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Some comments are given on recently proposed entropic gravity by Verlinde. We focus on the derivation of Newton's law of gravitation. It is shown that consistent classical relations are enough to result in the Newtonian gravity. In our…
In this paper some important inequalities are revisited. First, as motivation, we give another proof of the Hardy's inequality applying convenient vector fields as introduced by Mitidieri, see [6]. Then, we investigate a particular case of…
We generalize E. Verlinde's entropic gravity reasoning to a phase-space noncommutativity set-up. This allow us to impose a bound on the product of the noncommutative parameters based on the Equivalence Principle. The key feature of our…
In this paper, we discuss an equation which does not contain the Planck's constant, but it will turn out the Planck's constant when we apply the equation to the problems of particle diffraction.
Irreversibility is usually captured by a comparison between the process that happens and a corresponding "reverse process". In the last decades, this comparison has been extensively studied through fluctuation relations. Here we revisit…
By using the Verlinde's formalism[1], we propose that the positive numerical factor, in which Klinkhamer[2] states that it is necessary to define the fundamental length, can be associated to the parameter q of the Tsallis' nonextensive…
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…
This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…
The goal of this note is to improve on the currently available bounds for Stieltjes constants using the method of steepest descent applied by Coffey and Knessl to approximate Stieltjes constants.
This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.
In this paper we present some applications of the Stieltjes constants including, for example, new derivations of Binet's formulae for the log gamma function and the evaluation of some integrals related to the Barnes multiple gamma…
In this paper, we shall give an extension of operator Bellman inequality. This result is estimated via Kantorovich constant.
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
An experimental formula, sometimes named as Newton-collision-formula, (v1-v2) = - e.(u1-u2) relating relative-velocities before & after impact of two bodies under linear-collision, is commonly used successfully for study of…
We improve constants in the Rademacher-Menchov inequality.
We investigate the accuracy of the frozen--flow approximation (FFA), recently proposed by Matarrese \etal (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a…
In this paper we derive inferential results for a new index of inequality, specifically defined for capturing significant changes observed both in the left and in the right tail of the income distributions. The latter shifts are an apparent…
This note formulates a conjecture generalizing both the abc conjecture of Masser-Oesterl\'e and the author's diophantine conjecture for algebraic points of bounded degree. It also shows that the new conjecture is implied by the earlier…
I have shown conceptually that quantum state has a direct relationship to gravitational constant due to entropic force posed by Verlinde's argument and part of the Newton-Schr\"odinger equation (N-S) in the context of gravity induced…
In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…