High-speed techniques for estimating t1, t2, and density images

This work presents methods for estimating relaxation times T1 and T2 and proton density using a real time digital video processor. This device performs each mathematical step of the fitting algorithms in one video frame interval (1/30 s). Two-point fits of T1 and T2 may be generated in approximately 15 video frame intervals or about 0.5 s; generation of a T2 image from four acquired images requires about 30 video frame intervals or about 1 s. The hardware is common to many commercial MR scanners and requires no array processor. Such high-speed techniques can expedite the clinical use of computed images and facilitate the implementation of image synthesis.     

Qualitative analysis of motion properties of semistate models of large-scale systems

This paper studies the behavior of motions of large-scale (LS) semistate systems (SSS) governed byP _i (t)x _i =M _i (t,x _i )x _i +f _i (t)+h _i (t, x), i=1,2,...,s, =(x ₁ ^T x ₂ ^T x _s ^T )^T, where matricesP _i (t) are singular. Using Lyapunov's approach and the tools for LS system analysis, a variant of attractivity and ultimate boundedness of appropriate time-variable sets are investigated. The results are based on a specific choice of the aggregate functions. It is assumed that the reduction of equations to a normal form of lower order is inconvenient. The aggregation-decomposition approach used in this paper reduces the dimensionality of an aggregate matrix of the system to the number of its systems. Motion properties of LS systems are deduced from the properties of its isolated subsystems, the character of interconnections, and the conditions imposed on the system aggregate matrix. Sufficient algebraic conditions for the above-mentioned motion properties are developed.     

First-order transitions in spherical models: Finite-size scaling

Finite-size behavior near the first-order phase boundary of ferromagnetic spherical models is investigated for block- and cylinder-shaped systems ind dimensions. The bulk thermodynamic singularities are rounded and, asymptotically for large size, obey appropriate scaling laws. Both short-range interactions and long-range couplings, decaying like 1/r^d+ with >0, are analyzed: the short-range results agree precisely with a recently developed scaling theory forO(n) symmetric systems in the limitn. More generally, the scaling functions are universal, depending only on . Explicit aspects of the shape and interactions enter only in the spin wave or Goldstone mode contributions which appear, technically, as corrections to scaling. An appendix analyzes the truncation error in the approximation, by many-fold sums, of multivariate integrals with integrands diverging like [_ja_{j j} ² ]^- as 0.     

Topological properties of the electronic density of CO-MgF2 and OC-MgF2 adducts

By means of Bader's approach on topological properties of the electronic density, the major stability of the O-bonded adduct over the C-bonded one between MgF₂ and CO is reinforced.     

Mechanism of the cyclization of dimethyl diethynyl silane with selenium tetrabromide: Computational and structural studies, and monitoring

The structure of 2,4-dibromo-2-dibromomethyl-3,3-dimethyl-1-selena-3-silacyclopentene-4, formed by regioselective electrophilic addition of SeBr₄ to dimethyl diethynyl silane, has been determined using X-ray analysis technique. Quantum chemistry methods were used to study elementary stages of the reaction. It was found that the first stage consisted of SeBr₄ conversion into bimolecular complex Br₂?SeBr₂, initiated by dimethyl diethynyl silane. Possible formation of five-membered and six-membered heterocycles involves different cyclization mechanisms. The formation of only five-membered heterocycle is explained by kinetically preferable ring closure through four-center transition state. The conclusions obtained by calculations were confirmed by monitoring of the reaction using ¹H NMR method.     

Synthesis and anion binding properties of 2,5-diamidothiophene polypyrrole Schiff base macrocycles

[reaction: see text] Two easy-to-synthesize polypyrrolic 2,5-diamidothiophene Schiff base macrocycles are reported, along with their anion binding properties as determined via UV-vis spectroscopic titrations carried out in dichloroethane. There is a striking difference between the interactions with anions of the two macrocycles, a finding ascribed to differences in their rigidity. For example, the more flexible dipyrromethane-derived macrocycle displays a 1.2:1 hydrogen sulfate versus nitrate selectivity, while its more rigid bipyrrole-derived congener shows a 7.4:1 selectivity in favor to hydrogen sulfate.     

