Systematic Study of Lattice Specific Heat of Filled Skutterudites

The lattice specific heat C lat of La-based filled skutterudites La T 4 X 12 ( T = Fe, Ru and Os; X = P, As, and Sb) has been systematically studied, and both the Debye temperature Θ D and the Einstein temperature Θ E of La T 4 X 12 were carefully estimated. We confirmed that a correlation exists between Θ D and the reciprocal of the square root of average atomic mass for La T 4 P 12 , La T 4 As 12 , and La T 4 Sb 12 . The Θ D of filled skutterudites was found to depend mainly on the nature of the species X forming the cage. The temperature dependence of C lat / T 3 for La T 4 X 12 exhibited a large broad maximum at low temperatures (10–30 K), which suggests a nearly dispersionless low-energy optical mode characterized by Einstein specific heat. Since no such broad maximum exists for the unfilled skutterudite RhP 3 , the low-energy optical modes are associated with vibration involving La ions in the X 12 cage (the so-called “guest ion modes”). The Θ E of filled skutterudites was found to roughly correspond to the energy of low-energy guest ion optical modes. Furthermore, a good correlation was shown to exist between Θ E and r R–X - r R3+ , where r R–X is the R – X distance and r R3+ is the effective ionic radius of R 3+ . As r R–X - r R3+ increased, Θ E was found to decrease

Dual Inoculation of Rhizobium and Arbuscular Mycorrhizal Fungi Increases Soil-Total Nitrogen, Available Phosphorus, and Yield of Soybean in Vertisols

Soybean is a protein source food crop with high economic value. So far, national production has not been able to meet domestic demand resulting in continuing import of soybean. The use of rhizobium and arbuscular mycorrhizal fungi (AMF) as biological fertilizers could be an alternative to increase soybean production. The research aimed to investigate the effect of dual inoculation of rhizobium and arbuscular mycorrhizal fungi (AMF) on root nodules formation, AMF development, total-N and available P of Vertisols, and yield of soybean. This study was designed in a completely randomized design) with 4 treatments namely no inoculation (R0), rhizobium inoculation (R1), AMF inoculation (R2), and dual inoculation of rhizobium and AMF (R3), with four replications. The variables observed were the number of effective root nodules, AMF spore density, AMF colonization, soil total-N, available P, plant height, number of pods, and seed weight. The results showed that dual inoculation of rhizobium and AMF had a better effect on the number of effective root nodules, AMF spore density, AMF colonization, soil total- N, available P, plant height, number of pods, and seed weight compared to the single inoculation and un-inoculated treatment

A bijection between noncrossing and nonnesting partitions of types A and B

The total number of noncrossing partitions of type $\Psi$ is the $n$th Catalan number $\frac{1}{n+1}\binom{2n}{n}$ when $\Psi=A_{n-1}$, and the binomial $\binom{2n}{n}$ when $\Psi=B_n$, and these numbers coincide with the correspondent number of nonnesting partitions. For type A, there are several bijective proofs of this equality, being the intuitive map that locally converts each crossing to a nesting one of them. In this paper we present a bijection between nonnesting and noncrossing partitions of types A and B that generalizes the type A bijection that locally converts each crossing to a nesting.Comment: 11 pages, 11 figures. Inverse map described. Minor changes to correct typos and clarify conten

Nichols algebras over groups with finite root system of rank two II

We classify all non-abelian groups G for which there exists a pair (V,W) of absolutely simple Yetter–Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional, under two assumptions: the square of the braiding between V and W is not the identity, and G is generated by the support of V and W. As a corollary, we prove that the dimensions of such V and W are at most six. As a tool we use the Weyl groupoid of (V,W).Fil: Heckenberger, István. Philipps Universität Marburg; AlemaniaFil: Vendramin, Claudio Leandro. Philipps Universität Marburg; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin