Curvature properties of metric nilpotent Lie algebras which are independent of metric

This paper consists of two parts. First, motivated by classic results, we determine the subsets of a given nilpotent Lie algebra \(\mathfrak {g}\) (respectively, of the Grassmannian of two-planes of \(\mathfrak {g}\)) whose sign of Ricci (respectively, sectional) curvature remains unchanged for an arbitrary choice of a positive definite inner product on \(\mathfrak {g}\). In the second part we study the subsets of \(\mathfrak {g}\) which are, for some inner product, the eigenvectors of the Ricci operator with the maximal and with the minimal eigenvalue, respectively. We show that the closure of these subsets is the whole algebra \(\mathfrak {g}\), apart from two exceptional cases: when \(\mathfrak {g}\) is two-step nilpotent and when \(\mathfrak {g}\) contains a codimension one abelian ideal.     

Molecular dynamics of glucose in solution: a quasielastic neutron scattering study

The molecular dynamics of glucose dissolved in heavy water have been investigated at 280 K by the technique of quasielastic neutron scattering. The scattering was described by a dynamic structure factor that accounts for decoupled diffusive jumps and free rotational motions of the glucose molecules. With increasing glucose concentration, the diffusion constant decreases by a factor five and the time between jumps increases considerably. Our observations validate theoretical predictions concerning the impact of concentration on the environment of a glucose molecule and the formation of cages made by neighboring glucose molecules at higher concentrations.     

An unusual cleavage reaction of a peptide observed during dithiotreitol and tris(2-carboxyethyl)phosphine reduction: application to sequencing of HpTx2 spider toxin using nanospray tandem mass spectrometry

A recombinant peptidic spider toxin, HpTx2, was investigated directly by nanoelectrospray tandem mass spectrometry (MS/MS). This 30-residue toxin possesses a highly knotted structure with cystines arranged in close proximity. The low-energy collision-induced dissociation MS/MS spectrum of the [M+4H](4+) ion permitted characterization of the C-terminal sequence of HpTx2 up to Cys(26) that is involved in a disulfide bridge. Chemical pre-treatment with DTT or TCEP was then investigated, and it was found that an unexpected cleavage reaction of HpTx2 gave two smaller peptides which were completely sequenced by MS/MS experiments using a Qq-TOF mass spectrometer. This unusual hydrolysis reaction facilitated the determination of the complete sequence of the HpTx2 toxin.     

A fast and parallel route to cyclic isothioureas and guanidines with use of microwave-assisted chemistry

A fast and simple approach to novel cyclic isothioureas and related guanidine derivatives is presented in this study. The construction of the central basic scaffolds is achieved solely by the application of microwave-assisted chemistry, without any need of activating agents or protecting group manipulations. The product formation of various substituted guanidines from the corresponding isothiouronium salts was controlled by the nucleophilicity of the counterion and influenced by the reaction temperature. Further, a new fast-track access to tetrahydropyrimidin-2-ylamines was developed.     

Primary reactions of bacteriophytochrome observed with ultrafast mid-infrared spectroscopy

