Subalgebras that are cyclic as submodules

Let R be an associative, commutative, unital ring. By a R-algebra we mean a unital R-module A together with a R-module homomorphism : _R ⁿ AA (n2). We raise the question whether such an algebra possesses either an idempotent or a nilpotent element. In section 1 an affirmative answer is obtained in case R=k is an algebraically closed field and dim_kA<, as well as in case R=, dimS<, and n0(2). Section 2 deals with the case of reduced rings R and R-algebras which are finitely generated and projective as R-modules. In section 3 we show that the generic algebra over an integral domain D fails to have nilpotent elements in any integral domain extending its base ring D_n,m, and thus acquires an idempotent element in some integral domain extending D_n,m.Partially supported by National Science Foundation Grant GP-38229.     

A short proof of a theorem of Ruelle

Using the existence of conformal measures in the sense ofSullivan [4] andDenker, Urbaski [2] we give a simple proof of Ruelle's Theorem, that the Hausdorff dimension of a hyperbolic Julia set is the solution of the equationP(R,–tlog|R|)=0.     

Glycopeptide analysis by matrix-assisted laser desorption/ionization tandem time-of-flight mass spectrometry reveals novel features of horseradish peroxidase glycosylation

We explored matrix-assisted laser desorption/ionization (MALDI) tandem time-of-flight (TOF/TOF) mass spectrometry for the analysis of N-glycosylated peptides, using horseradish peroxidase (HRP) as a test case. Two different types of cleavage were observed in the TOF/TOF fragmentation spectra: Firstly, cleavages of peptide bonds yielded fragments with the attached N-glycans staying intact, thus revealing information on peptide sequence and glycan attachment site. Secondly, fragmentation of the glycan moiety was characterized by cleavage of glycosidic bonds as well as a (0,2)X-ring fragmentation of the innermost N-acetylglucosamine of the chitobiose core. Loss of the complete N-glycan moiety occurred by cleavage of both the N-glycosidic bond and the side-chain amide group of the N-glycosylated asparagine, yielding a characteristic peak doublet with a mass difference of 17 Da, which revealed the individual masses of the N-glycan and the peptide moiety. Analysis of a HRP tryptic digest at the sub-picomole level allowed the characterization of various N-glycosylated peptides including those with internal disulfide linkages, a glycopeptide linked via a disulfide bond to another peptide, and a 5 kDa glycopeptide carrying two N-glycans. The potential of our approach was illustrated by the detection of the following novel features of HRP glycosylation: (i) The conjugation of a xylosylated trimannosyl N-glycan without core-fucosylation to site Asn316, showing for the first time unambiguously the occupation of this site; and (ii) A disaccharide N-acetylhexosamine1deoxyhexose1 attached to N-glycosylation sites Asn285 and Asn298, which might represent a Fuc(alpha1-3)GlcNAc- moiety arising from the processing of N-glycans by a horse-radish endoglycosidase during biosynthesis of HRP.     

Proficiency tests for pharmaceuticals in different waters

To date there are no German or international standards for the analysis of pharmaceuticals in waters. The efficiency of the analytical methods—predominantly LC-MS/MS and GC-MS—used for trace analysis of pharmaceuticals is proved for the first time by proficiency tests using natural waters.Two proficiency tests for up to 11 different groups of pharmaceuticals in river water and waste water were carried out in 2000 (28 participants) and 2002 (20 participants). The spiking concentrations were 60–800 ng/L for surface water and 80–1280 ng/L for waste water. For most determinants good recovery rates (80–120%) and variations (around 35% for surface water and 50% for waste water) were reported.     

Structure, ordering, and bonding of half antiperovskites: PbNi3/2S and BiPd3/2S

In a model study the crystal structures of shandite (Pb₂Ni₃S₂), parkerite (Bi₂Ni₃S₂) and their Pd homologues are investigated in terms of ordered half antiperovskites AM_3/2S (A = Pb, Bi; M = Ni, Pd). This addresses fundamental questions on the structural relations, ordering and chemical bonding. From crystal structure investigations a new cubic parkerite variant is presented for Bi₂Pd₃S₂ that fits in an ordering model equivalently to shandite and parkerite. Type–antitype relations to ordered oxygen deficit perovskites are presented. With the relation to the superconductor Ni₃MgC a model is deduced that provides the complete crystal structure and symmetry in terms of the Ni and Pd ordering in antiperovskite superstructures. Therein a systematic ab initio investigation on the relative stability of shandite and parkerite structures is carried out for the first time. From the DFT modelling results the preferences of the ordering variants and the distinct differences in the atomic coordination spheres are discussed. The bonding in the systems is investigated by site projected density of states and covalent bond energy calculations.     

