On reciprocal symmetry
نویسنده
چکیده
On the positive half-line, there are two natural, and complementary, analogues of the single notion of symmetry of distributions on the real line. One is the R-symmetry recently proposed and investigated by Mudholkar and Wang (2007); the other is the ‘log-symmetry’ investigated here. Log-symmetry can be thought of either in terms of a random variable having the same distribution as its reciprocal or as ordinary symmetry of the distribution of the logged random variable. Various properties, analogies, comparisons and consequences are pursued.
منابع مشابه
Reciprocal and unidirectional scattering of parity-time symmetric structures
Parity-time (PT) symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the (PT) symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are intensively studied. Here, we show the reciprocal reflection/transmission in (PT)-symmetric system is closely related to the type of (PT) symmetry, that is, ...
متن کاملSysabs - A program for the visualization of crystal data symmetry in reciprocal space
A computer program running under X-windows on any unix system has been developed for the visualization of symmetry in reciprocal space using reduced data from crystal measurements. The program was demonstrated using a test crystal of the inclusion compound of camphor(+) in thiourea, in the moderately high symmetry space group R32. The results indicate the usefulness of the visualization approac...
متن کاملOn structured singular values of reciprocal matrices
Computing the structured singular value (or ) is a bottleneck of the robustness analysis and synthesis of control systems. In this paper, it is shown that is identical to the maximum singular value for an important class of matrices called reciprocal, which re ects the intrinsic symmetry of physical world.
متن کاملIntrinsic rippling enhances static non-reciprocity in a graphene metamaterial.
In mechanical systems, Maxwell-Betti reciprocity means that the displacement at point B in response to a force at point A is the same as the displacement at point A in response to the same force applied at point B. Because the notion of reciprocity is general, fundamental, and is operant for other physical systems like electromagnetics, acoustics, and optics, there is significant interest in un...
متن کاملNo many-scallop theorem: collective locomotion of reciprocal swimmers.
To achieve propulsion at low Reynolds number, a swimmer must deform in a way that is not invariant under time-reversal symmetry; this result is known as the scallop theorem. However, there is no many-scallop theorem. We demonstrate here that two active particles undergoing reciprocal deformations can swim collectively; moreover, polar particles also experience effective long-range interactions....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007