Crystal field states of Kondo lattice heavy fermions CeRuSn3 and CeRhSn3

Inelastic neutron scattering experiments have been carried out to determine the crystal field states of the Kondo lattice heavy fermions CeRuSn3 and CeRhSn3. Both the compounds crystallize in LaRuSn3-type cubic structure (space group Pm-3n) in which the Ce atoms occupy two distinct crystallographic sites with cubic (m-3) and tetragonal (-4m.2) point symmetries. The INS data of CeRuSn3 reveal the presence of a broad excitation centered around 6-8 meV which is accounted by a model based on crystal electric field (CEF) excitations. On the other hand, the INS data of isostructural CeRhSn3 reveal three CEF excitations around 7.0, 12.2 and 37.2 meV. The neutron intensity sum rule indicates that the Ce ions at both cubic and tetragonal Ce sites are in Ce3+ state in both CeRuSn3 and CeRhSn3. The CEF level schemes for both the compounds are deduced. We estimate the Kondo temperature T_K = 3.1(2) K for CeRuSn3 from neutron quasielastic linewidth in excellent agreement with that determined from the scaling of magnetoresistance which gives T_K = 3.2(1) K. For CeRhSn3 the neutron quasielastic linewidth gives T_K = 4.6 K. For both CeRuSn3 and CeRhSn3, the ground state of Ce3+ turns out to be a quartet for the cubic site and a doublet for the tetragonal site.Comment: 12 pages, 13 figures, 2 tables, to appear in Phys. Rev.

On Binary Matroid Minors and Applications to Data Storage over Small Fields

Locally repairable codes for distributed storage systems have gained a lot of interest recently, and various constructions can be found in the literature. However, most of the constructions result in either large field sizes and hence too high computational complexity for practical implementation, or in low rates translating into waste of the available storage space. In this paper we address this issue by developing theory towards code existence and design over a given field. This is done via exploiting recently established connections between linear locally repairable codes and matroids, and using matroid-theoretic characterisations of linearity over small fields. In particular, nonexistence can be shown by finding certain forbidden uniform minors within the lattice of cyclic flats. It is shown that the lattice of cyclic flats of binary matroids have additional structure that significantly restricts the possible locality properties of $\mathbb{F}_{2}$-linear storage codes. Moreover, a collection of criteria for detecting uniform minors from the lattice of cyclic flats of a given matroid is given, which is interesting in its own right.Comment: 14 pages, 2 figure

Physical properties of noncentrosymmetric superconductor LaIrSi3: A {\mu}SR study

The results of heat capacity C_p(T, H) and electrical resistivity \rho(T,H) measurements down to 0.35 K as well as muon spin relaxation and rotation (\muSR) measurements on a noncentrosymmetric superconductor LaIrSi3 are presented. Powder neutron diffraction confirmed the reported noncentrosymmetric body-centered tetragonal BaNiSn3-type structure (space group I4\,mm) of LaIrSi3. The bulk superconductivity is observed below T_c = 0.72(1) K. The intrinsic \Delta C_e/\gamma_n T_c = 1.09(3) is significantly smaller than the BCS value of 1.43, and this reduction is accounted by the \alpha-model of BCS superconductivity. The analysis of the superconducting state C_e(T) data by the single-band \alpha-model indicates a moderately anisotropic order parameter with the s-wave gap \Delta(0)/k_B T_c = 1.54(2) which is lower than the BCS value of 1.764. Our estimates of various normal and superconducting state parameters indicate a weakly coupled electron-phonon driven type-I s-wave superconductivity in LaIrSi3. The \muSR results also confirm the conventional type-I superconductivity in LaIrSi3 with a preserved time reversal symmetry and hence a singlet pairing superconducting ground state.Comment: 11 pages, 8 figures, 2 table

Phytoplankton communities and acclimation in a cyclonic eddy in the southwest Indian Ocean

A study of phytoplankton in a cyclonic eddy was undertaken in the Mozambique Basin between Madagascar and southern Africa during austral winter. CHEMTAX analysis of pigment data indicated that the community comprised mainly haptophytes and diatoms, with Prochlorococcus, prasinophytes and pelagophytes also being prominent to the east and west of the eddy. There was little difference in community structure, chlorophyll-specific absorption [a*ph(440)] and pigment:TChla ratios between the surface and the sub-surface chlorophyll maximum (SCM), reflecting acclimation to fluctuating light conditions in a well mixed upper layer. Values for a*ph(440) were low for diatom dominance, high where prokaryote proportion was high, and intermediate for flagellate dominated communities. Chlorophyll c and fucoxanthin:TChla ratios were elevated over most of the eddy, while 19′-hexanoyloxyfucoxanthin ratios increased in the eastern and western sectors. In a community comprising mainly flagellates and Prochlorococcus to the west of the eddy, there was high a*ph(440) at the surface and elevated ratios for divinyl chlorophyll a, chlorophyll b and 19′-hexanoyloxyfucoxanthin at the SCM. An increase in diadinoxanthin:TChla ratios and a decline in the quantum efficiency of photochemistry in PSII under high light conditions, indicated some photoprotection and photoinhibition at the surface even in a well mixed environment. Diadinoxanthin was the main photoprotective carotenoid within the eddy, while zeaxanthin was the dominant photoprotective pigment outside the eddy. The results of this study will be useful inputs into appropriate remote sensing models for estimating primary production and the size class distribution of phytoplankton in eddies in the southwest Indian Ocean

Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids

To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid

MacWilliams Identities for mm-tuple Weight Enumerators

Since MacWilliams proved the original identity relating the Hamming weight enumerator of a linear code to the weight enumerator of its dual code there have been many different generalizations, leading to the development of $m$-tuple support enumerators. We prove a generalization of theorems of Britz and of Ray-Chaudhuri and Siap, which build on earlier work of Kl{\o}ve, Shiromoto, Wan, and others. We then give illustrations of these $m$-tuple weight enumerators.Comment: 17 pages. Accepted to SIAM Journal on Discrete Mathematic

Relative generalized hamming weights and extended weight polynomials of almost affine codes

This is a post-peer-review, pre-copyedit version of an article published in Lecture Notes in Computer Science, International Castle Meeting on Coding Theory and Applications ICMCTA 2017: Coding Theory and Applications, 207-216. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-319-66278-7_17 .This paper is devoted to giving a generalization from linear codes to the larger class of almost affine codes of two different results. One such result is how one can express the relative generalized Hamming weights of a pair of codes in terms of intersection properties between the smallest of these codes and subcodes of the largest code. The other result tells how one can find the extended weight polynomials, expressing the number of codewords of each possible weight, for each code in an infinite hierarchy of extensions of a code over a given alphabet. Our tools will be demi-matroids and matroids

Fluctuations of indicator and index microbes as indication of pollution over three years in the Plankenburg and Eerste Rivers, Western Cape, South Africa

The Plankenburg and Eerste Rivers (Western Cape) have been reported to be contaminated with faecal coliforms. Water is drawn from both rivers for irrigation of fresh produce. The potential risk in the use of these rivers as irrigation sources was assessed by determining the fluctuations of ‘indicator’ and ‘index’ microbes over 3 years. Selected physico-chemical (water temperature, pH, COD, conductivity and alkalinity) and microbiological parameters, including coliforms, faecal coliforms, Escherichia coli and enterococci, as ‘indicators’ of faecal pollution, and Salmonella, Listeria and Staphylococcus, as ‘index’ of the presence of potential pathogens, were monitored.No correlation was found between water temperature and COD (r2 = 0.0003), whereas for temperature and pH a significant trend (p = 0.0004), but low correlation (r2 = 0.108), was observed. With the exception of the faecal coliforms (E. coli), no significant trends and no correlations between temperature and the dependent variables were found. For the faecal coliforms there was a significant trend (p = 0.0289) with temperature but not a good correlation (r2 = 0.0434), but the impact of temperature over time was significant (p = 0.0047). This is important, when the World Health Organisation (WHO) and South African Department of Water Affairs (DWA) guidelines for faecal coliforms are applied, as it indicates that temperaturedoes impact the faecal coliform numbers. The presence of indicator organisms did not only indicate unsanitary conditions, but also the presence of potential pathogens such as Staphylococcus, Klebsiella, Listeria and Salmonella. Based on these results the microbial quality of these rivers was found to be unacceptable and does not meet the WHO and DWA guidelines for safe irrigation. There was also a high risk of exposure to human pathogens when water from these rivers is used to irrigate produce that is consumed without further processing.Keywords: Irrigation water, faecal pollution, indicator and index organisms, Plankenburg and Eerste River

On character generators for simple Lie algebras

We study character generating functions (character generators) of simple Lie algebras. The expression due to Patera and Sharp, derived from the Weyl character formula, is first reviewed. A new general formula is then found. It makes clear the distinct roles of ``outside'' and ``inside'' elements of the integrity basis, and helps determine their quadratic incompatibilities. We review, analyze and extend the results obtained by Gaskell using the Demazure character formulas. We find that the fundamental generalized-poset graphs underlying the character generators can be deduced from such calculations. These graphs, introduced by Baclawski and Towber, can be simplified for the purposes of constructing the character generator. The generating functions can be written easily using the simplified versions, and associated Demazure expressions. The rank-two algebras are treated in detail, but we believe our results are indicative of those for general simple Lie algebras.Comment: 50 pages, 11 figure