On semiprojectivity of -algebras of directed graphs

It is shown that if is a countable, transitive directed graph with finitely many vertices, then is semiprojective.

     

Quantum Spheres and Projective Spaces as Graph Algebras

 The C ^* -algebras of continuous functions on quantum spheres, quantum real projective spaces, and quantum complex projective spaces are realized as Cuntz-Krieger algebras corresponding to suitable directed graphs. Structural results about these quantum spaces, especially about their ideals and K-theory, are then derived from the general theory of graph algebras. It is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle, respectively. Received: 31 January 2001 / Accepted: 29 July 2002 Published online: 7 November 2002 RID="*" ID="*" Supported by grant No. R04–2001–000–00117–0 from the Korea Science & Engineering Foundation. RID="**" ID="**" Partially supported by the Research Management Committee of the University of Newcastle.     

Retention of configuration in the action of human plasma 3'-exonuclease on oligo(deoxynucleoside phosphorothioate). A new method for assignment of absolute configuration at phosphorus in isotopomeric deoxyadenosine 5'-O-[(18)O]phosphorothioate

A new method of analysis has allowed the exonucleolytic cleavage by human 3'-exonuclease to be determined. Hydrolysis by human plasma 3'-exonuclease proceeds with retention of configuration at phosphorus. The new method determines the sense of chirality at phosphorus in isotopomeric adenosine 5'-O-[(18)O]phosphorothioates. This is based on stereospecific two-step conversion of the mono-thionucleotide into the corresponding deoxyadenosine 5'-O-alpha-[(18)O]thiotriphosphate, followed by the use of terminal deoxyribonucleotidyl transferase and MALDI TOF mass spectrometry of the resulting elongated primer. Retention of configuration in the reaction of plasma 3'-exonuclease implies a two-step mechanism with two displacements on phosphorus. Inversion at each step leads to overall retention.     

6,7‐diaza‐1‐methoxy‐ 5‐methyl‐2, 8‐dioxabicyclo[3.2.1]oct‐6‐ene. An unstable bicyclic precursor of a dioxa carbonyl ylide and carbenes by ylide ring opening

Synthesis of a bicyclic 2,2‐dioxa oxadiazoline (6,7‐diaza‐1‐methoxy‐5‐methyl‐2,8‐dioxabicyclo[3.2.1]oct‐6‐ene) is reported. Its thermolysis at 27°C is about 200 times as fast as the thermolysis of a monocyclic oxadiazoline model system. Presumably, a cyclic dioxa carbonyl ylide is formed initially and the ylide then undergoes a bond scission to afford either a dioxacarbene or a dialkylcarbene or it cyclizes to an oxirane. A small fraction of a dialkylcarbene was trapped as the product of addition to dimethyl acetylenedicarboxylate (DMAD). Computations of the barriers to the loss of N₂ from the oxadiazolines and to the formation of the carbenes from the carbonyl ylide resulting from thermolysis of the bicyclic oxadiazoline are compared to corresponding barriers for a similar monocyclic oxadiazoline. The rate acceleration is accounted for in terms of geometric factors. The complex products from the decomposition of the bicyclic oxadiazoline were not studied. Copyright © 2007 John Wiley & Sons, Ltd.     

Bestimmung von Mikromengen Schwefel nach Aufspaltung des S8-Ringes in Indium-, Blei-, Antimonund Wismutsulfiden mit Hilfe einer induzierten Reaktion von Natriumazid mit Jod

Zusammenfassung Die Bestimmungsmethode für Mikromengen elementaren, in Sulfiden enthaltenen Schwefels mit Natriumazid und Jod wurde modifiziert. Der Analyse geht die Aufspaltung des S₈-Ringes voraus, die man dank der nukleophilen Wirkung von N₃ ^– in DMF-Lösung erreicht. Diese Methode wurde auf die Bestimmung des Schwefels in Indium-, Blei-, Antimon- und Wismutsulfid angewandt. Sie ist einfach und empfindlich. Ihre Fehlergrenze liegt bei ± 4%.

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Determination of microamounts of sulfur after cleavage of the S₈ king in indium, lead, antimony and bismuth sulfides by means of an induced reaction of sodium azide with iodine

Summary The determination of microamounts of elemental sulfur contained in sulfides using sodium azide and iodine was modified. The analysis was preceded by cleavage of the S₈ ring, which is achieved by virtue of the nucleophilic action of N₃ ^– in DMF solution. This method was applied to the determination of sulfur in indium, lead, antimony and bismuth sulfides. It is simple and sensitive. Its limit of error is ±4%.

     

Dynamics of a quantum phase transition

We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.     

Tower techniques for cosimplicial resolutions

Let be a simplicial model category and J : a simplicial coaugmented functor. Given an object X, the assignment nJⁿ⁺¹X defines a cofacial resolution (an augmented cosimplicial space without its codegeneracy maps). Following Bousfield and Kan we define J^sX = tot^s([n] Jⁿ⁺¹X). An object X is called J-injective if it is a retract of JX in Ho() via the natural map. We show that certain homotopy limits of J-injective objects are J_s-injective. Our method is to use the notion of pro-weak equivalences which was first introduced in a different language and context by David Edwards and Harold Hastings. The key observation is that a cofacial resolution X (-1) X which admits a left contraction gives rise to a pro-weak equivalence of towers {X(-1)}_s0{tot^SX}_{s 0}.The first author was supported in part by National Science Foundation grant DMS-0296117