Invariant metrics

Mathematische Annalen -     

Non-uniformity correction of human brain imaging at high field by RF field mapping of B1+ and B1-

A new method of non-uniform image correction is proposed. Image non-uniformity is originated from the spatial distribution of RF transmission and reception fields, represented as B(1)(+) and B(1)(-), respectively. In our method, B(1)(+) mapping was performed invivo by a phase method. In B(1)(-) mapping, images with multiple TEs were acquired with a multi-echo adiabatic spin echo (MASE) sequence which enables homogeneous excitation. By T(2) fitting of these images an M(0) map (M(0)(MASE)) was obtained, in which signal intensity was expressed as the product of B(1)(-) and M?(1-e?(TR/T1)) . The ratio of this M(0)(MASE) map to the B(1)(+) map showed a similar spatial pattern in different human brains. These ratios of M(0)(MASE) to B(1)(+) in 24 subjects were averaged and then fitted with a spatially polynomial function to obtain a ratio map of B(1)(-)/B(1)(+)(α). Uniform image was achieved in spin echo (SE), MASE and inversion recovery turboFLASH (IRTF) images using measured B(1)(+) and calculated B(1)(-) by αB(1)(+). Water fractions in gray and white matters obtained from the M(0) images corrected by this method were in good agreement with previously reported values. From these experimental results, the proposed method of non-uniformity correction is validated at 4.7 T imaging.     

Surface Tension of Multi-phase Flow with Multiple Junctions Governed by the Variational Principle

We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie et al. (J Comput Phys 113:134–147, 1994) as a variational problem related to an infinite dimensional Lie group, the volume-preserving diffeomorphism. The variational principle to the action integral with the surface energy reproduces their Euler equation of the two-phase field with the surface tension. Since the surface energy of multiple interfaces even with singularities is not difficult to be evaluated in general and the variational formulation works for every action integral, the new formulation enables us to extend their expression to that of a multi-phase (N-phase, N\geqslant2N\geqslant2) flow and to obtain a novel Euler equation with the surface tension of the multi-phase field. The obtained Euler equation governs the equation for motion of the multi-phase field with different surface tension coefficients without any difficulties for the singularities at multiple junctions. In other words, we unify the theory of multi-phase fields which express low dimensional interface geometry and the theory of the incompressible fluid dynamics on the infinite dimensional geometry as a variational problem. We apply the equation to the contact angle problems at triple junctions. We computed the fluid dynamics for a two-phase field with a wall numerically and show the numerical computational results that for given surface tension coefficients, the contact angles are generated by the surface tension as results of balances of the kinematic energy and the surface energy.     

Asymmetric synthesis of isoquinuclidines by Diels–Alder reaction of 1,2-dihydropyridine utilizing a chiral Lewis acid catalyst

The chiral isoquinuclidine derivative, 2-azabicyclo[2.2.2]octane ring system, endo-(7R)-3 was obtained in good yield with excellent diastereoselectivity (up to 92% de) by Diels–Alder reaction of 1-(phenoxycarbonyl)-1,2-dihydropyridine 1 with N-acryloyl-(4S)-4-benzyloxazolidin-2-one (4S)-2 using titanium-(2R,3R)-TADDOLate 4 as a chiral Lewis acid catalyst in toluene at 0 °C. On the other hand, endo-(7S)-3 was obtained in good yield with excellent diastereoselectivity (up to 97% de) by Diels–Alder reaction of 1 with (4R)-2 using Cu(OTf)₂/(4S,4′S)-bis(oxazoline) catalyst 8 as a chiral Lewis acid catalyst in dichloromethane at 0 °C. In these reactions, the choice of solvent and the combination of titanium-(2R,3R)-TADDOLate 4 {or Cu(II)/(4S,4′S)-bis(oxazoline) 8} and dienophile (4S)-2 {or (4R)-2} are very important. The stereochemistry of endo-(7R)-3 has been established to be (1R,4S,7R) and the reaction mechanism is proposed.     

