We revisited Cauchy Machine for solving blind space-variant imaging problem on the pixel by pixel basis. Under-determinacy of the pixel by pixel blind-matrix inversion was accomplished non-statistically by a physicsconstraint of open information systems in a dynamic balance by minimizing the thermodynamics free energy H=U-T0S where U is estimation error energy, T0 is temperature and S is the en...

The Cauchy-Schwarz, Buzano and Kre\u{\i}n inequalities are three about inner product. main goal of this article is to present refinements Cauchy-Schwarz inequalities, a new proof refined version Kre\u{\i}n-type inequality. Applications that include Buzano-type for certain operators, operator norm numerical radius Hilbert space operators will be presented.

We show that several weakenings of the Cauchy condition are all equivalent under the assumption of countable choice, and investigate to what extent choice is necessary. We also show that the syntactically reminiscent notion of metastability allows similar variations, but in terms of its computational content is an empty notion. §1. Almost Cauchyness. Apart from the last section, we work in Bish...

Abstract. We consider the Cauchy problem We consider the Cauchy problem ut = uxx + f(u), x ∈ R, t > 0, u(x, 0) = u0(x), x ∈ R, where f is a locally Lipschitz function on R with f(0) = 0, and u0 is a nonnegative function in C0(R), the space of continuous functions with limits at ±∞ equal to 0. Assuming that the solution u is bounded, we study its large-time behavior from several points of view. ...

We investigate the effects of pair creation on the internal geometry of a black hole, which forms during the gravitational collapse of a charged massless scalar field. Classically, strong central Schwarzschild-like singularity forms, and a null, weak, mass-inflation singularity arises along the Cauchy horizon, in such a collapse. We consider here the discharge, due to pair creation, below the e...

We investigate the effects of pair creation on the internal geometry of a black hole, which forms during the gravitational collapse of a charged massless scalar field. Classically, strong central Schwarzschild-like singularity and a null, weak, mass-inflation singularity arises along the Cauchy horizon, in such a collapse. We consider here the discharge, due to pair creation, below the event ho...

I define canonical utility functions via an explicit formula that inherits semicontinuity, continuity, Cauchy continuity, and uniform continuity from preferences. This construction is used to (i) show Rader’s and Debreu’s theorems in a fast and transparent way, (ii) refine these results for Cauchy and uniformly continuous preferences on a metric space X , (iii) extend such preferences from X to...

We use the Holevo information to estimate distinguishability of microstates of a black hole in anti-de Sitter space by measurements one can perform on a subregion of a Cauchy surface of the dual conformal field theory. We find that microstates are not distinguishable at all until the subregion reaches a certain size and that perfect distinguishability can be achieved before the subregion covers...

The computability of the solution operator of the Cauchy problem for the Fifth-order CamassaHolm equation is studied in this paper. Firstly, a nonlinear map KR : H → C (R;H (R)) is defined from the initial value φ to the solution u. Then we used the relevant knowledge of type-2 theory of effectivity, functional analysis and Sobolev space to prove that when s > (6 √ 10− 17) / 4, the solution ope...

The Fokker–Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For special cases of such a Fokker– Planck equation we describe a construction of exact solution of the Cauchy problem. In the general case, we construct the leadin...