1,720,996 research outputs found
Set theory INC# based on intuitionistic logic with restricted modus ponens rule
Get PDFIn this book set theory INC# based on intuitionistic logic with restricted modus ponens
rule is proposed. It proved that intuitionistic logic with restricted modus ponens rule can
to safe Cantor naive set theory from a triviality. Similar results for paraconsistent set
theories were obtained in author papers [13]-[16]
Large deviations principles of Non-Freidlin-Wentzell type
Get PDFoai:arXiv.org:0803.2072Generalized Large deviation principles was developed for Colombeau-Ito SDE
with a random coefficients. We is significantly expand the classical theory of
large deviations for randomly perturbed dynamical systems developed by Freidlin
and Wentzell.Using SLDP approach, jumps phenomena, in financial markets, also
is considered. Jumps phenomena, in financial markets is explained from the
first principles, without any reference to Poisson jump process. In contrast
with a phenomenological approach we explain such jumps phenomena from the first
principles, without any reference to Poisson jump process.Comment: 189 pages. arXiv admin note: substantial text overlap with
arXiv:math/0411386 by other author
Colombeau Solutions to Einstein Field Equations in General Relativity: Gravitational Singularities, Distributional SAdS BH Spacetime-Induced Vacuum Dominance
Get PDFThis book deals with Colombeau solutions to Einstein field equations in general relativity: Gravitational singularities, distributional SAdS BH spacetime-induced vacuum dominance. This book covers key areas of Colombeau nonlinear generalized functions, distributional Riemannian, geometry, distributional schwarzschild geometry, Schwarzschild singularity, Schwarzschild horizon, smooth regularization,
nonsmooth regularization, quantum fields, curved spacetime, vacuum fluctuations, vacuum dominance etc. This book contains various materials suitable for students, researchers and academicians of this area
Model λ(φ^2n )_4,n≥2 Quantum Field Theory: A Nonstandard Approach Based on Nonstandard Pointwise-Defined Quantum Fields
No full textA new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^* algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^2n )_4,n≥2 quantum field theory models are Lorentz covariant
Foundation of paralogical nonstandard analysis. Part I.
Get PDFThis is an article about foundation of paralogical nonstandard analysis and its
applications to the continuous function without a derivative presented by absolutely
convergent trigonometrical series and another famous problems of trigonometrical
and orthogonal series
Einstein’s 1927 gedanken experiment revisited
Get PDFIn 1935, Einstein, Podolsky and Rosen (EPR) originated the famous “EPR paradox”
[1]. This argument concerns two spatially separated particles which have both
perfectly correlated positions and momenta, as is predicted possible by quantum
mechanics. The EPR paper spurred investigations into the nonlocality of quantum
mechanics, leading to a direct challenge of the philosophies taken for granted by most
physicists.The EPR conclusion was based on the assumption of local realism, and
thus the EPR argument pinpoints a contradiction between local realism and the
completeness of quantum mechanics.
Einstein’s 1927 gedanken experiment by using the probability representation of quantum states explained successfully
Internal Set Theory IST# Based on Hyper Infinitary Logic with Restricted Modus Ponens Rule: Nonconservative Extension of the Model Theoretical NSA
Get PDFThe incompleteness of set theory ZF C leads one to look for natural nonconservative extensions
of ZF C in which one can prove statements independent of ZF C which appear to be “true”.
One approach has been to add large cardinal axioms.Or, one can investigate second-order
expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is
a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the
inclusion of Tarski’s axiom which implies the existence of inaccessible cardinals. See also related
set theory with a filter quantifier ZF (aa). In this paper we look at a set theory NC#
∞# , based
on bivalent gyper infinitary logic with restricted Modus Ponens Rule In this paper we deal
with set theory NC#
∞# based on bivalent gyper infinitary logic with Restricted Modus Ponens
Rule. Nonconservative extensions of the canonical internal set theories IST and HST are propose
The Solution of the Invariant Subspace Problem. Complex Hilbert Space. External Countable Dimensional Linear spaces Over Field *Rc#. Part II.
Get PDFWe present a new approach to the invariant subspace problem for complex Hilbert spaces.This approach
based on nonconservative Extension of the Model Theoretical NSA. Our main result will be that: if T is a
bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace
New exact quasi-classical asymptotic beyond WKB approximation and beyond Maslov formal expansion
Get PDFNew exact quasi-classical asymptotic of solutions to th
There is no standard model of ZFC
Get PDFMain results are:(i) Let M_st be standard model of ZFC. Then ~Con(ZFC+∃M_st),
(ii) let k be an inaccessible cardinal then ~Con(ZFC+∃k),[10],11]
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