Die «Zip»-Reaktion: Eine neue Ringerweiterungsreaktion. Synthese von 17-, 21- und 25-gliedrigen Polyaminolactamen. 4. Mitteilung über Umamidierungsreaktionen

The Zip-reaction: A New Method for the Synthesis of Macrocyclic Polyaminolactams The 21- and 25-membered aminolactams 11 and 25 were synthesized from the 13-membered lactam 4 . To introduce the ring enlargement unit (a propylamino group) 4 was N-alkylated using acrylonitrile and the resulting product hydrogenated. Repetition of this reaction sequence gave 3 , which was converted in the presence of base in 90% yield to the ring-enlarged macrocyclic base 11 (Scheme 2). In a similar but stepwise synthesis consisting of two separate ring-enlargement reactions 4 was transformed to 11 via 13 (Scheme 4). Introducing three ringenlargement units into 4 the 25-membered aminolactam 25 was synthesized in 84% yield (Scheme 5). The mechanism of the ring-enlargement reaction is given in Scheme 3. In comparison to a zip-fastener or zipper this reaction is called “zipreaction”.     

Chelation or Non-Chelation Control in Addition Reactions of Chiral α- and β- Alkoxy Carbonyl Compounds [New Synthetic Methods (44)]

The addition of C-nucleophiles such as Grignard reagents or enolates to chiral α- or β-alkoxy aldehydes or ketones creates a new center of chirality and is therefore diastereogenic. In order to control stereoselectivity, two strategies have been developed: (1) Use of Lewisacidic reagents which form intermediate chelates, these being attacked stereoselectively from the less hindered side (chelation control); (2) use of reagents incapable of chelation, stereoselective attack being governed by electronic and/or steric factors (non-chelation control). Generally, the two methods lead to the opposite sense of diastereoselectivity. It is possible to predict the outcome by careful choice of organometallic reagents containing elements such as Li, Mg, B, Si, Sn, Cu, Zn, or Ti. For corrigendum see DOI: 10.1002/anie.198407461     

EXCITED STATE BEHAVIOR OF PHYTOCHROME Pr

The primary excited state processes of phytochrome, the plant chromoprotein responsible for most photomorphogenetic responses, are investigated by picosecond intensity-dependent transmission measurements. At sufficient high excitation intensity (starting at photon flux densities of about 1′10²⁵ cm^?2 s^?l) a moderate bleaching of the absorption is observed. For the quantitative analysis of the experimental data a rate equation system approach for the energy levels responsible for the ultrafast transformation P_r→ lumi-R and the photon transport through the sample was utilized. The following was found for the excited state parameters of the phytochrome P_r: (1) an excited state absorption of the same order of magnitude as the ground state absorption (cross section: S?_exc= 4′10^?16 cm^?2 at 650 nm), (2) a fast relaxation of the higher excited singlet state on the femtosecond time scale.     

Remarks on the correlation function implied by the Bjerrum theory of ion pairing

The Friedman theory of correlation functions implied by the Bjerrum theory is generalized by taking into account additional terms and by improving the basic expression for the free energy. By combining the mean spherical approximation (MSA) and the mass action law (MAL) good agreement with HNC and MC data is reached.     

Cycloadditions of Aryl‐Substituted 1,2,4‐Triazines with 2‐Cyclopropylidene‐1,3‐dimethylimidazolidine – Zwitterions as Discrete Intermediates

Cycloadditions of 2‐cyclopropylidene‐1,3‐dimethylimidazolidine ( 1 ), a strong, electron‐rich C‐nucleophile, with a variety of aryl‐substituted 1,2,4‐triazines occur at temperatures between ?100 and +100°, depending on the substitution pattern. At low temperatures, zwitterions, formed by nucleophilic attack of 1 on the triazines, could be detected spectroscopically and, in some cases, isolated. Two types of zwitterions were found: 1) those where the new bond was linked to C(5) of the triazine and which were formed in a reversible dead‐end equilibrium, and 2) those where the new bond was linked either to C(3) or C(6). The latter exhibited the same regiochemistry as the final cycloadducts, and might be intermediates of a two‐step Diels–Alder reaction. Energies and structural characteristics for stationary points in the reaction of monosubstituted triazines with 1 in the gas phase and in CH₂Cl₂ solution were calculated at the Becke3LYP/6‐311+G(d,p)//Becke3LYP/6‐31G(d) level of theory. Different reaction mechanisms are discussed on the basis of steric, electronic, and solvent effects.