Nickel(II) and Copper(II) Complexes of β‐Unsubstituted 5,15‐Diazaporphyrins and Pyridazine‐Fused Diazacorrinoids: Metal–Template Syntheses and Peripheral Functionalizations

The present paper reports the first comprehensive study on the synthesis, structures, optical and electrochemical properties, and peripheral functionalizations of nickel(II) and copper(II) complexes of β‐unsubstituted 5,15‐diazaporphyrins (M‐DAP; M=Ni, Cu) and pyridazine‐fused diazacorrinoids (Ni‐DACX; X=N, O). These two classes of compounds were constructed starting from mesityldipyrromethane by a metal–template method. Ni‐DAP and Cu‐DAP were prepared in high yields by the reaction of the respective metal–bis(dibromodipyrrin) complexes with NaN₃–CuX (X=I, Br), whereas Ni‐DACN and Ni‐DACO were formed as predominant products by the reaction with NaN₃. In both cases, the metal centers change their geometry from tetrahedral to square planar during the aza‐annulation; X‐ray crystallographic analyses of M‐DAPs showed highly planar diazaporphyrin π planes. The Q band of Ni‐DAP was redshifted and intensified compared with that of a nickel–porphyrin reference, due to the involvement of electronegative nitrogen atoms at the meso positions. It was found that the peripheral bromination of Ni‐DAP and Ni‐DACO occurred regioselectively to afford Ni‐DAP‐Br₄ and Ni‐DACO‐Br, respectively. These brominated derivatives underwent Stille reactions with tributyl(phenyl)stannane to give the corresponding phenylated derivatives, Ni‐DAP‐Ph₄ and Ni‐DACO‐Ph. On the basis of the absorption spectra and X‐ray analysis, it has been concluded that the attached phenyl groups efficiently conjugate with the diazaporphyrin π system. The present results unambiguously corroborate that the β‐unsubstituted DAPs and DACXs are promising platforms for the development of a new class of π‐conjugated azaporphyrin‐based materials.     

Aminohydroxyacetone synthons: versatile intermediates for the organocatalytic asymmetric aldol reaction

A practical method for the synthesis of 1,3-aminohydroxyacetone synthons was developed, and their utility in the organocatalytic asymmetric aldol reaction was demonstrated in a short synthesis of aza-sugars.     

Numerical analysis of the velocity of SiC growth by the top seeding method

Velocity of crystal growth of SiC in a process of solution growth was studied on the basis of a global model of heat and mass transfer in conjunction with a phase diagram of the Si–C system. The growth rate was estimated by flux of carbon to a seed crystal. The results of calculation showed that growth velocity was increased when temperature of a seed crystal was increased. The temperature dependence of growth velocity was mainly determined by the phase diagram of the Si–C system, although the flow pattern was slightly modified by changing temperature distribution in the furnace.     

Crystal structure and phase transition of single crystalline CsNH2SO3

Differential scanning calorimetry (DSC) and X‐ray diffraction measurements have been performed on cesium sulfamate CsNH₂SO₃ single crystal. Two distinct endothermic peaks in the DSC curves are observed at 330 and 436 K. It is pointed out that the peak at 330 K is attributed to the structural phase transition, and the other peak at 436 K is associated with the thermal decomposition of the crystal. The structures in room‐ and high‐temperasture phases are determined, and the space group of the sample crystal is found to change from monoclinic P 2₁/c to orthorhombic Pnma. The structure of the room‐temperature phase consists of two different types of N‐H···O hydrogen bond, but in the high‐temperature phase there is no specific hydrogen bond between the NSO₃ pseudo‐tetrahera. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On circulant thin Lehman matrices

The class of Lehman matrices is a key structure of characterization of minimally non-ideal clutters. The notion of \(1\) -overlapped factorizations of cyclic groups produces an infinite family of circulant thin Lehman matrices. In this paper, we prove essential properties of the \(1\) -overlapped factorizations of cyclic groups and completely determine the shapes of circulant thin Lehman matrices with small constant line sum, which solves the ideal counterpart of the so-called Grinstead’s conjecture for the circulant partitionable graphs in this case.