Electrochemical Frequency Modulation: New Approach and Revision of Previous Model

A careful evaluation of the earlier model (1-2) for electrochemical frequency modulation (EFM) involving two sinusoidal applied potentials for the determination of corrosion parameters shows an algebraic error. Although the missing term in the original derivation appears to be insignificant, it is found that errors involved in corrosion current determination, and especially in evaluation of the Tafel slopes can be very significant, which is of consequence because of the rising popularity of this technique. The magnitude of error is found to be a function of the inherent corrosion characteristics (anodic and cathodic Tafel slopes) of the corroding material as well as the applied peak potential of the modulation. A corrected model with detailed steps showing the appropriate math is presented. In addition, using the experimental data available in the literature, the errors involved in estimating the corrosion parameters by the earlier EFM model of Bosch et al (1-2) are evaluated. The corrected corrosion current and the Tafel slopes can be recovered from the incorrect model without the benefit of the harmonic currents, as shown in this paper.The analysis is also presented for the case of only one applied sinusoidal frequency modulation, which offers several advantages over the multiple frequency modulation.

Fluctuations in Extractable Work and Bounds on the Charging Power of Quantum Batteries

Motivated by a recent disagreement about the claim that fluctuations in the free energy operator bound the charging power of a quantum battery, we present a critical analysis of the original derivation. The analysis shows that the above claim does not hold for both closed- and open-system dynamics. Our results indicate that the free energy operator is not a consistent quantifying operator for the work content of a charging quantum battery.

Feynman’s propagator in Schwinger’s picture of Quantum Mechanics

A novel derivation of Feynman’s sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac–Feynman–Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function [Formula: see text] on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian [Formula: see text] allows us to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman’s original derivation of the propagator for a point particle described by a classical Lagrangian L.

Why Black-Scholes Equations Are Effective Beyond Their Usual Assumptions: Symmetry-Based Explanation

Nobel-Prize-winning Black-Scholes equations are actively used to estimate the price of options and other financial instruments. In practice, they provide a good estimate for the price, but the problem is that their original derivation is based on many simplifying statistical assumptions which are, in general, not valid for financial time series. The fact that these equations are effective way beyond their usual assumptions leads to a natural conclusion that there must be an alternative derivation for these equations, a derivation that does not use the usual too-strong assumptions. In this paper, we provide such a derivation in which the only substantial assumption is a natural symmetry: namely, scale-invariance of the corresponding processes. Scale-invariance also allows us to describe possible generalizations of Black-Scholes equations, generalizations that we hope will lead to even more accurate estimates for the corresponding prices.

The Errors of Art and Nature

This chapter analyzes the law of facility of errors. All the early applications of the error law could be understood in terms of a binomial converging to an exponential, as in Abrahan De Moivre's original derivation. All but Joseph Fourier's law of heat, which was never explicitly tied to mathematical probability except by analogy, were compatible with the classical interpretation of probability. Just as probability was a measure of uncertainty, this exponential function governed the chances of error. It was not really an attribute of nature, but only a measure of human ignorance—of the imperfection of measurement techniques or the inaccuracy of inference from phenomena that occur in finite numbers to their underlying causes. Moreover, the mathematical operations used in conjunction with it had a single purpose: to reduce the error to the narrowest bounds possible. With Adolphe Quetelet, all that began to change, and a wider conception of statistical mathematics became possible. When Quetelet announced in 1844 that the astronomer's error law applied also to the distribution of human features such as height and girth, he did more than add one more set of objects to the domain of this probability function; he also began to break down its exclusive association with error.

Detrital zircons and the interpretation of palaeogeography, with the Variscan Orogeny as an example

Analysis of the distribution of detrital zircon grains is one of the few parameters by which Precambrian palaeogeography may be interpreted. However, the break-up of Pangea and the subsequent dispersal of some of its fragments around the Indian Ocean demonstrate that zircon analysis alone may be misleading, since zircons indicate their original derivation and not their subsequent plate-tectonic pathways. Based on analysis of Precambrian–Ordovician zircon distributions, the presence of microcontinents and separating oceans in the north Gondwanan realm has been rejected in favour of an undivided pre-Variscan continental northwards extension of Africa to include Iberia, Armorica and neighbouring southern European terranes, based on analysis of Precambrian–Ordovician zircon distribution. However, contrasting views, indicating the presence of three peri-Gondwanan oceans with complete Wilson cycles, are reinforced here by a critical reappraisal of the significance of that Variscan area detrital zircon record together with a comparison of the evolution of the present-day Indian Ocean, indicating that Iberia, Armorica and other terranes were each separate from the main Gondwanan craton during the early Palaeozoic Era.

A sceptical analysis of quantized inertia

ABSTRACT We perform an analysis of the derivation of quantized inertia (QI) theory, formerly known with the acronym MiHsC, as presented by McCulloch. Two major flaws were found in the original derivation. We derive a discrete blackbody radiation spectrum, deriving a different formulation for F(a) than the one presented in the original theory. We present a numerical result of the new solution which is compared against the original prediction.

Hybrid Atomic Orbitals in Organic Chemistry. Part 1: Critique of Formal Aspects

The importance of hybrid atomic orbitals, both historically and mathematically, is reviewed. Our new analysis of the original derivation of the sp3, sp2, sp model reveals serious errors. Based on a critical survey of the literature, we submit six formal criteria that deprecate the use of hybrid orbitals in a pedagogical context. A sound mathematical basis of sp3 and sp2 formulae does not exist; hybrid atomic orbitals have hence no legitimate role in the teaching of organic chemistry.

Hybrid Atomic Orbitals in Organic Chemistry. Part 1: Critique of Formal Aspects

The importance of hybrid atomic orbitals, both historically and mathematically, is reviewed. Our new analysis of the original derivation of the sp3, sp2, sp model reveals serious errors. Based on a critical survey of the literature, we submit six formal criteria that deprecate the use of hybrid orbitals in a pedagogical context. A sound mathematical basis of sp3 and sp2 formulae does not exist; hybrid atomic orbitals have hence no legitimate role in the teaching of organic chemistry.