Optimal mortgage loan securitization and the subprime crisis

We analyze the process of mortgage loan securitization that has been a root cause of the current subprime mortgage crisis (SMC). In particular, we solve an optimal securitization problem for banks that has the cash outflow rate for financing a portfolio of mortgage-backed securities (MBSs) and the bank’s investment in MBSs as controls. In our case, the associated Hamilton–Jacobi–Bellman equation (HJBE) has a smooth solution when the optimal controls are computed via a power utility function. Finally, we analyze this optimization problem and its connections with the SMC.     

Iron pentacarbonyl as a precursor for molecule-based magnets: formation of Fe[TCNE](2) (T(c) = 100 K) and Fe[TCNQ](2) (T(c) = 35 K) magnets

The reaction of tetracyanoethylene (TCNE) and 7,7,8,8-tetracyano-p-quinodimethane (TCNQ) with Fe(CO)(5) leads to formation of magnetically ordered materials of Fe[TCNE](2) (T(c) = 100 K) and Fe[TCNQ](2) (T(c) = 35 K) composition, respectively. In contrast, the reaction with 1,2-dichloro-5,6-dicyanobenzoquinone (DDQ) leads to a paramagnetic material.     

A multigrid method with unstructured adaptive grids for steady Euler equations

The multigrid method based on multi-stage Jacobi relaxation, earlier developed by the authors for structured grid calculations with Euler equations, is extended to unstructured grid applications. The meshes are generated with Delaunay triangulation algorithms and are adapted to the flow solution.     

Relationship between the properties of radical cations and the rate constants and the substitution patterns in electrophilic aromatic substitution

By a charge transfer mechanism for electrophilic aromatic substitution the logarithmic plot of overall rate constants for substitution against ionization potentials is correctly predicted. Also, orientation of substitution is found to be correlated with the hyperfine coupling constants of the aromatic radical cation. The presence of radical cations under the conditions of electrophilic substitution is discussed.     

Multijet structure in quantum chromodynamics

Field theories naturally give rise to multiple jets of hadrons in short-distance processes, such as e⁺ e^? annihilation. In particular, a low-energy jet of hadrons distributed in some cone of opening angle δ would be naively expected to evolve at high energies into multiple jets within the angle δ. We explore to what extent this will happen in quantum chromodynamics.     

Receiving beam patterns in the horizontal plane of a harbor porpoise (Phocoena phocoena)

Receiving beam patterns of a harbor porpoise were measured in the horizontal plane, using narrow-band frequency modulated signals with center frequencies of 16, 64, and 100 kHz. Total signal duration was 1000 ms, including a 200 ms rise time and 300 ms fall time. The harbor porpoise was trained to participate in a psychophysical test and stationed itself horizontally in a specific direction in the center of a 16-m-diameter circle consisting of 16 equally-spaced underwater transducers. The animal's head and the transducers were in the same horizontal plane, 1.5 m below the water surface. The go/no-go response paradigm was used; the animal left the listening station when it heard a sound signal. The method of constants was applied. For each transducer the 50% detection threshold amplitude was determined in 16 trials per amplitude, for each of the three frequencies. The beam patterns were not symmetrical with respect to the midline of the animal's body, but had a deflection of 3-7 degrees to the right. The receiving beam pattern narrowed with increasing frequency. Assuming that the pattern is rotation-symmetrical according to an average of the horizontal beam pattern halves, the receiving directivity indices are 4.3 at 16 kHz, 6.0 at 64 kHz, and 11.7 dB at 100 kHz. The receiving directivity indices of the porpoise were lower than those measured for bottlenose dolphins. This means that harbor porpoises have wider receiving beam patterns than bottlenose dolphins for the same frequencies. Directivity of hearing improves the signal-to-noise ratio and thus is a tool for a better detection of certain signals in a given ambient noise condition.     

Measurements of motionally averaged heteronuclear dipolar couplings in MAS NMR using R-type recoupling

A novel MAS NMR approach is presented for the determination of heteronuclear dipolar couplings in unoriented materials. The technique is based on the proton-detected local field (PDLF) protocol, and achieves dipolar recoupling by R-type radio-frequency irradiation. The experiment, which is called R-PDLF spectroscopy, is demonstrated on solid and liquid-crystalline systems. For mobile systems, it is shown that the R-PDLF scheme provides better dipolar resolution as compared to techniques combining conventional separated local field (SLF) spectroscopy with R-type recoupling.