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OALib Journal期刊

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Elements of Real Hilbert Spaces Theory  [PDF]
Daniel Sepunaru
Open Access Library Journal (OALib Journal) , 2015, DOI: 10.4236/oalib.1101554
Abstract: We discuss an alternative version of non-relativistic Newtonian mechanics in terms of real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme is in accordance with the standard formulation. Heisenberg-Schrodinger non-relativistic quantum mechanics is considered adequate and complete. Since the suggested theory is dispersion free, linear superposition principle is not violated but cannot affect results of measurements due to spectral decomposition theorem for self-adjoint operators (the collapse of wave function).
Set-Valued Non-Linear Random Implicit Quasivariational Inclusions  [PDF]
Salahuddin  , Mohammad Kalimuddin Ahmad
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.43063
Abstract: In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.
有限维Hilbert空间中框架的最大鲁棒性擦除
Maximal robustness to erasures in finite-dimensional Hilbert Spaces
潘建丽,朱玉灿
福州大学学报(自然科学版) , 2015, DOI: 10.7631/issn.1000-2243.2015.03.0293
Abstract: 对有限维Hilbert空间中的一些特殊框架进行讨论，即通过对特殊复框架右乘一个酉矩阵，从而构造出Hn的最大鲁棒性擦除的等模、实紧框架. 最后给出相应的结论并进行证明.
In this paper，we mainly discussed some special frames in finite-dimensional Hilbert spaces，namely，we construct real，equal tight frames with maximum robustness to erasures for Hn from complex frames by multiplying a unitary matrix. Finally，we give the corresponding conclusions and also prove them
A Vector Matrices Realization of Hurwitz Algebras  [PDF]
Daniel Sepunaru
Journal of Modern Physics (JMP) , 2018, DOI: 10.4236/jmp.2018.914151
Abstract: We present here a realization of Hurwitz algebra in terms of 2 × 2 vector matrices which maintain the correspondence between the geometry of vector spaces that is used in the classical physics and the algebraic foundation underlying quantum theory. The multiplication rule we use is a modification of the one originally introduced by M. Zorn. We demonstrate that our multiplication is not intrinsically non-associative; the realization of the real and complex numbers is commutative and associative, the real quaternions maintain associativity and the real octonion matrices form an alternative algebra. Extension to the calculus of the matrices (with Hurwitz algebra valued matrix elements) of the arbitrary dimensions is straightforward. We briefly discuss applications of the obtained results to extensions of standard Hilbert space formulation in quantum physics and to alternative wave mechanical formulation of the classical field theory.
On the Problem of Eigenschaften in Quantum and Classical Mechanics  [PDF]
Daniel Sepunaru
Journal of Modern Physics (JMP) , 2018, DOI: 10.4236/jmp.2018.914152
Abstract: We argue that in contrast to the classical physics, measurements in quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant relative phases. Simultaneity is needed since measurement changes the state of the system (in both quantum and in classical physics). We call that measurement procedure holographic detection. Mathematically, it is described by a set of mutually commuting selfadjoint operators that are similar and closely related to projections. We present explicit examples and discuss general features of the corresponding experimental setup which we identify as the quantum reference frame.
A note on tensor fields in Hilbert spaces
BILIOTTI, LEONARDO;MERCURI, FRANCESCO;TAUSK, DANIEL V.;
Anais da Academia Brasileira de Ciências , 2002, DOI: 10.1590/S0001-37652002000200003
Abstract: we discuss and extend to infinite dimensional hilbert spaces a well-known tensoriality criterion for linear endomorphisms of the space of smooth vector fields in n.
A note on tensor fields in Hilbert spaces
BILIOTTI LEONARDO,MERCURI FRANCESCO,TAUSK DANIEL V.
Anais da Academia Brasileira de Ciências , 2002,
Abstract: We discuss and extend to infinite dimensional Hilbert spaces a well-known tensoriality criterion for linear endomorphisms of the space of smooth vector fields in n.
A Monotonicity Condition for Strong Convergence of the Mann Iterative Sequence for Demicontractive Maps in Hilbert Spaces  [PDF]
Akuchu Besheng George, Celestin Akwumbuom Nse
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.515212
Abstract:


Let be a real Hilbert space and C be a nonempty closed convex subset of H. Let T : C → C be a demicontractive map satisfying 〈Tx, x〉 ≥ ‖x‖2 for all x ∈ D (T). Then the Mann iterative sequence given by xn + 1 = (1 - an) xn + anT xn, where an ∈ (0, 1) \"\"n ≥ 0, converges strongly to an element of F (T):= {x ∈ C : Tx = x}. This strong convergence is obtained without the compactness-type assumptions on C, which many previous results (see e.g. [1]) employed.


New Implementation of Reproducing Kernel Method for Solving Functional-Differential Equations  [PDF]
Aboalfazl Abdollazadeh, Farhad Moradi, Hossein Pourbashash
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.710095
Abstract: In this paper, we apply the new algorithm of reproducing kernel method to give the approximate solution to some functional-differential equations. The numerical results demonstrate the accuracy of the proposed algorithm.
On Hypercomplex Extensions of Quantum Theory  [PDF]
Daniel Sepunaru
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.65075
Abstract: This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions with external fields.
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