1,748 research outputs found
Expansive actions on uniform spaces and surjunctive maps
We present a uniform version of a result of M. Gromov on the surjunctivity of
maps commuting with expansive group actions and discuss several applications.
We prove in particular that for any group and any field \K, the
space of -marked groups such that the group algebra \K[G] is
stably finite is compact.Comment: 21 page
Modified Regge calculus as an explanation of dark energy
Using Regge calculus, we construct a Regge differential equation for the time
evolution of the scale factor in the Einstein-de Sitter cosmology model
(EdS). We propose two modifications to the Regge calculus approach: 1) we allow
the graphical links on spatial hypersurfaces to be large, as in direct particle
interaction when the interacting particles reside in different galaxies, and 2)
we assume luminosity distance is related to graphical proper distance
by the equation , where the inner product can differ from its usual
trivial form. The modified Regge calculus model (MORC), EdS and CDM
are compared using the data from the Union2 Compilation, i.e., distance moduli
and redshifts for type Ia supernovae. We find that a best fit line through
versus gives a correlation of
0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit
CDM gives SSE = 1.79 using = 69.2 km/s/Mpc, = 0.29
and = 0.71. The best fit EdS gives SSE = 2.68 using =
60.9 km/s/Mpc. The best fit MORC gives SSE = 1.77 and = 73.9 km/s/Mpc
using = 8.38 Gcy and kg, where is the
current graphical proper distance between nodes, is the scaling factor
from our non-trival inner product, and is the nodal mass. Thus, MORC
improves EdS as well as CDM in accounting for distance moduli and
redshifts for type Ia supernovae without having to invoke accelerated
expansion, i.e., there is no dark energy and the universe is always
decelerating.Comment: 15 pages text, 6 figures. Revised as accepted for publication in
Class. Quant. Gra
Answering Mermin's Challenge with Conservation per No Preferred Reference Frame
In 1981, Mermin published a now famous paper titled, "Bringing home the
atomic world: Quantum mysteries for anybody" that Feynman called, "One of the
most beautiful papers in physics that I know." Therein, he presented the
"Mermin device" that illustrates the conundrum of quantum entanglement per the
Bell spin states for the "general reader." He then challenged the "physicist
reader" to explain the way the device works "in terms meaningful to a general
reader struggling with the dilemma raised by the device." Herein, we show how
"conservation per no preferred reference frame (NPRF)" answers that challenge.
In short, the explicit conservation that obtains for Alice and Bob's
Stern-Gerlach spin measurement outcomes in the same reference frame holds only
on average in different reference frames, not on a trial-by-trial basis. This
conservation is SO(3) invariant in the relevant symmetry plane in real space
per the SU(2) invariance of its corresponding Bell spin state in Hilbert space.
Since NPRF is also responsible for the postulates of special relativity, and
therefore its counterintuitive aspects of time dilation and length contraction,
we see that the symmetry group relating non-relativistic quantum mechanics and
special relativity via their "mysteries" is the restricted Lorentz group.Comment: 18 pages, 9 figures. This version as revised and resubmitted to
Scientific Report
Representation theory of wreath products of finite groups.
This is an exposition on the representation theory of wreath products of finite groups, with many examples worked out
Exponential beams of electromagnetic radiation
We show that in addition to well known Bessel, Hermite-Gauss, and
Laguerre-Gauss beams of electromagnetic radiation, one may also construct
exponential beams. These beams are characterized by a fall-off in the
transverse direction described by an exponential function of rho. Exponential
beams, like Bessel beams, carry definite angular momentum and are periodic
along the direction of propagation, but unlike Bessel beams they have a finite
energy per unit beam length. The analysis of these beams is greatly simplified
by an extensive use of the Riemann-Silberstein vector and the Whittaker
representation of the solutions of the Maxwell equations in terms of just one
complex function. The connection between the Bessel beams and the exponential
beams is made explicit by constructing the exponential beams as wave packets of
Bessel beams.Comment: Dedicated to the memory of Edwin Powe
Finite Gel'fand pairs and their applications to Probability and Statistics
We present a general introduction to finite Gel’fand pairs and their associated spherical functions
yielding different characterizations, examine a few explicit examples, and, for each of these examples,
analyze the corresponding probabilistic problem, which will then be solved by applying the general results
and the machinery developed for a particular Gel’fand pair
Induced representations and Mackey theory
This is an exposition on Mackey theory for induced representations of finite group
Von Neumann Regular Cellular Automata
For any group and any set , a cellular automaton (CA) is a
transformation of the configuration space defined via a finite memory set
and a local function. Let be the monoid of all CA over .
In this paper, we investigate a generalisation of the inverse of a CA from the
semigroup-theoretic perspective. An element is von
Neumann regular (or simply regular) if there exists
such that and , where is the composition of functions. Such an
element is called a generalised inverse of . The monoid
itself is regular if all its elements are regular. We
establish that is regular if and only if
or , and we characterise all regular elements in
when and are both finite. Furthermore, we study
regular linear CA when is a vector space over a field ; in
particular, we show that every regular linear CA is invertible when is
torsion-free elementary amenable (e.g. when ) and , and that every linear CA is regular when
is finite-dimensional and is locally finite with for all .Comment: 10 pages. Theorem 5 corrected from previous versions, in A.
Dennunzio, E. Formenti, L. Manzoni, A.E. Porreca (Eds.): Cellular Automata
and Discrete Complex Systems, AUTOMATA 2017, LNCS 10248, pp. 44-55, Springer,
201
A note on a local ergodic theorem for an infinite tower of coverings
This is a note on a local ergodic theorem for a symmetric exclusion process
defined on an infinite tower of coverings, which is associated with a finitely
generated residually finite amenable group.Comment: Final version to appear in Springer Proceedings in Mathematics and
Statistic
On the density of periodic configurations in strongly irreducible subshifts
Let be a residually finite group and let be a finite set. We prove
that if is a strongly irreducible subshift of finite type
containing a periodic configuration then periodic configurations are dense in
. The density of periodic configurations implies in particular that every
injective endomorphism of is surjective and that the group of automorphisms
of is residually finite. We also introduce a class of subshifts , including all strongly irreducible subshifts and all irreducible sofic
subshifts, in which periodic configurations are dense
- …