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...

varicella-zoster viruses complications involving the cns are estimated to occur rarely, transverse myelitis after varicella-zoster virus in most patients is characterized by an abrupt onset of progressive weakness and sensory disturbance in the lower extremities , like other viruses. we describe the case of 17 year-old boy who experienced cervical transverse myelitis after chickenpox with inabi...

A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution structure’ consisting of equivariant iterated fibrations of the boundary faces. T...

We discuss the problem of the stability of the isotropy of the universe in the space of ever-expanding spatially homogeneous universes with a compact spatial topology. The anisotropic modes which prevent isotropy being asymptotically stable in Bianchi-type V IIh universes with non-compact topologies are excluded by topological compactness. Bianchi type V and type V IIh universes with compact to...

This article presents a new performance measure, the actuation eeciency, which describes isotropy in acceleration capability for non-redundant manipulators. It measures the imbalance between the end-eeector accelerations achievable in diierent directions. Prior to this, no measure of this characteristic was adequate for a six degree-of-freedom manipulator, because its end-eeector motions are re...

We formulate statistical isotropy of CMB anisotropy maps in its most general form. We also present a fast and orientation independent statistical method to determine deviations from statistical isotropy in CMB polarization maps. Importance of having statistical tests of departures from SI for CMB polarization maps lies not only in interesting theoretical motivations but also in testing cleaned ...