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.     

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.     

Production of picosecond, kilojoule, and petawatt laser pulses via Raman amplification of nanosecond pulses

Raman amplification in plasma has been promoted as a means of compressing picosecond optical laser pulses to femtosecond duration to explore the intensity frontier. Here we show for the first time that it can be used, with equal success, to compress laser pulses from nanosecond to picosecond duration. Simulations show up to 60% energy transfer from pump pulse to probe pulse, implying that multikilojoule ultraviolet petawatt laser pulses can be produced using this scheme. This has important consequences for the demonstration of fast-ignition inertial confinement fusion.     

The Structural Basis for Optimal Performance of Oligothiophene‐Based Fluorescent Amyloid Ligands: Conformational Flexibility is Essential for Spectral Assignment of a Diversity of Protein Aggregates

Protein misfolding diseases are characterized by deposition of protein aggregates, and optical ligands for molecular characterization of these disease‐associated structures are important for understanding their potential role in the pathogenesis of the disease. Luminescent conjugated oligothiophenes (LCOs) have proven useful for optical identification of a broader subset of disease‐associated protein aggregates than conventional ligands, such as thioflavin T and Congo red. Herein, the molecular requirements for achieving LCOs able to detect nonthioflavinophilic Aβ aggregates or non‐congophilic prion aggregates, as well as spectrally discriminate Aβ and tau aggregates, were investigated. An anionic pentameric LCO was subjected to chemical engineering by: 1) replacing thiophene units with selenophene or phenylene moieties, or 2) alternating the anionic substituents along the thiophene backbone. In addition, two asymmetric tetrameric ligands were generated. Overall, the results from this study identified conformational freedom and extended conjugation of the conjugated backbone as crucial determinants for obtaining superior thiophene‐based optical ligands for sensitive detection and spectral assignment of disease‐associated protein aggregates.     

How to Inflate in the Right Places-An Analysis of Design Characteristics to Cope with Variations in Gas Transmission Networks

This paper considers how much margin to allow when designing a large pipe network based on predictions of future gas supply and demand. Thus it deals with forecasting from the engineering aspect of how to cope with variations from the predicted pattern of events.The subject of the paper is the British Gas National Transmission System. The detail of the paper concerns some of the margins used to design the system, in particular their purpose, size and application.The methods used to analyse the margins are: simulation, regression, distribution fitting, convolution and risk analysis.The conclusion of the work is that different parts of the network require different sizes of margin to retain the same level of security, since the impact of localized forecasting errors and predicted plant failures varies significantly across the grid.