3,076 research outputs found
A short proof of Kneser's addition theorem for abelian groups
Martin Kneser proved the following addition theorem for every abelian group
. If are finite and nonempty, then where . Here we give a short
proof of this based on a simple intersection union argument.Comment: 3 page
Thermal testing by internal IR heating of the FEP module
A spacecraft module, to be integrated with the FLTSATCOM spacecraft, was tested in a simulated orbit environment separate from the host spacecraft. Thermal vacuum testing of the module was accomplished using internal IR heating rather than conventional external heat sources. For this configuration, the technique produced boundary conditions expected for flight to enable verification of system performance and thermal design details
Powers of sets in free groups
We prove that |A^n| > c_n |A|^{[\frac{n+1}{2}]} for any finite subset A of a
free group if A contains at least two noncommuting elements, where c_n>0 are
constants not depending on A. Simple examples show that the order of these
estimates are the best possible for each n>0.Comment: 3 page
Comment on "Peierls Gap in Mesoscopic Ring Threated by a Magnetic Flux"
In a recent letter, Yi et al. PRL 78, 3523 (1997), have considered the
stability of a Charge Density Wave in a one-dimensional ring, in the presence
of an Aharonov-Bohm flux. This comment shows that, in one dimension, the
stability of the Charge Density Wave depends on the parity of the number of
electrons in the ring. This effect is similar to the parity effect known for
the persistent current in one-dimensional rings.Comment: Latex, 1 page, 2 figure
Freeze-dried ammonia borane-polyethylene oxide composites: Phase behaviour and hydrogen release
A solid-state hydrogen storage material comprising ammonia borane (AB) and polyethylene oxide (PEO) has been produced by freeze-drying from aqueous solutions from 0% to 100% AB by mass. The phase mixing behaviour of AB and PEO has been investigated using X-ray diffraction which shows that a new ‘intermediate’ crystalline phase exists, different from both AB and PEO, as observed in our previous work (Nathanson et al., 2015). It is suggested that hydrogen bonding interactions between the ethereal oxygen atom (–O–) in the PEO backbone and the protic hydrogen atoms attached to the nitrogen atom (N–H) of AB molecules promote the formation of a reaction intermediate, leading to lowered hydrogen release temperatures in the composites, compared to neat AB. PEO also acts to significantly reduce the foaming of AB during hydrogen release. A temperature-composition phase diagram has been produced for the AB-PEO system to show the relationship between phase mixing and hydrogen release
Local distinguishability of quantum states in infinite dimensional systems
We investigate local distinguishability of quantum states by use of the
convex analysis about joint numerical range of operators on a Hilbert space. We
show that any two orthogonal pure states are distinguishable by local
operations and classical communications, even for infinite dimensional systems.
An estimate of the local discrimination probability is also given for some
family of more than two pure states
SIC-POVMs and the Extended Clifford Group
We describe the structure of the extended Clifford Group (defined to be the
group consisting of all operators, unitary and anti-unitary, which normalize
the generalized Pauli group (or Weyl-Heisenberg group as it is often called)).
We also obtain a number of results concerning the structure of the Clifford
Group proper (i.e. the group consisting just of the unitary operators which
normalize the generalized Pauli group). We then investigate the action of the
extended Clifford group operators on symmetric informationally complete POVMs
(or SIC-POVMs) covariant relative to the action of the generalized Pauli group.
We show that each of the fiducial vectors which has been constructed so far
(including all the vectors constructed numerically by Renes et al) is an
eigenvector of one of a special class of order 3 Clifford unitaries. This
suggests a strengthening of a conjuecture of Zauner's. We give a complete
characterization of the orbits and stability groups in dimensions 2-7. Finally,
we show that the problem of constructing fiducial vectors may be expected to
simplify in the infinite sequence of dimensions 7, 13, 19, 21, 31,... . We
illustrate this point by constructing exact expressions for fiducial vectors in
dimensions 7 and 19.Comment: 27 pages. Version 2 contains some additional discussion of Zauner's
original conjecture, and an alternative, possibly stronger version of the
conjecture in version 1 of this paper; also a few other minor improvement
Utility of Parental Mediation Model on Youth’s Problematic Online Gaming
The Parental Mediation Model PMM) was initially designed to regulate children’s attitudes towards the traditional media. In the present era, because of prevalent online media there is a need for similar regulative measures. Spending long hours on social media and playing online games increase the risks of exposure to the negative outcomes of online gaming. This paper initially applied the PMM developed by European Kids Online to (i) test the reliability and validity of this model and (ii) identify the effectiveness of this model in controlling problematic online gaming (POG). The data were collected from 592 participants comprising 296 parents and 296 students of four foreign universities, aged 16 to 22 years in Kuala Lumpur (Malaysia). The study found that the modified model of the five-factor PMM (Technical mediation, Monitoring mediation, Restrictive mediation, Active Mediation of Internet Safety, and Active mediation of Internet Use) functions as a predictor for mitigating POG. The findings suggest the existence of a positive relation between ‘monitoring’ and ‘restrictive’ mediation strategies and exposure to POG while Active Mediation of Internet Safety and Active mediation of Internet use were insignificant predictors. Results showed a higher utility of ‘technical’ strategies by the parents led to less POG. The findings of this study do not support the literature suggesting active mediation is more effective for reducing youth’s risky behaviour. Instead, parents need to apply more technical mediations with their children and adolescents’ Internet use to minimize the negative effects of online gaming
Qudits of composite dimension, mutually unbiased bases and projective ring geometry
The Pauli operators attached to a composite qudit in dimension may
be mapped to the vectors of the symplectic module
( the modular ring). As a result, perpendicular vectors
correspond to commuting operators, a free cyclic submodule to a maximal
commuting set, and disjoint such sets to mutually unbiased bases. For
dimensions , and 18, the fine structure and the incidence
between maximal commuting sets is found to reproduce the projective line over
the rings , , ,
and ,
respectively.Comment: 10 pages (Fast Track communication). Journal of Physics A
Mathematical and Theoretical (2008) accepte
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