The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Interference and ‘which way’ information

An overview is given of typical examples of interference experiments that confirm the general quantum mechanical rule that distinguishability of the paths destroys interference. It will be shown that path information can be gained in different ways: from the screen's or the atom's recoil in Young-type optical experiments; from the spontaneously emitted photon in atom optics; and from the idler photon, in a striking interference experiment with a photon pair being involved. In all cases, the physical mechanism that actually makes the interference pattern disappear is elucidated.     

Quasi sure analysis and Stratonovich anticipative stochastic differential equations

Summary Consider a stochastic differential equation on ^d with smooth and bounded coefficients. We apply the techniques of the quasi-sure analysis to show that this equation can be solved pathwise out of a slim set. Furthermore, we can restrict the equation to the level sets of a nondegenerate and smooth random variable, and this provides a method to construct the solution to an anticipating stochastic differential equation with smooth and nondegenerate initial condition.     

η5-cyclopentadienyl-η5-syn-1-methylpentadienylrhodium and iridium cations - preparation and reactions with nucleophiles

η⁵-cyclopentadienyl-η⁵-syn-1-methylpentadienyliridium(I) hexafluorophosphate, a novel complex containing an open chain pentadienyl ligand, has been prepared $\text{via}$ protonation of η⁵-cyclopentadienyl-η⁴-hexa-2,4-dien-1-ol iridium. It and the corresponding rhodium salt are attacked by methoxide ion at the central 3-position of the dienyl group to give 1,4-diene complexes. This contrasts with nucleophilic attack on pentadienyltricarbonyliron cations which occurs at the terminal positions of the dienyl group.     

Exact solution (within a double-zeta basis set) of the schrodinger electronic equation for water

Using recently developed theoretical techniques it has been possible to achieve an exact variational solution of the Schrödinger equation within a modest basis set or one-eleltron functions. The full configuration interaction for this system included a total of 256473 ¹A₁ spin-and space-adapted configurations. Comparison with many-body perturbation theory proves to be quite interesting.     

Synthesis, crystal structure, and properties of MnNCN, the first carbodiimide of a magnetic transition metal

Synthesis, single-crystal structure determination, and magnetic properties are reported for manganese carbodiimide, MnNCN. The presumably unstable but inert phase adopts the trigonal system (R3m) with a = 3.3583(4) A, c = 14.347(2) A, V = 140.13(3) A3, and Z = 3. Divalent manganese is octahedrally coordinated by nitrogen atoms at 2.26 A, and the NCN(2-) unit adopts the linear [N=C=N](2-) carbodiimide shape with two C=N double bonds of 1.23 A. MnNCN contains high-spin Mn(II) with five unpaired electrons and behaves like an antiferromagnet with an ordering temperature below 30 K.