Triangular bases of integral closures

In this work, we consider the problem of computing triangular bases of integral closures of one-dimensional local rings. Let $(K, v)$ be a discrete valued field with valuation ring $\mathcal{O}$ and let $\mathfrak{m}$ be the maximal ideal. We take $f \in \mathcal{O}[x]$, a monic irreducible polynomial of degree $n$ and consider the extension $L = K[x]/(f(x))$ as well as $\mathcal{O}_{L}$ the integral closure of $\mathcal{O}$ in $L$, which we suppose to be finitely generated as an $\mathcal{O}$-module. The algorithm $\operatorname{MaxMin}$, presented in this paper, computes triangular bases of fractional ideals of $\mathcal{O}_{L}$. The theoretical complexity is equivalent to current state of the art methods and in practice is almost always faster. It is also considerably faster than the routines found in standard computer algebra systems, excepting some cases involving very small field extensions

Spectral Analysis Program (SAP)

Program eliminates or reduces time-consuming aspects of computation of power spectrum for high-frequency communication system. This program was written in FORTRAN IV for UNIVAC 1230 or 1108 computer

Optimality of programmable quantum measurements

We prove that for a programmable measurement device that approximates every POVM with an error $\le \delta$, the dimension of the program space has to grow at least polynomially with $\frac{1}{\delta}$. In the case of qubits we can improve the general result by showing a linear growth. This proves the optimality of the programmable measurement devices recently designed in [G. M. D'Ariano and P. Perinotti, Phys. Rev. Lett. \textbf{94}, 090401 (2005)]

Prioritizing Interdictions on a Shortest Path Network

We consider a variant to the shortest path network interdiction problem with symmetric information from Israeli and Wood (Networks 40, 97-111,2002) which arises in the context of nuclear smuggling prevention. In the basic shortest path interdiction problem, an interdictor has a limited number of interdictions with which he can lengthen arcs in a network in order to maximize the length of the network’s shortest path. This thesis considers the case in which the interdictor does not make all of the interdictions at once. Rather, the interdictor must make the interdictions over a set number of periods. Each period has a budget for the number of interdictions that can be placed during the period. The interdictor must prioritize the interdictions and decide the order in which the interdictions should take place. This problem is formulated as an integer program with an objective to maximize the average of the shortest paths across all periods

Random subspaces for encryption based on a private shared Cartesian frame

A private shared Cartesian frame is a novel form of private shared correlation that allows for both private classical and quantum communication. Cryptography using a private shared Cartesian frame has the remarkable property that asymptotically, if perfect privacy is demanded, the private classical capacity is three times the private quantum capacity. We demonstrate that if the requirement for perfect privacy is relaxed, then it is possible to use the properties of random subspaces to nearly triple the private quantum capacity, almost closing the gap between the private classical and quantum capacities.Comment: 9 pages, published versio

Modeling and Analysis of Power Processing Systems

The feasibility of formulating a methodology for the modeling and analysis of aerospace electrical power processing systems is investigated. It is shown that a digital computer may be used in an interactive mode for the design, modeling, analysis, and comparison of power processing systems

Information Flow in Entangled Quantum Systems

All information in quantum systems is, notwithstanding Bell's theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is transmitted through 'classical' (i.e. decoherent) information channels.Comment: PostScript version now available: http://www.qubit.org/people/patrickh/Papers/InformationFlow.p

Entropy and Entanglement in Quantum Ground States

We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the entropy is exponentially large in the correlation length, and we present strong evidence supporting a conjecture that there exist such systems with arbitrarily large entropy. However, we then show that, under an assumption on the density of states which is believed to be satisfied by many physical systems such as the fractional quantum Hall effect, that an efficient matrix product state representation of the ground state exists in any dimension. Finally, we comment on the implications for numerical simulation.Comment: 7 pages, no figure

FLUID STRUCTURE INTERACTION OF UNDULATING FLUID FLOW IN FLEXIBLE TUBING WITH PARTIAL CONSTRICTIONS

Around the world, there are many different physical systems that utilize cyclic flows. Cyclic flows operate in many fields of study ranging from human health applications to mechanical systems. Many of these physical systems are prone to blockages forming, which alter the fluid flow volume and apply increased cyclic hoop stresses, leading to increased material fatigue and premature failure. This study investigates the fluid structure interaction of constricted undulating fluid flow through flexible tubing by observing the Von Mises stress alterations of the flexible tube structure and the fluid volume profiles within the tube. Utilizing a programmable solenoid activation system, physical testing was performed and compared to numerical simulations to test validity. These numerical simulations were then extrapolated to further cyclic fluid flow scenarios. These scenarios include increasing constriction size within the tube and altering the frequency of flow rate differential. With the recorded data, further trends within the data are developed to understand both the structural and fluid effects in differing constricted cyclic fluid flow framework including maritime 2190 TEP diesel oil flow through mechanical piston pumps and hemodynamic studies to predict atherosclerosis severity in the human aorta.Distribution Statement A. Approved for public release: Distribution is unlimited.Outstanding ThesisEnsign, United States Nav