A short proof of Kneser's addition theorem for abelian groups

Martin Kneser proved the following addition theorem for every abelian group $G$. If $A,B \subseteq G$ are finite and nonempty, then $|A+B| \ge |A+K| + |B+K| - |K|$ where $K = \{g \in G \mid g+A+B = A+B \}$. 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 $d^2$ Pauli operators attached to a composite qudit in dimension $d$ may be mapped to the vectors of the symplectic module $\mathcal{Z}_d^{2}$ ($\mathcal{Z}_d$ 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 $d=6,~10,~15,~12$, and 18, the fine structure and the incidence between maximal commuting sets is found to reproduce the projective line over the rings $\mathcal{Z}_{6}$, $\mathcal{Z}_{10}$, $\mathcal{Z}_{15}$, $\mathcal{Z}_6 \times \mathbf{F}_4$ and $\mathcal{Z}_6 \times \mathcal{Z}_3$, respectively.Comment: 10 pages (Fast Track communication). Journal of Physics A Mathematical and Theoretical (2008) accepte