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.     

Determination of T1-spin-lattice relaxation time in a two-level system by continuous wave multiquantum electron paramagnetic resonance spectroscopy in a presence of tetrachromatic microwave irradiation

Applicability of continuous wave multiquantum EPR methods to study relaxation times at X-band is examined. Multiquantum transitions excited in a two-level system by tetrachromatic irradiation are used for these studies. The Bloch equation model is applied to simulate lineshapes of the three quantum transitions as a function of frequency difference between exciting fields. The dependence of multiquantum transition signals on relaxation times and microwave amplitude is shown. On this basis a method of deducing relaxation times from these signals is formulated. The case of a homogeneously and inhomogeneously broadened resonance line is considered. Two experimental methods are used to verify the proposed hypothesis: the X-band continuous wave multiquantum EPR with four frequencies microwave field and saturation recovery EPR. The values of T₁ obtained from CW MQ EPR and SR EPR are compared.     

On Cyclotomic Numbers and the Reduction Map for the K-Theory of the Integers

We apply the recently proven compatibility of Beilinson and Soulé elements in K-theory to investigate density of rational primes p, for which the reduction map K _2n+1() K_{2n+1}(F_p)is nontrivial. Here n is an even, positive integer and F_p denotes the field of p elements. In the proof we use arithmetic of cyclotomic numbers which come from Soulé elements. Divisibility properties of the numbers are related to the Vandiver conjecture on the class group of cyclotomic fields. Using the K-theory of the integers, we compute an upper bound on the divisibility of these cyclotomic numbers.     

Type factors generated by purely infinite simple C*-algebras associated with free groups

Let be a free product of at least two but at most countably many cyclic groups. With each such group we associate a family of C*-algebras, denoted and generated by the reduced group C*-algebra and a collection of projections onto the -spaces over certain subsets of . We determine , the weak closure of in , and use this result to show that many of the C*-algebras in question are non-nuclear.

     

Two-dimensional imaging of two types of radicals by the CW-EPR method

New EPR resonators were developed by using a ceramic material with a high dielectric constant, epsilon=160. The resonators have a high quality factor, Q=10(3), and enhance the sensitivity of an EPR spectrometer up to 170 times. Some advantages of the new ceramic resonators are: (1) cheaper synthesis and simplified fabricating technology; (2) wider temperature range; and (3) ease of use. The ceramic material is produced with a titanate of complex oxides of rare-earth and alkaline metals, and has a perovskite type structure. The resonators were tested with X-band EPR spectrometers with cylindrical (TE(011)) and rectangular (TE(102)) cavities at 300 and 77K. We discovered that EPR signal strength enhancement depends on the dielectric constant of the material, resonator geometry and the size of the sample. Also, an unusual resonant mode was found in the dielectric resonator-metallic cavity structure. In this mode, the directions of microwave magnetic fields of the coupled resonators are opposite and the resonant frequency of the structure is higher than the frequency of empty metallic cavity.     

The investigation of femoroacetabular impingement using motion capture,FEM and multi-body simulations

In recent years, femoroacetabular impingement (FAI) has become increasingly common. As published in the literature, FAI is caused by an unphysiological contact between the proximal femur and the acetabular rim, which may lead to pain, limitation of movement, and damage of cartilage. In this paper, patient-specific finite element simulations of the movement of the hip based on gait motion data and MRI segmentation were conducted to check stresses of the acetabulum and femur, and additionally whether a bony contact is present or not. The study's findings show no bony contact between femur and acetabulum, which may lead to the hypothesis that the labrum and its deformation and/or the articular capsule are involved in the mechanism of FAI. In order to verify this hypothesis more simulations including labrum and capsule must be performed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)