Structure and photochemistry of 18-diazo-1,4,7,10,13,16-hexaoxacyclononadeca-17,19-dione and its sodium and potassium complexes. Control of the ground-state conformation of 2-diazo-1,3-dicarbonyl fragment via host-guest complexation

[reaction: see text] The macrocyclic 18-diazo-1,4,7,10,13,16-hexaoxacyclononadeca-17,19-dione (3-diazo-2,4-dioxo-19-crown-6, 1) readily forms complexes with potassium (2, stability constant in methanol is K(K+) = 229 +/- 25 M(-1)) and sodium ions (3, K(Na+) = 84.2 +/- 7.9 M(-1) in methanol). According to B3LYP/6-31G+(d,p) calculations and temperature-dependent 1H NMR spectroscopy, the predominant conformation of 1 has a Z,Z arrangement of the diazo and carbonyl groups. The X-ray crystal structure analysis showed that the potassium complex (2) has the same Z,Z arrangement, while the sodium analogue (2) exists in conformation with Z,E geometry of the diazodicarbonyl moiety. Direct 254 nm photolysis of diazo compounds 1-3 in methanol results in the formation of 3-methoxy-2,4-dioxo-19-crown-6 (5), the product of the insertion of corresponding alpha,alpha'-dicarbonylcarbene into the O-H bond of the solvent. The triplet-sensitized photolysis of diazomalonates 1-3 produces 2,4-dioxo-19-crown-6 (6), which is apparently formed via the triplet state of the intervening carbene.     

Study of the feasibility of focused microwave-assisted soxhlet extraction of N-methylcarbamates from soil

A fast microwave-assisted dansylation procedure has been developed for the derivatization of N-nitrosamines prior to high-performance liquid chromatography determination. N-Nitrosomorpholine, N-nitrosodimethylamine, N-nitrosodiethylamine, N-nitrosopyrrolidine and N-nitrosopiperidine are first denitrosated by hydrobromic acid-acetic acid to produce secondary amines, which are then quantitatively dansylated in 5 min using radiation power of 378 W and a maximum pressure of 1.4 bar inside the reactor. The reaction mixture is separated on a C18 column with acetonitrile-water (55:45, v/v) as mobile phase with fluorimetric detection at 531 nm (excitation at 339 nm). The detection limits range from 8 to 75 pg for N-nitrosomorpholine and N-nitrosodiethylamine, respectively. The method was applied to study the recoveries of N-nitrosamines in beer and their determination in cigarette smoke.     

A mechanism from quantum chemical studies for methane formation in methanogenesis

The mechanism for methane formation in methyl-coenzyme M reductase (MCR) has been investigated using the B3LYP hybrid density functional method and chemical models consisting of 107 atoms. The experimental X-ray crystal structure of the enzyme in the inactive MCR(ox1)(-)(silent) state was used to set up the initial model structure. The calculations suggest a mechanism not previously proposed, in which the most remarkable feature is the formation of an essentially free methyl radical at the transition state. The reaction cycle suggested starts from a Michaelis complex with CoB and methyl-CoM coenzymes bound and with a squareplanar coordination of the Ni(I) center in the tetrapyrrole F(430) prosthetic group. In the rate-limiting step the methyl radical is released from methyl-CoM, induced by the attack of Ni(I) on the methyl-CoM thioether sulfur. In this step, the metal center is oxidized from Ni(I) to Ni(II). The resulting methyl radical is rapidly quenched by hydrogen-atom transfer from the CoB thiol group, yielding the methane molecule and the CoB radical. The estimated activation energy is around 20 kcal/mol, which includes a significant contribution from entropy due to the formation of the free methyl. The mechanism implies an inversion of configuration at the reactive carbon. The size of the inversion barrier is used to explain the fact that CF(3)-S-CoM is an inactive substrate. Heterodisulfide CoB-S-S-CoM formation is proposed in the final step in which nickel is reduced back to Ni(I). The suggested mechanism agrees well with experimental observations.     

Tris(pentafluorophenyl)silyl enol ethers: synthesis and aldol reactions

Silyl enol ethers bearing three pentafluorophenyl groups at the silicon atom are described. These compounds undergo uncatalyzed aldol reactions with aliphatic, α,β-unsaturated, and aromatic aldehydes. The observed reactivity is analyzed in terms of the Lewis acidity of the silyl fragment.