相关论文: Correcting a minor error in Cantor's calculation o…
We give a simple recursive formula to obtain the general sum of the first $N$ natural numbers to the $r$th power. Our method allows one to obtain the general formula for the $(r+1)$th power once one knows the general formula for the $r$th…
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we…
Let C be a Cantor set. For a real number t let C+t be the translate of C by t, We say two real numbers s,t are equivalent if the intersection of C and C+s is a translate of the intersection of C and C+t. We consider a class of Cantor sets…
A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast…
We have found the graviton contribution to the one-loop quantum correction to the Newton law. This correction results in interaction decreasing with distance as 1/r^3 and is dominated numerically by the graviton contribution. The previous…
In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since…
In the present article, modeling certain rational numbers, that are represented in terms of Cantor series, are described. The statements on relations between digits in the representations of rational numbers by Cantor series (for the case…
Corrections to Einstein's equations that become important at small curvatures are considered. The field equations are derived using a Palatini variation in which the connection and metric are varied independently. In contrast to the…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
With consideration of quantization of space, we relate Newton's gravitation with the Second Law of thermodynamics. This leads to a correction to its original form, which takes into consideration the role of classical measurement. Our…
Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty…
It is shown that the pillars of transfinite set theory, namely the uncountability proofs, do not hold. (1) Cantor's first proof of the uncountability of the set of all real numbers does not apply to the set of irrational numbers alone, and,…
Three-loop QCD corrections to the vector current correlator are considered. The large momentum procedure is applied in order to evaluate mass corrections up to order $(m^2/q^2)^6$. The inclusion of the first seven terms to the ratio…
We present a quantum error correcting code that is invariant under the conditional time evolution between spontaneous emissions and which can correct for one general error. The code presented here generalizes previous error correction codes…
Non-perturbative corrections to hadronic observables represent a critical obstacle to increasing accuracy at colliders. Long taken to scale simply as $1/Q$, where $Q$ is the centre-of-mass scattering energy, recent work has opened the path…
It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much…
We correct an error in our treatment of the tadpole contribution to the fluctuation determinant of the sphaleron, and also a minor mistake in a previous estimate. Thereby the overall agreement between the two existing exact computations and…
Whatever other beliefs there may remain for considering Cantor's diagonal argument as mathematically legitimate, there are three that, prima facie, lend it an illusory legitimacy; they need to be explicitly discounted appropriately. The…
We discuss a simple method to evaluate the QCD corrections to $\Delta\rho$. It assumes that the perturbative expansion in terms of $\ms$ parameters is meaningful and, unlike other studies, exploits significant available information…
We calculate isotope mass shift for several light ions using Dirac wave functions and mass shift operator with relativistic corrections of the order of $(\alpha Z)^2$. Calculated relativistic corrections to the specific mass shift vary from…