9,591 research outputs found

    Cyclotomic matrices over real quadratic integer rings

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    We classify all cyclotomic matrices over real quadratic integer rings and we show that this classification is the same as classifying cyclotomic matrices over the compositum all real quadratic integer rings. Moreover, we enumerate a related class of symmetric matrices; those matrices whose eigenvalues are contained inside the interval [-2,2] but whose characteristic polynomials are not in Z[x].Comment: 13 page

    Simulation and measurement of hts josephson heterodyne oscillator

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    We report continuing investigations into practical applications of the ac Josephson effect as the basis for a voltage-tunable radio-frequency oscillator. We have previously demonstrated experimentally that useful power levels (10 s of nW) and linewidths of a few kHz can be achieved in the heterodyne output from a High-Temperature-Superconducting Resistive SQUID (HTS-RSQUID) operating in the frequency range 1-50 MHz. Those results were achieved with 2-junction R-SQUIDs incorporating current-biased shunt resistors of a few micro-ohms. We have now modified the fabrication procedures, and adjusted the shunt resistors and bias current values so that higher frequencies can be achieved. The Josephson junctions are of step-edge type, rather than the bi-crystal type used in our earlier work. The step-edge technique permits much more flexibility in the geometrical lay-out and utilizes the more cost-effective single-crystal MgO substrates. In the present paper, we report numerical simulations and experimental measurements on these devices in the frequency range up to 2 GHz

    The Caldwell theater complex

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    The Analysis of an Integrated Model of Therapy Using Structural and Gottman Method Approaches: A Case Study

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    The purpose of this study was to investigate the usefulness of an integrated model of therapy for one therapist. Qualitative and quantitative data were gathered from three family dyads. Ten therapy sessions were coded and analyzed to evaluate fidelity to the treatment model. Several themes emerged from the data that provided a foundation for analysis and clarification of the integrated model. The results of this research are organized into four research categories: fidelity to the integrated model, clients and change, how one session or case informs another, and how therapeutic decisions were made. Results indicate that the therapist maintained fidelity to the integrated model and client changes resulted. An analysis of the treatment model is discussed, along with schemes for decision-making and the implementation of therapeutic techniques. Clinical implications and limitations are discussed

    Independence Polynomials of Molecular Graphs

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    In the 1980\u27s, it was noticed by molecular chemists that the stability and boiling point of certain molecules were related to the number of independent vertex sets in the molecular graphs of those chemicals. This led to the definition of the Merrifield-Simmons index of a graph G as the number of independent vertex sets in G. This parameter was extended by graph theorists, who counted independent sets of different sizes and defined the independence polynomial F_G(x) of a graph G to be \sum_k F_k(G)x^k where for each k, F_k(G) is the number of independent sets of k vertices. This thesis is an investigation of independence polynomials of several classes of graphs, some directly related to molecules of hydrocarbons. In particular, for the graphs of alkanes, alkenes, and cycloalkanes, we have determined the Merrifield-Simmons index, the independence polynomial, and, in some cases, the generating function for the independence polynomial. These parameters are also determined in several classes of graphs which are natural generalizations of the hydrocarbons. The proof techniques used in studying the hydrocarbons have led to some possibly interesting results concerning the coefficients of independence polynomials of regular graphs with large girth
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