Two principles explain emergence. First, in the Receipt’s reference frame, Deg(S) = 4 3 Deg(R ), where Supply S is an isotropic radiative energy source, Receipt R receives S’s energy, and Deg is a system’s degrees of freedom based on its mean path length. S’s 3 more degrees of freedom relative to R enables R ’s growth and increasing complexity. Second, ρ(R ) = Deg(R )× ρ(r), where ρ(R ) represe...

Optical texture patterns contain three quasi-independent cues to planar surface orientation: perspective scaling, projective foreshortening and density. The purpose of this work was to estimate the perceptual weights assigned to these texture cues for discriminating surface orientation and to measure the visual system’s reliance on an isotropy assumption in interpreting foreshortening informati...

Abstract In this note, we derive an extension of the conventional Einstein variation mass formula with a specific expression arising from Lorentz invariant equation for energy rate $$\hbox {d}e/\hbox {d}p$$ d e / p where $$e = mc^...

Two important results in quadratic form theory, Pfister’s local-global principle and the isotropy theorem (see [5]), can be stated more generally for spaces of orderings (an abstract version of real spectras of formally real fields), for which they are expressed as local-global principles: A property of quadratic forms (expressed as a so-called positive-primitive formula) holds if and only if i...

*Correspondence: [email protected] 3Department of Mathematics Education and ERI, Gyeongsang National University, Jinju, Republic of Korea Full list of author information is available at the end of the article Abstract We use the p-adic q-integral and group action to count the number of the generating functions of modified q-Euler polynomials in a prescribed set. Some generating function yield...

We derive minimal conditions on a symmetry group of a linearly elastic material that implies its isotropy. A natural setting for the formulation and analysis is provided by the group representation theory where the necessary and sufficient conditions for isotropy are expressed in terms of the irreducibility of certain group representations. We illustrate the abstract results by (re)deriving sev...