A graph theoretic approach to graded identities for matrices

We consider the algebra M_k(C) of k-by-k matrices over the complex numbers and view it as a crossed product with a group G of order k by embedding G in the symmetric group S_k via the regular representation and embedding S_k in M_k(C) in the usual way. This induces a natural G-grading on M_k(C) which we call a crossed product grading. This grading is the so called elementary grading defined by any k-tuple (g_1,g_2,..., g_k) of distinct elements g_i in G. We study the graded polynomial identities for M_k(C) equipped with a crossed product grading. To each multilinear monomial in the free graded algebra we associate a directed labeled graph. This approach allows us to give new proofs of known results of Bahturin and Drensky on the generators of the T-ideal of identities and the Amitsur-Levitsky Theorem. Our most substantial new result is the determination of the asymptotic formula for the G-graded codimension of M_k(C).Comment: 21 pages, 3 figure

Workplace Disability Diversity and Job-Related Well-Being in Britain: A WERS2004 Based Analysis

This paper attempts to establish empirically whether there is a link between workplace disability and employee job-related well-being. Using nationally representative linked employer-employee data for Britain, I employ alternative econometric techniques to account for unobserved workplace heterogeneity. I find that workplace disability diversity is associated with lower employee well-being among people with no reported disability. Tests conducted also indicate that workplace equality policies do not ameliorate this effect.disability diversity, job-related well-being, linked employer-employee data, Britain

Electrochemical impedance spectroscopy of mixed conductors under a chemical potential gradient: a case study of Pt|SDC|BSCF

The AC impedance response of mixed ionic and electronic conductors (MIECs) exposed to a chemical potential gradient is derived from first principles. In such a system, the chemical potential gradient induces a gradient in the carrier concentration. For the particular system considered, 15% samarium doped ceria (SDC15) with Ba_(0.5)Sr_(0.5)Co_(0.8)Fe_(0.2O3-) (BSCF) and Pt electrodes, the oxygen vacancy concentration is a constant under the experimental conditions and it is the electron concentration that varies. The resulting equations are mapped to an equivalent circuit that bears some resemblance to recently discussed equivalent circuit models for MIECs under uniform chemical potential conditions, but differs in that active elements, specifically, voltage-controlled current sources, occur. It is shown that from a combination of open circuit voltage measurements and AC impedance spectroscopy, it is possible to use this model to determine the oxygen partial pressure drop that occurs between the gas phase in the electrode chambers and the electrode|electrolyte interface, as well as the interfacial polarization resistance. As discussed in detail, this resistance corresponds to the slope of the interfacial polarization curve. Measurements were carried out at temperatures between 550 and 650 °C and oxygen partial pressure at the Pt anode ranging from 10^(-29) to 10^(-24) atm (attained using H_2/H_2O/Ar mixtures), while the cathode was exposed to either synthetic air or neat oxygen. The oxygen partial pressure drop at the anode was typically about five orders of magnitude, whereas that at the cathode was about 0.1 atm for measurements using air. Accordingly, the poor activity of the anode is responsible for a loss in open circuit voltage of about 0.22 V, whereas the cathode is responsible for only about 0.01 V, reflecting the high activity of BSCF for oxygen electro-reduction. The interfacial polarization resistance at the anode displayed dependences on oxygen partial pressure and on temperature that mimic those of the electronic resistivity of SDC15. This behavior is consistent with hydrogen electro-oxidation occurring directly on the ceria surface and electron migration being the rate-limiting step. However, the equivalent resistance implied by the oxygen partial pressure drop across the anode displayed slightly different behavior, possibly indicative of a more complex reaction pathway

Unhappy Working with Men? Workplace Gender Diversity and Employee Job-Related Well-Being in Britain: A WERS2004 Based Analysis

This paper attempts to establish empirically the link between workplace gender diversity and employee job-related well-being. Using nationally representative linked employer-employee data for Britain, I employ econometric techniques that account for unobserved workplace heterogeneity. I find that gender diversity is associated with lower employee well-being among women in several of the equations estimated. The magnitudes of the estimated effects also tend to increase with (women's) group size. Workplace equality policies do not appear to ameliorate these effects.gender diversity, job-related well-being, linked employer-employee data, Britain

The Nature and Extent of Job Separations in Germany: Some New Evidence from SOEP

This paper analyses job separations in Germany using data from the German Socio-Economic Panel spanning from 1984 to 2003. Based on detailed reasons for job separation and different SOEP samples, the paper attempts to establish the nature of job separations in Germany. It brings to light some patterns of separations that have hitherto been unexplored. The findings of the study suggest, among others, that minority group status is important in characterising job separations, particularly in the event of exogenous shocks. Targeting minorities in the face of a major shock of the sort experienced in Germany might be a policy option.job separations, job turnover, economics of minorities

Workplace Job Satisfaction in Britain: Evidence from Linked Employer-Employee Data

This paper examines the determinants of job satisfaction in Britain using nationally representative linked employer-employee data (WERS2004) and alternative econometric techniques. It uses eight facets of job satisfaction for the purpose. As well as underscoring the importance of accounting for unobserved workplace heterogeneity, the paper is able to highlight some new findings that relate to differential effects of dependent children and other dependents, type of employment contract and gaps between employees' skill and skills requirements of their job. Working long hours is found to be positively associated with intrinsic aspect of jobs. Public sector employment is positively associated with all facets of job satisfaction except satisfaction with pay.job satisfaction, linked employer-employee data, Britain

Citizen science to fill hydro-meteorological data gaps in rural watersheds

Poster prepared for a share fair, Addis Ababa, May 201

Influence of Silica Nanoparticles on the Crystallization Behavior of and Proton Relaxation in Cesium Hydrogen Sulfate

The influence of nanoparticulate SiO_2 on the crystallization behavior of CsHSO_4 from aqueous solution has been quantitatively evaluated using powder X-ray diffraction (XRD) and ^1H magic angle spinning nuclear magnetic resonance (NMR) spectroscopy. It is shown that SiO_2 induces amorphization of a portion of CsHSO_4 and crystallization of the otherwise metastable phase II form of CsHSO_4. The fraction of amorphized CsHSO_4 (as determined from an evaluation of the XRD peak intensity) was found to increase from 0% in the absence of SiO_2 to fully amorphized in the presence of 90 mol % (~70 wt %) SiO_2. Within the crystalline portion of the composites, the weight fraction of CsHSO_4 phase III was observed to fall almost monotonically from 100% in the absence of SiO_2 to about 40% in the presence of 70 mol % SiO_2 (from both XRD and NMR analysis). These results suggest a crystallization pathway in which SiO_2 particles incorporate an amorphous coating of CsHSO_(4-)like material and are covered by nanoparticulate CsHSO_(4-II), which coexists with independently nucleated particles of CsHSO_(4-III). In composites with small molar fractions of CsHSO_4, the entirety of the acid salt is consumed in the amorphous region. At high CsHSO_4 content, the extent of amorphization becomes negligible, as does the extent of crystallization in metastable phase II. The phase distribution was found to be stable for over 1 year, indicating the strength of the stabilization effect that SiO_2 has on phase II of CsHSO_4