Upadhyay, "Field-dependent symmetries
in Friedmann-Robertson-Walker models," Annals of Physics, vol.
The following proposition that defines the relationship between point symmetries
, multipliers, and conservation laws constructed via the Noether operator in  can be easily proved.
Using the Lagrangian of plane and spherical symmetric static spacetimes, a complete list of Noether symmetries
have been obtained and new first integral have been found.
are thus a more relaxed form of variational symmetries
, and they also give rise to conservation laws and first integral as variational symmetries
do by Nrether's theorem.
In addressing many variants of excision and circumcision as well as other practices such as the elongation of the labia, and various forms of circumcision in Jewish, Islamic, and African contexts, Fearful Symmetries
provides an unprecedented, panoptical view of both practices.
All in all there are 10 symmetries
(point groups) that allow for the 2-fold helicoidal twisting of macroscopic crystals.
These appear to be all the possible theoretical symmetries
. In particular, it is impossible to create a "letter" with two but not three symmetries
, i.e., with left-right and rotational (but not up-down), with up-down and rotational (but not left-right), or with left-right and up-down (but not rotational) symmetry.
Because of the advantages of making students aware of the connections and symmetries
between results established in different parts of a course, this paper has identified the important links regarding analysis of firm behavior in product and resource markets which are suitable for presentation in an introductory microeconomics course.
With no exceptions, each crystal was found to conform to one of only 32 ways of combining these symmetry axes, the so-called "crystallographic" point group symmetries
. External forms of periodic crystals were found to be limited to combinations of only 47 forms (32 general and 15 special) made of symmetrically arranged bounding planes (5).
(or is it Louise?) to the bloodletting symmetries
of Kubrick's The Shining.
4 shows an example of such CBED patterns from which the whole (3-dimensional) pattern symmetries
of fivefold [1[tau]0], threefold  and twofold  orientations were derived ([tau]-irrational "golden mean" number).
The experiment will improve the existing tests of these important fundamental symmetries
of nature by a factor of 1000 and should provide tests of various theories of quantum gravity, such as string theory, which predict violations of CPT and Lorentz invariance.