Finitely correlated states on quantum spin chains

We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a finite-dimensional vector space. These states can be considered as generalized valence bond states, and they are dense in the set of all translation invariant states. We develop a complete theory of the ergodic decomposition of such states, including the decomposition into periodic Néel ordered states. The ergodic components have exponential decay of correlations. All states considered can be obtained as local functions of states of a special kind, so-called purely generated states, which are shown to be ground states for suitably chosen finite range VBS interactions. We show that all these generalized VBS models have a spectral gap. Our theory does not require symmetry of the state with respect to a local gauge group. In particular we illustrate our results with a one-parameter family of examples which are not isotropic except for one special case. This isotropic model coincides with the one-dimensional antiferromagnet, recently studied by Affleck, Kennedy, Lieb, and Tasaki.     

Abbau von Palustrin zu (−)-Dihydropalustraminsäure ((2R, 6S, 1′S)-[6-(1′-Hydroxypropyl)-2-piperidyl]essigsäure) und Struktur von Palustrin und Palustridin. Mitteilung über Schachtelhalmalkaloide

Degradation of palustrin to (?)-dihydropalustramic acid ((2R,6S,1′S)-[6-(1′-hydroxypropyl)-2-piperidyl]acetic acid), and the structure of palustrin and palustridin The structure of the macrocyclic alkaloid palustrin is shown to be 1a . Its piperidine unit can be obtained as (?)-dihydropalustramic acid ( 6a ) by the following sequence of degradation reactions (Scheme 1): catalytic hydrogenation of 1a followed by methylation and Hofmann degradation provides the allyl base 4 . the regioselectivity of the Hofmann elimination is explained by intramolecular proton abstraction at C(3) by C(18)-O^?. Catalytic reduction of 4 and subsequent acidic hydrolysis yielded 6a and N, N-dimethylputrescine (?N,N-dimethyl-1,4-butanediamine; 7 ). Loss of the N-alkyl group in the formation of 6a occurs during the catalytic hydrogenation step. This interpretation is supported by the results of model experiments. The position of the double bond in 1a is deduced from the IR. spectrum of the bromo-δ-lactone 19 prepared by treatment of 1a with N-bromosuccinimide at pH 4 (Scheme 3). Some of our previously published results on the degradation of dihydropalustrin ( 2a ) are obviously at variance with the newly proposed structure for palustrin ( 1a ). They can easily be explained by assuming a partial hydrogenolysis of the C(17)-N(1) bond during the preparation of dihydropalustrin from palustrin. Periodate cleavage of dihydropalustramic acid methyl ester ( 6b ) liberates propionaldehyde, which can be trapped by working at pH 7.5 (Scheme 2); at lower pH values it condenses rapidly with the simultaneously generated 3,4,5,6-tetrahydropyridine derivative 15 . The structure of the condensation product is proposed to be 16 on the basis of the isolation of its hydrogenation product, an isomeric dihydropalustramic acid ( 17 ).     

4-Aminobicyclo[2.2.2]octanone Derivatives with Antiplasmodial and Antitrypanosomal Activities

4-Aminobicyclo[2.2.2]octanones were converted to their N-oxides and to 4-aminobicyclo[2.2.2]octanes. Furthermore, the 6,7-bis-(4-methoxyphenyl) analogues were synthesized. All products were screened for their activities against Trypanosoma b. rhodesiense and Plasmodium falciparum. The pharmacological results were compared with those of formerly tested bicyclo[2.2.2]octanones and bicyclo[2.2.2]octanols. Structure-activity relationships are discussed.     

A fluorescence-based method for direct measurement of submicrosecond intramolecular contact formation in biopolymers: an exploratory study with polypeptides.

A fluorescent amino acid derivative (Fmoc-DBO) has been synthesized, which contains 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) as a small, hydrophilic fluorophore with an extremely long fluorescence lifetime (325 ns in H2O and 505 ns in D2O under air). Polypeptides containing both the DBO residue and an efficient fluorescence quencher allow the measurement of rate constants for intramolecular end-to-end contact formation. Bimolecular quenching experiments indicated that Trp, Cys, Met, and Tyr are efficient quenchers of DBO (k(q) = 20, 5.1, 4.5, and 3.6 x 10(8) M(-1) x s(-1) in D2O), while the other amino acids are inefficient. The quenching by Trp, which was selected as an intrinsic quencher, is presumed to involve exciplex-induced deactivation. Flexible, structureless polypeptides, Trp-(Gly-Ser)n-DBO-NH2, were prepared by standard solid-phase synthesis, and the rates of contact formation were measured through the intramolecular fluorescence quenching of DBO by Trp with time-correlated single-photon counting, laser flash photolysis, and steady-state fluorometry. Rate constants of 4.1, 6.8, 4.9, 3.1, 2.0, and 1.1 x 10(7) s(-1) for n = 0, 1, 2, 4, 6, and 10 were obtained. Noteworthy was the relatively slow quenching for the shortest peptide (n = 0). The kinetic data are in agreement with recent transient absorption studies of triplet probes for related peptides, but the rate constants are significantly larger. In contrast to the flexible structureless Gly-Ser polypeptides, the polyproline Trp-Pro4-DBO-NH2 showed insignificant fluorescence quenching, suggesting that a high polypeptide flexibility and the possibility of probe-quencher contact is essential to induce quenching. Advantages of the new fluorescence-based method for measuring contact formation rates in biopolymers include high accuracy, fast time range (100 ps-1 micros), and the possibility to perform measurements in water under air.     

Bordismus verzweigter Überlagerungen von Niedrigdimensionalen Sphären

The concept of bordism between branched coverings is a generalization of the concept of regular homotopy between such maps as given in [3].The main result of this article states that for n=2,3 any two branched coverings of the n-sphere with a finite and equal number of sheets are bordant.

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Diese Arbeit entstand während eines Aufenthaltes des Autors am Sonderforschungsbereich Theoretische Mathematik der Universität Bonn.     

On the matrix monotonicity of generalized inversion

Let A, B be two matrices of the same order. We write A>B(A>?B) iff A? B is a positive (semi-) definite hermitian matrix. In this paper the well-known result if

$\text{A>B>θ, then B}{}^{\mathrm{?1}}\text{>A}{}^{\mathrm{?1}}\text{> θ}$

(cf. Bellman [1, p.59]) is extended to the generalized inverses of certain types of pairs of singular matrices A,B?θ, where θ denotes the zero matrix of appropriate order.     

Messung der Polarisation von Neutronen der9Be(α,n)12C-Reaktion

The angular distribution of the polarization of neutrons from the⁹Be(,n)¹²C reaction leading to the ground state in¹²C has been investigated at -energies of 2.40 and 2.80 MeV. The polarization has been determined by left-right asymmetry measurements of the intensities of neutrons elastically scattered on⁴He nuclei. Values of the analysing power of⁴He have been calculated using the phase shift data of Stammbach and Walter [1]. The degree of polarization observed varies between + 55% and —44%. All results obtained in this experiment are in good agreement with the results of polarization measurements of other authors except the results of Lietz et al. [2].