoint (Hamiltonian) potential operator.
The physical modelling framework is governed by a deductive structure of an appropriately defined scheme of κ_n-quanta numbers. The two baseline dynamical quanta, the electrino and the positrino, define a „ground state energy“ Hilbert space, called dynamical vacuum energy system. The mathematical construction of those baseline κ_n-quanta numbers is based on the fact that there is a Schnirelmann density of ½ for the set of odd integers and only a Schnirelmann density of zero for the set of even integers. Therefore, the related κ_n-quanta numbers provide a mathematically existing vacuum density of the electrinos (related to the odd integers), while the mathematical vacuum density of the positrinos (related to the even integers) is zero. Accordingly, there is a kind of “probability“ that a positrino meets an electrino (which becomes the birthday of a neutrino) and there is also a kind of “conditional probability“ that a neutrino meets an electrino (which becomes the birthday of an electron), and a kind of“conditional probability“ that a neutrino meets a positrino (which becomes the birthday of a positron). Similar creation processes may happen in the deductive the energy Hilbert scale structure up to the 1-component Dirac 2.0 layer.
The integration of the gravitational dynamics into the UFT may be governed by (1) the Mach2.0 principle (this is basically the Mach principle plus Dirac’s „new basis for cosmology“, (DiP2), by (2) the „global nonlinear stability of the Minkowski space“, (DeC), (KlS), and by (3) tensorial integral equations of the Einstein field equations, (LaK). The new framework indicates to revisit „The Universe Around Us“, (JeJ), (JüF), and the philosophy of C. S. Peirce, a kind of logical idealism, where logic and mathematics provide the most important principles of metaphysics, (PaH), (EcU).
Based on the Hilbert scale H(a) defined by the orthogonal set of eigenpairs of the Stokes operato... more Based on the Hilbert scale H(a) defined by the orthogonal set of eigenpairs of the Stokes operator we present a global unique weak solution of the generalized 3D Navier-Stokes initial value problem. The global boundedness is a consequence of the Sobolevskii-estimate of the non-linear term (SoP) accompanied by a newly proposed "dynamic fluid energy" concept represented by an extended H(1/2) energy Hilbert space.
The proof of the Riemann Hypothesis is enabled by a new integral and series representation of the... more The proof of the Riemann Hypothesis is enabled by a new integral and series representation of the meromorphic Zeta function occuring in the symmetrical form of the Riemann functional equation
A toolbox to build a non-harmonic Fourier series based two-semicircle method, e.g., the zeros of ... more A toolbox to build a non-harmonic Fourier series based two-semicircle method, e.g., the zeros of the Digamma function and a special Kummer function, Paley-Wiener spaces, gap & density theorems, Kadec-1/4 theorem, nonharmonic fourier series, ...
Japan Journal of Applied Mathematics, 1986
The Ritz method for strong elliptic pseudo-differential equations is discussed. 'Optimal' local e... more The Ritz method for strong elliptic pseudo-differential equations is discussed. 'Optimal' local error estimates are derived if the underlying 'approximation-spaces' are finite elements. The analysis covers simultaneously pseudo-differential operators of positive and negative order. In case of positive order an additional regularity assumption for the 'approximation-spaces' is needed.
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Papers by Dr. Klaus Braun
The mathematical modelling framework of the UFT is based on the Hilbert-Krein space theory and the concept of a Krein space intrinsic self-adjoint (Hamiltonian) potential operator.
The physical modelling framework is governed by a deductive structure of an appropriately defined scheme of κ_n-quanta numbers. The two baseline dynamical quanta, the electrino and the positrino, define a „ground state energy“ Hilbert space, called dynamical vacuum energy system. The mathematical construction of those baseline κ_n-quanta numbers is based on the fact that there is a Schnirelmann density of ½ for the set of odd integers and only a Schnirelmann density of zero for the set of even integers. Therefore, the related κ_n-quanta numbers provide a mathematically existing vacuum density of the electrinos (related to the odd integers), while the mathematical vacuum density of the positrinos (related to the even integers) is zero. Accordingly, there is a kind of “probability“ that a positrino meets an electrino (which becomes the birthday of a neutrino) and there is also a kind of “conditional probability“ that a neutrino meets an electrino (which becomes the birthday of an electron), and a kind of“conditional probability“ that a neutrino meets a positrino (which becomes the birthday of a positron). Similar creation processes may happen in the deductive the energy Hilbert scale structure up to the 1-component Dirac 2.0 layer.
The integration of the gravitational dynamics into the UFT may be governed by (1) the Mach2.0 principle (this is basically the Mach principle plus Dirac’s „new basis for cosmology“, (DiP2), by (2) the „global nonlinear stability of the Minkowski space“, (DeC), (KlS), and by (3) tensorial integral equations of the Einstein field equations, (LaK). The new framework indicates to revisit „The Universe Around Us“, (JeJ), (JüF), and the philosophy of C. S. Peirce, a kind of logical idealism, where logic and mathematics provide the most important principles of metaphysics, (PaH), (EcU).