Bier Spheres and Posets

In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n – 2)-spheres on 2n vertices, as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that “cut across an ideal.” Thus we arrive at a substantial generalization of Bier’s construction: the Bier posets Bier(P, I) of an arbitrary bounded poset P of finite length. In the case of face posets of PL spheres this yields cellular “generalized Bier spheres.” In the case of Eulerian or Cohen–Macaulay posets P we show that the Bier posets Bier(P, I) inherit these properties. In the boolean case originally considered by Bier, we show that all the spheres produced by his construction are shellable, which yields “many shellable spheres,” most of which lack convex realization. Finally, we present simple explicit formulas for the g-vectors of these simplicial spheres and verify that they satisfy a strong form of the g-conjecture for spheres.     

Ecophysiological Studies on the Vegetation of Madagascar: A δ13C and δD Survey for Incidence of Crassulacean Acid Metabolism (Cam) Among Orchids From Montane Forests and Succulents from the Xerophytic Thorn-Bush

Abstract

The incidence of Crassulacean acid metabolism (CAM) in plants collected at various habitats in Madagascar was investigated by survey of carbon and hydrogen isotope ratios ((δ¹³C and δD values). In about 50% of the epiphytic orchids from evergreen higher and lower montane forests the δ¹³C values were indicative for CAM. The remainder of the species are presumably C₃ plants. In all samples of malagasy epiphytic leafless orchids comprising 9 species, the δ¹³C values suggest extreme CAM with CO₂ uptake proceeding entirely during the night. All terrestrial orchids collected in the lower montane forests obviously acquire external carbon by C₃-photosynthesis, whereas Lissochilus decaryi, a terrestrial orchid from the semi-arid south of Madagascar and various other species of this genus are CAM plants. This is the first report of CAM occurrence in sympodial terrestrial orchids.

Judged by the δ¹³C values, all succulents (mainly Didiereaceae, Euphorbiaceae, Crassulaceae and Asclepiadaceae) collected at the xerophytic thorn-bush of the semi-arid south perform pronounced CAM. Where it applies, our δ¹³C measurements in the thorn-bush succulents revealed values being practically identical with those found by K. Winter in samples of the same species collected at the same site nearly 10 years earlier. This shows extreme constancy over long duration of time in the mode of CAM performed by the succulents of the malagasy thorn-bush vegetation. Since the δ¹³C survey now comprises all 11 known species of the Didiereaceae, it is unequivocally clear that all members of this family are CAM plants. Most of the individuals of the species of the Didiereaceae grown in a glass-house had slightly more negative δ¹³C values compared with those grown at the natural stands suggesting some contribution of C₃-photosynthesis to carbon acquisition under the evaporatively less demanding glass-house conditions (and perhaps higher CO₂ concentrations in the gas phase).

Despite of the fact that the hydrogen isotope composition of meteoric waters depends to a large extent on the altitude and temperature-climate of the site where the concerned plants grow, it was found that in samples obtained in the cooler higher evergreen montane forest as well as in the warmer lower evergreen montane forest and the lowland thorn-bush of the hot, semiarid south of Madagascar the δ values found in the organic matter (δD^org) were in the same range (between about - 10‰ to about - 90‰). This suggests that in our case the hydrogen isotope compositions of the meteoric waters were of minor importance in bringing about the δD^org values found in the plants.     

Die Kristallstruktur der hydratisierten Cyanokomplexe NMe4MnII[(Mn, Cr)III(CN)6] · 3 H2O und NMe4Cd[MIII(CN)6] · 3 H2O (MIII = Fe,Co): Verwandte des Berliner Blaus

The Crystal Structure of the Hydrated Cyano Complexes NMe₄Mn^II[(Mn, Cr)^III(CN)₆] · 3 H₂O and NMe₄Cd[M^III(CN)₆] · 3 H₂O (M^III = Fe, Co): Compounds Related to Prussian Blue The crystal structures of the isotypic tetragonal compounds (space group I4, Z = 10) NMe₄Mn^II · [(Mn, Cr)^III(CN)₆] · 3 H₂O (a = 1653.2(4), c = 1728.8(6) pm), NMe₄Cd[Fe(CN)₆] · 3 H₂O (a = 1642.7(1), c = 1733.1(1) pm) and NMe₄Cd[Co(CN)₆] · 3 H₂O (a = 1632.1(2), c = 1722.4(3) pm) were determined by X‐rays. They exhibit ⊥ c cyanobridged layers of octahedra [M^III(CN)₆] and [M^IIN₄(OH₂)₂], which punctually are interconnected also || c to yield altogether a spaceous framework. The M^II atoms at the positions linking into the third dimension are only five‐coordinated and form square pyramids [M^IIN₅] with angles N–M^II–N near 104° and distances of Mn–N: 1 × 214, 4 × 219 pm; Cd–N: 1 × 220 resp. 222, 4 × 226 resp. 228 pm. Further details and structural relations within the family of Prussian Blue are reported and discussed.     

