•  179
    Set theory INC# based on intuitionistic logic with restricted modus ponens rule (edited book)
    AP LAMBERT Academic Publishing (June 23, 2021). 2021.
    In 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].
  •  118
    A 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 the…Read more
  •  97
    We 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.
  • Our main result will be that: if T is a bounded linear operator on an infinite-dimensional separable complex Hilbert space H,it follow that T has a non-trivial closed invariant subspace.
  •  94
    The Solution of the Invariant Subspace Problem. Complex Hilbert space. Part I.
    Journal of Advances in Mathematics and Computer Science 37 (10): 51-89. 2022.
    We present
  •  101
    A 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^4 )_4 quantum field theory m…Read more
  •  165
    The 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 …Read more
  •  150
    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
  •  83
    Strong Large Deviations Principles of Non-Freidlin-Wentzell Type
    Communications 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
  •  145
    Main results are: (i) number e^{e} is transcendental; (ii) the both numbers e+π and e-π are irrational.
  •  114
    In 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
  •  161
    In this paper intuitionistic set theory INC# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.
  •  331
    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.
    In this article Russell’s paradox and Cantor’s paradox resolved successfully using intuitionistic logic with restricted modus ponens rule.
  •  180
    In this paper we argue that the current paradigm for AGN and quasars is essentially incomplete and a rivision is needed. Remind that the current paradigm for AGN and quasars is that their radio emission is explained by synchrotron radiation from relativistic electrons that are Doppler boosted through bulk motion. In this model, the intrinsic brightness temperatures cannot exceed 1011 to 1012 K. Typical Doppler boosting is expected to be able to raise this temperature by a factor of 10. The obser…Read more
  •  181
    Dark Matter Nature
    Journal 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
  •  125
    Einstein’s 1927 gedanken experiment revisited
    Journal 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
  •  438
    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
  •  162
    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
  •  115
    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
  •  201
    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
  •  197
    New exact quasi-classical asymptotic of solutions to the
  •  205
    New analytical approach for transition to slow 3-D turbulence
    Journal of Physics: Conference Series 633 (1): 6. 2015.
  •  295
    Distributional SAdS BH Spacetime-Induced Vacuum Dominance
    Journal 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
  •  275
    There is No Standard Model of ZFC and ZFC2. Part II.
    with Elena Men’Kova
    Advanced in Pure Mathematic 9 (9): 685-744. 2019.
    In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models or nonstandard model with standard part. An posible generalization of Lob’s theorem is considered.Main results are: (i) ConZFC Mst ZFC, (ii) ConZF V L, (iii) ConNF Mst NF, (iv) ConZFC2, (v) let k be inaccessible cardinal then ConZFC .
  •  237
    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
  •  99
    This 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.
  •  108
    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
  •  379
    This book is devoted to the presentation of the new quantum mechanical formalism based on the probability representation of quantum states. In the 20s and 30s it became evident that some properties in quantum mechanics can be assigned only to the quantum mechanical system, but not necessarily to its constituents. This led Einstein, Podolsky and Rosen (EPR) to their remarkable 1935 paper where they concluded that quantum mechanics is not a complete theory of nature (EPR paradox). In order to avoi…Read more
  •  103
    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