Structure and ion exchange properties of a new cobalt borate with a tunnel structure "templated" by Na+

The new anhydrous borate Na2Co2B12O21 has been synthesized by flux methods and studied by single-crystal X-ray diffraction (space group I2/a with a = 17.1447(15) A, b = 4.5530(5) A, c = 19.4408(15) A, beta = 103.212(5) degrees , V = 1477.4(2) A3, Z = 4). Refinement of its structure reveals it is the first metaborate exhibiting a tunnel network, with internal dimensions of 4.5 x 8.8 A2. Further single-crystal diffraction studies show that the Na+ ions within the tunnels are exchangeable with Li+ along with the absorption of water molecules to form Li2(H2O)2Co2B12O21, making this compound a unique non-siliceous zeotype.     

Ground state of magnetic dimers on metal surfaces

We present model studies of the ground state for magnetic dimers on metal surfaces. We find it can be neither ferromagnetic nor antiferromagnetic, but is often canted for nearest neighbors. Thus, the system cannot be described using bilinear exchange. We give a criterion which can be used quite generally to interrogate the local stability of ferromagnetically or antiferromagnetically aligned dimers, and which also may be used to infer the canting angle when canted states are stable.     

Low temperature solid-state NMR experiments of half-integer quadrupolar nuclides: caveats and data analysis

Solid-state NMR spectroscopy of half-integer quadrupolar nuclides has received a lot of interest recently with the advent of new methodologies and higher magnetic fields. We present here the extension of our previous low temperature method to an 18.8T system. This new probe entailed a total redesign including a cross coil and variable capacitors that are operational at cryogenic temperatures. The limitations to sensitivity are also discussed; including a new diode network, the utilization of a cryogenic band pass filter, and the consequences of the RF profiles of the coil. Further, details of the spectroscopy of quadrupolar nuclei in a protein are discussed, such as the observation of the outer transitions and how to distinguish them from the desired +/-1/2 transition.     

An alternate proof of Cohn's four squares theorem

While various techniques have been used to demonstrate the classical four squares theorem for the rational integers, the method of modular forms of two variables has been the standard way of dealing with sums of squares problems for integers in quadratic fields. The case of representations by sums of four squares in was resolved by Götzky, while those of and were resolved by Cohn. These efforts utilized modular forms. In previous work, the author was able to demonstrate Götzky's theorem by means of the geometry of numbers. Here Cohn's theorem on representation by the sum of four squares for is proven by a combination of geometry of numbers and quaternionic techniques.     

Do spherical polyelectrolyte brushes interdigitate?

The structure of spherical micelles of the diblock copolymer poly(styrene-block-acrylic acid) in water was investigated with small angle neutron scattering and contrast matching. We have monitored intermicelle correlation and the extension of the polyelectrolyte chains in the coronal layer through the overlap concentration. Irrespective of ionic strength, the corona shrinks with increasing packing fraction. Furthermore, at high charge and minimal screening conditions, the corona layers interpenetrate once the volume fraction exceeds the critical value 0.53+/-0.02.     

Synthesis of certain 5-substituted thieno[2,3-b]thiophene-2-sulfonamides and thieno[2,3-b]thiophene-2-sulfonamide 6,6-dioxides

A series of the title compounds were prepared for evaluation as inhibitors of carbonic anhydrase II. Oxidation of 5-substituted thieno[2,3-b]thiophene-2-sulfonamides provided the first examples of thiophene[2,3-b]thiophene-2-sulfonarnide 6,6-dioxides. These cyclic vinyl sulfones readily underwent addi tion to give predominately that 4,5-cis addition product.     

Short proofs of the universality of certain diagonal quadratic forms

In a paper of Kim, Chan, and Rhagavan, the universal ternary classical quadratic forms over quadratic fields of positive discriminant were discovered. Here a proof of the universality of some of these quadratic forms is given using a technique of Liouville. Another quadratic form over the field of discriminant 8 is shown universal by a different elementary approach. Received: 30 October 2007     

The remarkable ability of lithium ion to reverse the stereoselectivity in the conjugate addition of Li[BuCuI] to a chiral N-crotonyl-2-oxazolidinone

[reaction: see text] The influence of lithium ions on the conjugate addition of the monoorganocuprate reagent, Li[BuCuI], to a chiral crotonate has been investigated. The results show that iodotrimethylsilane (TMSI) is crucial for the asymmetric conjugate addition of the copper reagent, but only in THF or when 12-crown-4 is used. The reaction is thought not to involve any halosilane in any critical steps in the organocopper mechanisms conducted in Et(2)O.