Phytochromes are red-light photoreceptor proteins that regulate a variety of responses and cellular processes in plants, bacteria, and fungi. The phytochrome light activation mechanism involves isomerization around the C(15)═C(16) double bond of an open-chain tetrapyrrole chromophore, resulting in a flip of its D-ring. In an important recent development, bacteriophytochrome (Bph) has been engineered for use as a fluorescent marker in mammalian tissues. Bphs covalently bind a biliverdin (BV) chromophore, naturally abundant in mammalian cells. Here, we report an ultrafast time-resolved mid-infrared spectroscopic study on the Pr state of two highly related Bphs from Rps. palustris , RpBphP2 (P2) and RpBphP3 (P3) with distinct photoconversion and fluorescence properties. We observed that the BV excited state of P2 decays in 58 ps, while the BV excited state of P3 decays in 362 ps. By combining ultrafast mid-IR spectroscopy with FTIR spectroscopy on P2 and P3 wild type and mutant proteins, we demonstrate that the hydrogen bond strength at the ring D carbonyl of the BV chromophore is significantly stronger in P3 as compared to P2. This result is consistent with the X-ray structures of Bph, which indicate one hydrogen bond from a conserved histidine to the BV ring D carbonyl for classical bacteriophytochromes such as P2, and one or two additional hydrogen bonds from a serine and a lysine side chain to the BV ring D carbonyl for P3. We conclude that the hydrogen-bond strength at BV ring D is a key determinant of excited-state lifetime and fluorescence quantum yield. Excited-state decay is followed by the formation of a primary intermediate that does not decay on the nanosecond time scale of the experiment, which shows a narrow absorption band at ～1540 cm(-1). Possible origins of this product band are discussed. This work may aid in rational structure- and mechanism-based conversion of BPh into an efficient near-IR fluorescent marker.     

Antimony implanted silicon: A comparison between the total implanted concentration profile and the donor concentration profile

Abstract

The total concentration profiles of various doses of antimony, implanted into silicon at 100 keV, have been determined by a new technique, using Kr⁺ ions to detect selectively the antimony (as Sb-M X-rays) at the expense of the silicon. Since most of these X-rays arise from only a few tens of Angstroms below the surface of the silicon, this allows the X-ray generation to be used in conjunction with an anodic stripping technique to obtain the antimony depth distribution. These profiles are compared with others, obtained by measuring the donor concentration as a function of depth, using standard Hall effect and conductivity measurements. A significant difference between these profiles was observed, which is thought to be due to the suppression of electrical activity which occurs as the result of lattice damage. Confirmatory evidence is presented in the form of electron microscope observations of the implanted region at various depths below the silicon surface.     

Rational design of materials with extreme negative compressibility: selective soft-mode frustration in KMn[Ag(CN)2]3

We show that KMn[Ag(CN)(2)](3) exhibits the strongest negative linear compressibility (NLC) effect over the largest pressure range yet observed. Variable pressure neutron powder diffraction measurements reveal that its crystal lattice expands along the c axis of its trigonal cell under increasing hydrostatic pressure, while contracting along the a axis. This corresponds to a "wine-rack"-like mechanism for NLC that we find also results in anisotropic negative thermal expansion (NTE) in the same material. Inclusion of extra-framework K(+) counterions has minimal effect on framework flexibility (and hence the magnitude of NTE/NLC) but selectively frustrates the soft phonon modes responsible for destroying NLC in the related material Ag(3)[Co(CN)(6)].     

The unique rht-MOF platform, ideal for pinpointing the functionalization and CO2 adsorption relationship

The uniqueness of the rht-MOF platform, based on the singular (3,24)-connected net, allows for the facile design and synthesis of functionalized materials for desired applications. Here we designed a nitrogen-rich trefoil hexacarboxylate (trigonal tri-isophthalate) ligand, which serves to act as the trigonal molecular building block while concurrently coding the formation of the targeted truncated cuboctahedral supermolecular building block (in situ), and enhancing the CO(2) uptake in the resultant rht-MOF.     

The Sprague–Grundy function of the real game Euclid

The game Euclid, introduced and named by Cole and Davie, is played with a pair of nonnegative integers. The two players move alternately, each subtracting a positive integer multiple of one of the integers from the other integer without making the result negative. The player who reduces one of the integers to zero wins. Unfortunately, the name Euclid has also been used for a subtle variation of this game due to Grossman in which the game stops when the two entries are equal. For that game, Straffin showed that the losing positions (a,b) with a<b are precisely the same as those for Cole and Davie’s game. Nevertheless, the Sprague–Grundy functions are not the same for the two games. We give an explicit formula for the Sprague–Grundy function for the original game of Euclid and we explain how the Sprague–Grundy functions of the two games are related.