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Boron forms various compounds with metal atoms occupying voids in the boron framework. As a synthesis method it has been found that the addition of small amounts of third elements like carbon, nitrogen, and silicon can result in the formation of novel and varied rare earth boron cluster structures. A wide variation of 1D, 2D, and 3D magnetic behavior with unexpectedly strong magnetic interactions has been discovered in rare earth boron icosahedra compounds which are magnetically dilute, f-electron insulators. As an intriguing phenomenon, the B12 icosahedra cluster, which is a building block of the structure, has been indicated to function as a novel mediator of magnetic interaction. These phenomena are borides. Attractive high temperature thermoelectric properties are also emerging in borides. Attractive high temperature thermoelectric properties are also emerging in this group of compounds, which is striking due to the great potential of utilizing waste heat. Recent developments on the long awaited n-type counterpart to boron carbide, the homologous series of RE-B-C(N) compounds, REB17CN, REB22C2N, and REB28.5C4, will be presented together with those of p-type REB44Si2. General new ways to improve the thermoelectric properties are also discussed. For example, seeding with highly electrically conductive metallic borides like REB4 and REB6 is found to be a way to significantly increase the thermoelectric figure of merit. Electric resistivity significantly decreases while Seebeck coefficients and thermal conductivity are not sizably affected. [ABSTRACT FROM AUTHOR]

We introduce tatami tilings, and present some of the many interesting questions that arise when studying them. Roughly speaking, we are considering tilings of rectilinear regions with 1 ×2 dimer tiles and 1 ×1 monomer tiles, with the constraint that no four corners of the tiles meet. Typical problems are to minimize the number of monomers in a tiling, or to count the number of tilings in a particular shape. We determine the underlying structure of tatami tilings of rectangles and use this to prove that the number of tatami tilings of an n ×n square with n monomers is n2n − 1. We also prove that, for fixed-height, the number of tatami tilings of a rectangle is a rational function and outline an algorithm that produces the coefficients of the two polynomials of the numerator and the denominator. [ABSTRACT FROM AUTHOR]

The Idi-dimer is an asymmetric carbon compound formed by a cross-link between two identical fibrin molecules. The test is specific for secondary fibrinolysis because the cross-linkage occurs with fibrin and not fibrinogen. A positive test is presumptive evidence of disseminated intravascular coagulation (DIC). [ABSTRACT FROM AUTHOR]