Realistic Type IIB supersymmetric Minkowski flux vacua

We show that there exist supersymmetric Minkowski vacua on Type IIB toroidal orientifold with general flux compactifications where the RR tadpole cancellation conditions can be relaxed elegantly. Then we present a realistic Pati–Salam like model. At the string scale, the gauge symmetry can be broken down to the Standard Model (SM) gauge symmetry, the gauge coupling unification can be achieved naturally, and all the extra chiral exotic particles can be decoupled so that we have the supersymmetric SMs with/without SM singlet(s) below the string scale. The observed SM fermion masses and mixings can also be obtained. In addition, the unified gauge coupling, the dilaton, the complex structure moduli, the real parts of the Kähler moduli and the sum of the imaginary parts of the Kähler moduli can be determined as functions of the four-dimensional dilaton and fluxes, and can be estimated as well.     

Allocation of Control Points in Stochastic Dynamic-Programming Models

The question of allocation of control points in stochastic dynamic-programming models from different areas is considered. A widely used approach is to choose equal time intervals between successive control points. Conditions under which this choice may cease to be optimal are discussed. Two different approaches to statement and solution of a production-control problem are presented.     

A Mössbauer Spectral Study of the Hull Steel and Rusticles Recovered from the Titanic

The recent recovery of steel from the Titanic has permitted a 295 K conversion electron Mössbauer spectral study of the Titanic hull plate steel oriented with the gamma-ray direction either perpendicular or parallel to the microstructural banding directions. The two spectra reveal virtually identical average orientations of the magnetization close to the plane of the plate. The hyperfine parameters are virtually identical to those of α-iron, a finding which agrees with the chemical analysis which reveals at most 0.21 wt% carbon corresponding to 3 wt% of cementite in pearlite. A 4.2 to 295 K transmission Mössbauer spectral study of the rusticles reveals small particles of geothite undergoing superparamagnetic relaxation with a blocking temperature of ca. 300 K. In addition approximately two percent of the Mössbauer spectral absorption area corresponds to a quadrupole doublet with hyperfine parameters typical of green rust. The identified iron containing components in the rusticles agree with the powder X-ray diffraction results which reveal the predominant presence of small particles of poorly crystallized goethite and traces of quartz and green rust. An average size of 20±5 nm for the goethite particles is obtained from both the average hyperfine field and the broadening of the X-ray diffraction peaks. The magnetic anisotropy constant of the goethite particles deduced from the hyperfine field and the particle size is 8×10³ J/m³.     

Adaptive-mesh radiation hydrodynamics—I. The radiation transport equation in a completely adaptive coordinate system

We formulate the radiation transport equation in a completely adaptive coordinate system, which we define as a system in which the mesh in spacetime, angles and frequency adapts automatically to the dynamical evolution of the radiation field and fluid flow.     

Adaptive-mesh radiation hydrodynamics—II. The radiation and fluid equations in relativistic flows

We derive the radiation and fluid equations for relativistic flows in conservative from in a completely adaptive coordinate system.     

A new algorithm for the assignment problem

We propose a new algorithm for the classical assignment problem. The algorithm resembles in some ways the Hungarian method but differs substantially in other respects. The average computational complexity of an efficient implementation of the algorithm seems to be considerably better than the one of the Hungarian method. In a large number of randomly generated problems the algorithm has consistently outperformed an efficiently coded version of the Hungarian method by a broad margin. The factor of improvement increases with the problem dimensionN and reaches an order of magnitude forN equal to several hundreds.Work supported by Grant NSF ENG-7906332.     

On the Proof of Universality for Orthogonal and Symplectic Ensembles in Random Matrix Theory

We give a streamlined proof of a quantitative version of a result from P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) which is crucial for the proof of universality in the bulk P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) and also at the edge P. Deift and D. Gioev, {Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices. Comm. Pure Appl. Math. (in press) for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the β=1,2,4 partition functions for log gases.     

Infinite Ergodic Walks in Finite Connected Undirected Graphs

The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of infinite walk length. As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navigability to the nodes by the different types of ergodic walks; as well as node’s fugacity in the course of prospective network expansion or shrinking.     

Three Aromatic Residues are Required for Electron Transfer during Iron Mineralization in Bacterioferritin

Ferritins are iron storage proteins that overcome the problems of toxicity and poor bioavailability of iron by catalyzing iron oxidation and mineralization through the activity of a diiron ferroxidase site. Unlike in other ferritins, the oxidized di‐Fe³⁺ site of Escherichia coli bacterioferritin (EcBFR) is stable and therefore does not function as a conduit for the transfer of Fe³⁺ into the storage cavity, but instead acts as a true catalytic cofactor that cycles its oxidation state while driving Fe²⁺ oxidation in the cavity. Herein, we demonstrate that EcBFR mineralization depends on three aromatic residues near the diiron site, Tyr25, Tyr58, and Trp133, and that a transient radical is formed on Tyr25. The data indicate that the aromatic residues, together with a previously identified inner surface iron site, promote mineralization by ensuring the simultaneous delivery of two electrons, derived from Fe²⁺ oxidation in the BFR cavity, to the di‐ferric catalytic site for safe reduction of O₂.