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Book "Set theory INC^# based on intuitionistic logic with restricted modus ponens rule"LAP LAMBERT Academic Publishing. 2021.
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Strong Large Deviations Principles of Non-Freidlin-Wentzell TypeCommunications in Applied Sciences 2 (2): 230-363. 2014.The paper presents, a new large deviations principles (SLDP) of non-Freidlin-Wentzell type, corresponding to the solutions Colombeau-Ito’s SDE. Using SLDP we present a new approach to construct the Bellman function ????(????, ????) and optimal control ????(????, ????) directly by way of using strong large deviations principle for the solutions Colombeau-Ito’s SDE. As important application such SLDP, the generic imperfect dynamic models of air-to-surface missiles are given in addition to the …Read more
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The Solution of the Invariant Subspace Problem. Part I. Complex Hilbert space.Journal of Advances in Mathematics and Computer Science 37 (10): 51-89. 2022.The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC 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 TG [1]-[3] It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which …Read more
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Set Theory INC_{∞^{#}}^{#} Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part III).Hyper inductive definitions. Application in transcendental number theory.Journal of Advances in Mathematics and Computer Science 36 (8): 43. 2021.
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Set theory INC# based on intuitionistic logic with restricted modus ponens rule (edited book)AP LAMBERT Academic Publishing (June 23, 2021). 2021.
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Set Theory INC# Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part.II) Hyper inductive definitionsJournal of Advances in Mathematics and Computer Science 36 (4): 22. 2021.
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Set Theory INC# Based on Intuitionistic Logic with Restricted Modus Ponens Rule (Part. I)Journal of Advances in Mathematics and Computer Science 36 (2): 73-88. 2021.
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Colombeau Solutions to Einstein Field Equations in General Relativity: Gravitational Singularities, Distributional SAdS BH Spacetime-Induced Vacuum Dominance (edited book)Book Publisher International. 2019.This 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 …Read more
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Einstein’s 1927 gedanken experiment revisitedJournal of Global Research in Mathematical Archives(JGRMA) 5 (7). 2018.In 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 …Read more
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Einstein field equations was originally derived by Einstein in 1915 in respect with canonical formalism of Riemann geometry,i.e. by using the classical sufficiently smooth metric tensor, smooth Riemann curvature tensor, smooth Ricci tensor,smooth scalar curvature, etc.. However have soon been found singular solutions of the Einstein field equations with degenerate and singular metric tensor and singular Riemann curvature tensor. These degenerate and singular solutions of the Einstein field equat…Read more
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FOURTH EUROPEAN CONGRESS OF MATHEMATICS STOCKHOLM,SWEDEN JUNE27 - JULY 2, 2004 Contributed papers L. Carleson’s celebrated theorem of 1965 [1] asserts the pointwise convergence of the partial Fourier sums of square integrable functions. The Fourier transform has a formulation on each of the Euclidean groups R , Z and Τ .Carleson’s original proof worked on Τ . Fefferman’s proof translates very easily to R . M´at´e [2] extended Carleson’s proof to Z . Each of the statements of the t…Read more
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Carleson’s celebrated theorem of 1965 [1] asserts the pointwise convergence of the partial Fourier sums of square integrable functions. The Fourier transform has a formulation on each of the Euclidean groups R , Z andΤ .Carleson’s original proof worked on Τ . Fefferman’s proof translates very easily to R . M´at´e [2] extended Carleson’s proof to Z . Each of the statements of the theorem can be stated in terms of a maximal Fourier multiplier theorem [5]. Inequalities for such operators can be tra…Read more
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In contemporary mathematics, a Colombeau algebra of Colombeau generalized functions is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this. Remark 1.1.1.Such a multiplication of distributions has been a long time mistakenly believed to be impossible because of Schwartz’ impossibility result, which basically states that…Read more
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Unruh effect revisitedJournal of Physics: Conference Series 1141 (1). 2018.The vacuum energy density of free scalar quantum field phgr in a Rindler distributional space-time with distributional Levi-Cività connection is considered. It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background space-time with distributional Levi-Cività connection the vacuum energy of…Read more
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Non-archimedean analysis on the extended hyperreal line *R_d and the solution of some very old transcendence conjectures over the field Q.Advances in Pure Mathematics 5 (10): 587-628. 2015.In 1980 F. Wattenberg constructed the Dedekind completiond of the Robinson non-archimedean field and established basic algebraic properties of d [6]. In 1985 H. Gonshor established further fundamental properties of d [7].In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completiond in transcendental number theory w…Read more
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Dark Matter NatureJournal of Physics: Conference Series 1391 (1). 2019.The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum eld theory is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdor- Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cuto and ther…Read more
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New exact quasi-classical asymptotic beyond WKB approximation and beyond Maslov formal expansionJournal of Physics: Conference Series 633 (1). 2015.
