The variation problem associated with the solution of Dirac's relativistic electron equation is reviewed here. Derivation of the min-max theorem is discussed. A new observation is that the spurious roots of negative energy satisfy a max-min theorem....
In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions o...
The self-similar expansion of a blast wave, well-studied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylor-von Neumann-Sedov (TvNS) derivation is not...
This self-contained pedagogical derivation of the Schwarzchild solution, in "3 + 1" formulation and conformal spatial gauge, (almost) avoids all affinity, curvature and index gymnastics....
Heavy duty truck mechanical configuration is often tailor designed and built for specific truck mission requirements. This renders the precise derivation of analytical dynamical models and controls for these trucks from first principles challenging,...
I am not counting scripts that are typologically categorized as being a direct derivation of another script. So for example I am not counting the Persian variant of the Arabic script or the various Eu...
Apr 14, 2022 · Using the word 'ass' to describe someone is considered vulgar in itself, but not severely so. Non-vulgar equivalents would be 'jerk', 'uncouth', etc. This is different from 'asshole', which …
This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and analyzed to ev...
The usual derivation of the Fokker-Planck partial differential eqn. assumes the Chapman-Kolmogorov equation for a Markov process. Starting instead with an Ito stochastic differential equation we argue that finitely many states of memory are allowed...
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory models. We...
As you all might know , today was class 12th physics boards examination. I was well prepared. All derivation on tip of my tongue, all formulas memorized, every pyq solved, cengage done , sl arora done...
We discuss the derivation of a ``cluster sum rule'' from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the assumptions an...
Vopson first published the multicaloric effect in multiferroics in 2012. However, a closer examination of the multicaloric effect and its derivation leads to a contradiction, in which the predicted changes in one of the order phase at a constant appl...
A recent rebuttal to criticism of Bell's analysis is shown to be defective by fault of failure to consider all hypothetical conditions input into the derivation of Bell Inequalitites....
Derivations of Borns Rule are of interest because they tell us what's connected to what in quantum mechanics if we ever need to change or modify it....
An alternative derivation of the radiation intensity in non-relativistic bremsstrahlung is provided utilizing the path integral formalism. By integrating out the gauge field, one obtains the effective action which it's imaginary part is interpreted a...
May 2, 2015 · I think something is wrong with the derivation you have - notably, the first equation, $\log (1-x)=-\sum_ {n=1}^ {\infty}x^n$ is not true - you probably want a log around the sum on the left.
Since its inception, Benders Decomposition (BD) has been successfully applied to a wide range of large-scale mixed-integer (linear) problems. The key element of BD is the derivation of Benders cuts, which are often not unique. In this paper, we intro...
After a short introduction to the generalized uncertainty principle (GUP), we discuss heuristic derivations of the Casimir effect, first from the usual Heisenberg uncertainty principle (HUP), and then from GUP. Results are compared with those obtaine...
Aug 18, 2025 · For basic EM wave propagating in free space, all field lines pass into and out of any flux surface, as in the third image, so $\nabla \cdot \vec E = 0$. Only if your flux surface includes a …