The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms

Numerical methods for problems involving the Drazin inverse

The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success

Impacts of Urbanization on Base Flow and Recharge Rates, Northeastern Illinois: Summary of Year 1 Activities

During year one of a two-year project to investigate the impacts of urbanization on base flow and ground-water recharge rates in northeastern Illinois, three gaged watersheds in urbanized areas of northeastern Illinois, and one watershed located in rural northwestern Illinois, have been selected for study. The gages have a common period of record extending from October 1952 through the present, a period during which the northeastern Illinois watersheds underwent substantial urbanization. Mean daily discharge data from the gages have been analyzed using an automated hydrograph separation technique, and monthly estimates of mean total discharge, base flow, and direct runoff have been calculated. Spearman rank correlation coefficients indicate a stronger correlation between precipitation and total discharge, base flow, and direct runoff in the northeastern Illinois watersheds than in the rural watershed. Smoothed time-series plots of total discharge, base flow, and direct runoff in the urban watersheds are less consistent with precipitation than similar plots constructed from the rural watershed data. The trends indicate that rates of direct runoff have overtaken rates of base flow in two of the three northeastern Illinois watersheds, but in one of these watersheds, this relationship probably reflects the cessation of effluent discharges to the stream. In general, double-mass curve analysis suggests that, relative to the rural watershed, base flow in the urban watersheds has proportionally decreased, and direct runoff has proportionally increased. The trends suggested by the smoothed time-series plots and the double-mass curves are consistent with a conceptual model of the northeastern Illinois watersheds in which sewering and impervious surfaces have reduced infiltration, and thence ground-water recharge and base flow, in the watersheds.Ope

TOPEX satellite concept. TOPEX option study report

Candidate bus equipment from the Viking, Applications Explorer Mission, and Small Scientific Satellite programs for application to the TOPEX mission options is assessed. Propulsion module equipment and subsystem candidates from the Applications Explorer Mission satellites and the Small Scientific Satellite spacecraft are evaluated for those TOPEX options. Several subsystem concepts appropriate to the TOPEX options are described. These descriptions consider performance characteristics of the subsystems. Cost and availability information on the candidate equipment and subsystems are also provided

Localization of Two-Dimensional Quantum Walks

The Grover walk, which is related to the Grover's search algorithm on a quantum computer, is one of the typical discrete time quantum walks. However, a localization of the two-dimensional Grover walk starting from a fixed point is striking different from other types of quantum walks. The present paper explains the reason why the walker who moves according to the degree-four Grover's operator can remain at the starting point with a high probability. It is shown that the key factor for the localization is due to the degeneration of eigenvalues of the time evolution operator. In fact, the global time evolution of the quantum walk on a large lattice is mainly determined by the degree of degeneration. The dependence of the localization on the initial state is also considered by calculating the wave function analytically.Comment: 21 pages RevTeX, 4 figures ep

Nondestructive testing of brazed rocket engine components

Report details study made of nondestructive radiographic, ultrasonic, thermographic, and leak test methods used to inspect and evaluate the quality of the various brazed joints in liquid-propellant rocket engine components and assemblies. Descriptions of some of the unique equipment and methods developed are included