In this paper paraconsistent first-order logic LP^{#}_{omega} with infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#}_{omega} is discussed.Axiomatical system HST^{#}_{omega} as paraconsistent gene
ralization of Hrbacek set theory HST is considered.
In this paper we leave the neighborhood of the singularity at the origin and turn to the singularity at the horizon. Using nonlinear superdistributional geometry and supergeneralized functions it seems possible to show that the horizon singularity is
not only a coordinate singularity without leaving Schwarzschild coordinates. However the Tolman formula for the total energy $E$ of a static and asymptotically flat spacetime,gives $E=mc^2$, as it should be. New class Colombeau solutions to Einstein field equations is obtained.New class Colombeau solutions to Einstein field equations is obtained. The vacuum energy density of free scalar quantum field ${Phi}$ with a distributional background spacetime also 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 spacetime with distributional Levi-Civit`a connection the vacuum energy of free quantum fields is forced, by the very same background distributional space-time such a Rindler distributional background space-time, to become dominant over any classical energy density component.This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on a Rindler distributional space-times with distributional Levi-Civit`a connection. In particular we obtain that the vacuum fluctuations $<{Phi}^2({delta})>$ have a singular behavior at a Rindler horizon $delta = 0$.Therefore sufficiently strongly accelerated observer burns up near the Rindler horizon. Thus Polchinski account does not violate of the Einstein equivalence principle.
Analytical non-perturbative study of the three-dimensional nonlinear stochastic partial differential equation with additive thermal noise, analogous to that proposed by V.N. Nikolaevskii [1]-[5]to describe longitudinal seismic waves, is presented. Th
e equation has a threshold of short-wave instability and symmetry, providing long wave dynamics. New mechanism of quantum chaos generating in nonlinear dynamical systems with infinite number of degrees of freedom is proposed. The hypothesis is said, that physical turbulence could be identified with quantum chaos of considered type. It is shown that the additive thermal noise destabilizes dramatically the ground state of the Nikolaevskii system thus causing it to make a direct transition from a spatially uniform to a turbulent state.
In 1942 Haskell B.Curry presented what is now called Curry 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 thi
s article the non-classical resolution of Currys Paradox and Shaw-Kwei paradox without rejection any contraction postulate is proposed.
Generalized 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.Usi
ng 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.
In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lobs theorem is considered.Main results is: (1) let $k$ be an inaccessible cardinal, then $
eg Con(ZFC+exists k)$,(2) there is a Lindelof $T_3$ indestructible space of pseudocharacter $leqslant aleph_1$ and size $aleph_2$ in $L$.
In this study, the generic imperfect dynamic models of air-to-surface missiles are given in addition to the related simple guidance law.
In this article, Generalized Principle of limiting 4-dimensional symmetry: The laws of physics in non-inertial frames must display the 4-dimensional symmetry of the Generalized Lorentz-Poincare group in the limit of zero acceleration,is proposed.Clas
sical solution of the relativistic length expansion in general accelerated system revisited.
In this paper possible completion $^*R_{d}$ of the Robinson non-archimedean field $^*R$ constructed by Dedekind sections. Given an class of analytic functions of one complex variable $f in C[[z]]$,we investigate the arithmetic nature of the values of
$f$ at transcendental points $e^{n}$. Main results are: 1) the both numbers $e+pi$ and $epi$ are irrational, 2) number $e^{e}$ is transcendental. Nontrivial generalization of the Lindemann-Weierstrass theorem is obtained
In this paper paraconsistent second order arithmetic Z#2 with unrestricted comprehension scheme is proposed. We outline the development of certain portions of paraconsistent mathematics within paraconsistent second order arithmetic Z#2.In particular
we defined infinite hierarchy Berrys and Richards inconsistent numbers as elements of the paraconsistent field R^#.
