Families of rationally connected varieties

We prove that every one-parameter family of complex rationally connected varieties has a section.

     

Finite Affine Groups: Cycle Indices, Hall–Littlewood Polynomials, and Probabilistic Algorithms

The study of asymptotic properties of the conjugacy class of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of this measure are given—three using symmetric function theory and one using Markov chains. This leads to non-trivial enumerative results. Cycle index generating functions are derived and are used to compute the large dimension limiting probabilities that an element of the affine group is separable, cyclic, or semisimple and to study the convergence to these limits. The semisimple limit involves both Rogers–Ramanujan identities. This yields the first examples of such computations for a maximal parabolic subgroup of a finite classical group.     

Reducing hypothalamic AGRP by RNA interference increases metabolic rate and decreases body weight without influencing food intake

Background  

Several lines of evidence strongly suggest that agouti-related peptide (AGRP) plays a key role in the regulation of metabolic function but ablation of the AGRP gene has no apparent effect on metabolic function. Since specific pharmacological antagonists of AGRP do not presently exist, we assessed if reduction of hypothalamic AGRP mRNA by RNA interference (RNAI) would influence metabolic function, an outcome suggesting that pharmacological antagonists might constitute useful reagents to treat obesity.     

On the minimum ropelength of knots and links

The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are C ^1,1 curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp. Oblatum 11-IV-2001 & 20-III-2002?Published online: 17 June 2002     

Manganese(I)‐Catalyzed C−H Activation: The Key Role of a 7‐Membered Manganacycle in H‐Transfer and Reductive Elimination

Manganese‐catalyzed C?H bond activation chemistry is emerging as a powerful and complementary method for molecular functionalization. A highly reactive seven‐membered Mn^I intermediate is detected and characterized that is effective for H‐transfer or reductive elimination to deliver alkenylated or pyridinium products, respectively. The two pathways are determined at Mn^I by judicious choice of an electron‐deficient 2‐pyrone substrate containing a 2‐pyridyl directing group, which undergoes regioselective C?H bond activation, serving as a valuable system for probing the mechanistic features of Mn C?H bond activation chemistry.     

Reagent‐Controlled α‐Selective Dehydrative Glycosylation of 2,6‐Dideoxy‐ and 2,3,6‐Trideoxy Sugars

We have found that activating either 2,3‐bis(2,3,4‐trimethoxyphenyl)cyclopropenone or 2,3‐bis(2,3,4‐trimethoxyphenyl)cyclopropene‐1‐thione with oxalyl bromide results in the formation of a species that promotes the glycosylation between 2,6‐dideoxy‐sugar hemiacetals and glycosyl acceptors in good yield and high α‐selectivity. Both reactions are mild and tolerate a number of sensitive functional groups including highly acid‐labile 2,3,6‐trideoxy‐sugar linkages.     

Amyloid Aggregates Arise from Amino Acid Condensations under Prebiotic Conditions

Current theories on the origin of life reveal significant gaps in our understanding of the mechanisms that allowed simple chemical precursors to coalesce into the complex polymers that are needed to sustain life. The volcanic gas carbonyl sulfide (COS) is known to catalyze the condensation of amino acids under aqueous conditions, but the reported di‐, tri‐, and tetra‐peptides are too short to support a regular tertiary structure. Here, we demonstrate that alanine and valine, two of the proteinogenic amino acids believed to have been among the most abundant on a prebiotic earth, can polymerize into peptides and subsequently assemble into ordered amyloid fibers comprising a cross‐β‐sheet quaternary structure following COS‐activated continuous polymerization of as little as 1 mm amino acid. Furthermore, this spontaneous assembly is not limited to pure amino acids, since mixtures of glycine, alanine, aspartate, and valine yield similar structures.     

Rearrangements in the Scholl oxidation: implications for molecular architectures

Rearrangements readily occur in Scholl oxidations and interfere with the construction of certain molecular architectures. 3,3?,4,4′,4″,4?,5′,5″-Octamethoxy-1,1′,2′,1″,2″,1?-quaterphenyl and 3,3?,4,4′,4′′,4?,5′,5′-octamethyl-1,1′,2′,1″,2″,1?-quaterphenyl, which were conceived as precursors to benzenoid strips, rearranged under Scholl conditions to the unexpected C_2v-substituted products 1,2,5,6,9,10,12,13-octamethoxydibenzo[fg,op]naphthacene and 1,2,5,6,9,10,12,13-octamethyldibenzo[fg,op]naphthacene. This corrects a widely propagated error in the literature in which the assignments of 1,2,5,6,9,10,12,13-octamethoxydibenzo[fg,op]naphthacene (C_2v) and 1,2,5,6,8,9,12,13-octamethoxydibenzo[fg,op] naphthacene (C_2h) are crossed. A mechanism involving the migration of an aryl ring on an arenium cation intermediate is proposed.     

Enantioselective total syntheses of nankakurines A and B: confirmation of structure and establishment of absolute configuration

Total syntheses of (+)-nankakurine A (2) and (+)-nankakurine B (3) were accomplished by a sequence that employs an intramolecular dipolar cycloaddition of an azomethine imine intermediate to form the azatricyclic moiety and establish the relative configuration of the spiropiperidine ring. These syntheses, together with the synthesis of the originally purported structure 1 of nankakurine A, rigorously establish the relative and absolute configuration of these structurally unusual Lycopodium alkaloids. The syntheses are sufficiently concise that gram quantities of (+)-nankakurine A (2) and (+)-nankakurine B (3) will be available for further biological studies.     

Photochemistry of adsorbed nitrate

In the atmosphere, gas-phase nitrogen oxides including nitric acid react with particle surfaces (e.g., mineral dust and sea salt aerosol) to yield adsorbed nitrate, yet little is known about the photochemistry of nitrate on the surface of these particles. In this study, nitrate adsorbed on alumina surfaces, a surrogate for mineral dust aerosol, is irradiated with broadband light (lambda > 300 nm) in the absence and presence of coadsorbed water, at <1% and 45 +/- 2% relative humidity (%RH), respectively, and molecular oxygen. Upon irradiation, the nitrate ion readily undergoes photolysis to yield nitrogen-containing gas-phase products, NO2, NO, and N2O. Although NO2, NO, and N2O form under the different conditions investigated, both coadsorbed water and molecular oxygen change the gas-phase product distribution, with NO being the major product under dry and humid conditions in the absence of molecular oxygen and NO2 the major product in the presence of molecular oxygen. To the best of our knowledge, this is the first study to investigate the role of solvation by coadsorbed water in the photochemistry of adsorbates at solid interfaces and the roles that molecular oxygen, adsorbed water, and relative humidity may have in photochemical processes on aerosol surfaces that have the potential to alter the chemical balance of the atmosphere.