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The EPR-B Paradox Resolution. Bell inequalities revisited.Journal of Physics: Conference Series, 1391 (1). 2019.One of the Bell's assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the in uence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell's inequality was derived in its traditional form, without resorting to the hypothes…Read more
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Distributional SAdS BH Spacetime-Induced Vacuum DominanceJournal of Advances in Mathematics and Computer Science 13 (6): 1-54. 2016.This paper dealing with extension of the Einstein eld equations using apparatus of contemporary generalization of the classical Lorentzian geometry named in literature Colombeau distributional geometry, see for example [1], [2], [3], [4], [5], [6], [7] and [32]. The regularizations of singularities presented in some solutions of the Einstein equations is an important part of this approach. Any singularities present in some solutions of the Einstein equations recognized only in the sense of Col…Read more
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There is No Standard Model of ZFC and ZFC2. Part II.Advanced in Pure Mathematic 9 (9): 685-744. 2019.
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New analytical approach for transition to slow 3-D turbulenceJournal of Physics: Conference Series 633 (1): 6. 2015.
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The Solution Cosmological Constant ProblemJournal of Modern Physics 10 (7): 729-794. 2019.The cosmological constant problem arises because the magnitude of vacuum energy density predicted by the Quantum Field Theory is about 120 orders of magnitude larger then the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdorff-Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cutoff ∗ Λ a…Read more
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Was Polchinski Wrong? Colombeau Distributional Rindler Space-Time with Distributional Levi-Cività Connection Induced Vacuum Dominance. Unruh Effect RevisitedJournal of High Energy Physics, Gravitation and Cosmology 2 (4): 361-440. 2018.The vacuum energy density of free scalar quantum field Φ in a Rindler distributional space-time with distributional Levi-Cività connection is considered. It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background space-time with distributional Levi-Cività connection the vacuum energy of fr…Read more
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Generalized Löb’s Theorem.Strong Reflection Principles and Large Cardinal Axioms. Consistency Results in Topology.Pure and Applied Mathematics Journal (Vol. 4, No. 1-1): 1-5. 2015.
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There is no standard model of ZFCJournal of Global Research in Mathematical Archives 5 (1): 33-50. 2018.
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Inconsistent Countable Set in Second Order ZFC and Nonexistence of the Strongly Inaccessible CardinalsBritish Journal of Mathematics and Computer Science 9 (5): 380-393. 2015.
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Relevant first-order logic LP# and Curry’s paradox resolutionPure and Applied Mathematics Journal Volume 4, Issue 1-1, January 2015 DOI: 10.11648/J.Pamj.S.2015040101.12. 2015.In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventin…Read more
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There is No Standard Model of ZFC and ZFC_2. Part I.Journal of Advances in Mathematics and Computer Science 2 (26): 1-20. 2017.In this paper we view the first order set theory ZFC under the canonical frst order semantics and the second order set theory ZFC_2 under the Henkin semantics. Main results are: (i) Let M_st^ZFC be a standard model of ZFC, then ¬Con(ZFC + ∃M_st^ZFC ). (ii) Let M_stZFC_2 be a standard model of ZFC2 with Henkin semantics, then ¬Con(ZFC_2 +∃M_stZFC_2). (iii) Let k be inaccessible cardinal then ¬Con(ZFC + ∃κ). In order to obtain the statements (i) and (ii) examples of the inconsistent c…Read more