Abstract:
Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory, quantum spin chain models, and strongly correlated electron systems like the Hubbard model. We introduce, in a unifying fashion, a hierachy of infinite-dimensional Lie superalgebras of quantum matrix models. One of these superalgebras pertains to the open string sector and another one the closed string sector. Physical observables of quantum matrix models like the Hamiltonian can be expressed as elements of these Lie superalgebras. This indicates the Lie superalgebras describe the symmetry of quantum matrix models. We present the structure of these Lie superalgebras like their Cartan subalgebras, root vectors, ideals and subalgebras. They are generalizations of well-known algebras like the Cuntz algebra, the Virasoro algebra, the Toeplitz algebra, the Witt algebra and the Onsager algebra. Just like we learnt a lot about critical phenomena and string theory through their conformal symmetry described by the Virasoro algebra, we may learn a lot about quantum chromodynamics, quantum gravity and condensed matter physics through this symmetry of quantum matrix models described by these Lie superalgebras.

Abstract:
We study phase coherent transport in a single channel system using the scattering matrix approach. It is shown that identical vanishing of the transmission amplitude occurs generically in quasi-1D systems if the time-reversal is a good symmetry. The transmission zeros naturally lead to abrupt phase changes (without any intrinsic energy scale) and in-phase resonances, providing insights to recent experiments on phase coherent transport through a quantum dot.

Abstract:
Inspired by the intimate relationship between Voiculescu's noncommutative probability theory (of type A) and large-N matrix models in physics, we look for physical models related to noncommutative probability theory of type B. These turn out to be fermionic matrix-vector models at the double large-N limit. In the context of string theory, they describe different orbifolded string worldsheets with boundaries. Their critical exponents coincide with that of ordinary string worldsheets, but their renormalised tree-level one-boundary amplitudes differ.

Abstract:
Angular momentum loss via the emission of gravitational waves must eventually drive compact binaries containing black holes and/or neutron stars to coalesce. The resulting events are primary candidate sources for detectors such as VIRGO and LIGO. We present calculations of gravitational radiation waveforms and luminosities for the coalescence of a black hole-neutron star binary, performed in the quadrupole approximation using a Newtonian smooth particle hydrodynamics code. We discuss the dependence of the waveforms and the total emitted luminosity as well as the final configuration of the system on the initial mass ratio and the degree of tidal locking.

Abstract:
We present the results of hydrodynamic (SPH) simulations showing the coalescence of a black hole with a neutron star to be a promising theoretical source of short duration gamma-ray bursts. The favorable features of the process include rapid onset, millisecond variability, a duration much longer than the dynamical timescale, and a range of outcomes sufficient to allow variety in the properties of individual gamma-ray bursts. Interestingly, the process of coalescence differs rather markedly from past predictions.

Abstract:
We present the results of Newtonian hydrodynamic simulations of the coalescence of a binary consisting of a black hole with a neutron star. The calculations show that for a wide range of initial conditions the core of the neutron star survives the initial mass transfer episode. We therefore identify black hole-neutron star binaries as the astrophysical production site of low mass neutron stars unstable to explosion. The relevance of the simulations to the theory of gamma-ray bursts is also discussed.

Abstract:
This paper proposes a cost reduction distribution policy for an integrated manufacturing system operating under quality assurance practice. We reexamine the problem studied by Chiu et al. [Numerical method for determination of the optimal lot size for a manufacturing system with discontinuous issuing policy and rework. International Journal for Numerical Methods in Biomedical Engineering, doi:10.1002/cnm.1369] and improve its replenishment lot-size solution in terms of lowering producer’s stock holding cost. Mathematical modeling and analysis is employed in this study and optimal replenishment lot size is derived. A numerical example is provided to show the practical usage of research result as well as to demonstrate significant savings in producer’s holding cost as compared to that in Chiu et al.

Abstract:
We derive the generalization of Wigner's causality bounds and Bethe's integral formula for the effective range parameter to arbitrary dimension and arbitrary angular momentum. We also discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy scattering. Some of our results were summarized earlier in a letter publication. In this work, we present full derivations and several detailed examples.

Abstract:
We generalize Wigner's causality bounds and Bethe's integral formula for the effective range to arbitrary dimension and arbitrary angular momentum. Moreover, we discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy quantum scattering.