The assembly of organic radical anions between metal-borate scaffolds

Metal-organic frameworks based on the Pb[B(Im)(4)](+) unit form layered structures analogous to those observed in clays and double layered hydroxide minerals. These layers can act as scaffolds for the organization of anionic organic guests. In this report, we use this scaffold to assemble TEMPO and PROXYL carboxylates in the interlayer spacings of Pb[B(Im)(4)](4-carboxy-TEMPO) 1 and Pb[B(Im)(4)](3-carboxy-PROXYL)(H(2)O)2, respectively. The resultant materials are paramagnetic, and the organization of the radical units differs between the two compounds. This results in changes in electronic structure of the radical unit, as observed by EPR spectroscopy.     

Lead and thallium tetrakis(imidazolyl)borates: modifying structure by varying metal and anion

We are using the coordinating anions tetrakis(imidazolyl)borate and tetrakis(4-methylimidazolyl)borate to construct new metal-organic framework structures. In this report, we are exploring materials similar in composition to the previously reported layered network structure Pb[B(Im)(4)](NO(3))(nH(2)O). The metal in this compound can be replaced with isoelectronic Tl(I), affording Tl[B(Im)(4)], and the borate can be modified by using 4-methylimidazole, resulting in Pb[B(4-MeIm)(4)](NO(3)) and Tl[B(4-MeIm)(4)]. Like the parent Pb[B(Im)(4)](NO(3))(nH(2)O), Tl[B(Im)(4)] and Tl[B(4-MeIm)(4)] are layered network structures but both lack anions or solvent molecules in the interlayer spacing. The material Pb[B(4-MeIm)(4)](NO(3)), however, exhibits a 3D network structure that lacks an open topology, resulting from the increased stereochemical activity (greater steric bulk toward other ligands) of the 4-methylimidazole ring. Both of the Tl(I) solids display longer M-N bonds than observed in the analogous Pb(II) compounds; these lengths account for the decreased effect of the stereochemical activity of the 4-methylimidazole ring in Tl[B(4-MeIm)(4)].     

(−)‐Englerin A is a Potent and Selective Activator of TRPC4 and TRPC5 Calcium Channels

Current therapies for common types of cancer such as renal cell cancer are often ineffective and unspecific, and novel pharmacological targets and approaches are in high demand. Here we show the unexpected possibility for the rapid and selective killing of renal cancer cells through activation of calcium‐permeable nonselective transient receptor potential canonical (TRPC) calcium channels by the sesquiterpene (?)‐englerin A. This compound was found to be a highly efficient, fast‐acting, potent, selective, and direct stimulator of TRPC4 and TRPC5 channels. TRPC4/5 activation through a high‐affinity extracellular (?)‐englerin A binding site may open up novel opportunities for drug discovery aimed at renal cancer.     

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.     

Tetrakis(imidazolyl)borate-based coordination polymers: group II network solids,M[B(Im)4]2(H2O)2 (M = Mg,Ca, Sr)

We are using the coordinating anion tetrakis(imidazolyl)borate to construct new metal-organic framework structures. In this report, we present three alkaline earth metal network solids incorporating this anion. All three compounds have the same formula, M[B(Im)(4)](2)(H(2)O)(2) (M = Mg, Ca, Sr), and the same coordination environment about the metal. However, the three compounds have different network structures with different degrees of hydrogen bonding; the Mg material forms a two-dimensional network and the Ca and Sr compounds form one-dimensional chains. In addition, we present the structure of the protonated anion B(HIm)(Im)(3) as a model for the default structure of this anion and discuss how the conformation of tetrakis(imidazolyl)borate can affect the structure of network solids.