Hypercubes, Leonard triples and the anticommutator spin algebra

This paper is about three classes of objects: Leonard triples, distance-regular graphs and the modules for the anticommutator spin algebra. Let \K denote an algebraically closed field of characteristic zero. Let $V$ denote a vector space over \K with finite positive dimension. A Leonard triple on $V$ is an ordered triple of linear transformations in $\mathrm{End}(V)$ such that for each of these transformations there exists a basis for $V$ with respect to which the matrix representing that transformation is diagonal and the matrices representing the other two transformations are irreducible tridiagonal. The Leonard triples of interest to us are said to be totally B/AB and of Bannai/Ito type. Totally B/AB Leonard triples of Bannai/Ito type arise in conjunction with the anticommutator spin algebra $\mathcal{A}$, the unital associative \K-algebra defined by generators $x,y,z$ and relations$$xy+yx=2z,\qquad yz+zy=2x,\qquad zx+xz=2y.$$ Let $D\geq0$ denote an integer, let $Q_{D}$ denote the hypercube of diameter $D$ and let $\tilde{Q}_{D}$ denote the antipodal quotient. Let $T$ (resp. $\tilde{T}$) denote the Terwilliger algebra for $Q_{D}$ (resp. $\tilde{Q}_{D}$). We obtain the following. When $D$ is even (resp. odd), we show that there exists a unique $\mathcal{A}$-module structure on $Q_{D}$ (resp. $\tilde{Q}_{D}$) such that $x,y$ act as the adjacency and dual adjacency matrices respectively. We classify the resulting irreducible $\mathcal{A}$-modules up to isomorphism. We introduce weighted adjacency matrices for $Q_{D}$, $\tilde{Q}_{D}$. When $D$ is even (resp. odd) we show that actions of the adjacency, dual adjacency and weighted adjacency matrices for $Q_{D}$ (resp. $\tilde{Q}_{D}$) on any irreducible $T$-module (resp. $\tilde{T}$-module) form a totally bipartite (resp. almost bipartite) Leonard triple of Bannai/Ito type and classify the Leonard triple up to isomorphism.Comment: arXiv admin note: text overlap with arXiv:0705.0518 by other author

Prior Day Effect in Forecasting Daily Natural Gas Flow from Monthly Data

Many needs exist in the energy industry where measurement is monthly yet daily values are required. The process of disaggregation of low frequency measurement to higher frequency values has been presented in this literature. Also, a novel method that accounts for prior-day weather impacts in the disaggregation process is presented, even though prior-day impacts are not directly recoverable from monthly data. Having initial daily weather and gas flow data, the weather and flow data are aggregated to generate simulated monthly weather and consumption data. Linear regression models can be powerful tools for parametrization of monthly/daily consumption models and will enable accurate disaggregation. Two-, three-, four-, and six-parameter linear regression models are built. RMSE and MAPE are used as means for assessing the performance of the proposed approach. Extensive comparisons between the monthly/daily gas consumption forecasts show higher accuracy of the results when the effect of prior-day weather inputs are considered

Managing Analysis: The Client\u27s Responsibility

In the space of about three decades, defense analysis has reached the stage at which it can be said that no major national security decisions are made without it. 1 The established Department of Defense decision ­making processes for programming, planning, and budgeting and for systems acquisition build in a formal way upon analytic inputs

Alien Registration- Brown, George F. (Bridgewater, Aroostook County)

https://digitalmaine.com/alien_docs/26226/thumbnail.jp

Legal effectiveness and external capital : the role of foreign debt

Previous research has documented weak, and sometimes conflicting, effects of legal quality on measures of firm debt. Using WorldScope data for 1,689 firms, as well as more detailed proprietary data for 315 firms across nine East Asian countries, the authors find that access to foreign financing appears to loosen borrowing constraints associated with poor legal systems. This helps resolve inconsistencies in prior findings and explains how legal protection is important for borrowing by firms. In particular, they find that legal effectiveness is important for determining the amount, maturity, and currency denomination of debt. The authors discuss several mechanisms by which firms can avoid the costs of poor legal systems with foreign borrowing. The paper contributes to the policy debate surrounding the importance of creditor rights for domestic lending.Municipal Financial Management,Banks&Banking Reform,Economic Theory&Research,Financial Intermediation,Environmental Economics&Policies

Exchange rate risk management : evidence from East Asia

The recent East Asian financial crisis provides a natural experiment for investigating foreign exchange risk management by nonfinancial corporations. During this period, the financial crisis exposed local firms to large depreciations in exchange rates and reduced access to foreign capital. The authors explore the exchange rate hedging practices of firms that hedged exposure to foreign debt in eight East Asian countries between 1996 and 1998. They identify and characterize East Asian companies that used foreign currency derivatives, documenting differences in size, financial characteristics, and exposure to domestic and foreign debt. They investigate the factors improtant in the use of foreign currency derivatives. Unlike studies of US firms, they find limited support for existing theories of optimal hedging. Instead, they find that firms use foreign earnings as a substitute for hedging with derivatives. And they find evidence that firms engage in"selective"hedging. They investigate the relative performance of hedgers during and after the crisis. They find no evidence that East Asian firms eliminated their foreign exchange exposure by using derivatives. Firms that used derivatives before the crisis performed just as poorly as nonhedgers during the crisis. After the crisis, firms that hedged performed somewhat better than nonhedgers, but this result appears to be explained by a larger post-crisis currency exposure for hedgers (an exchange rate risk premium), which had limited access to derivatives during this period.Payment Systems&Infrastructure,Financial Intermediation,Economic Theory&Research,Banks&Banking Reform,Environmental Economics&Policies,Banks&Banking Reform,Economic Theory&Research,Environmental Economics&Policies,Strategic Debt Management,Financial Intermediation

Mathematical Models for Natural Gas Forecasting

It is vital for natural gas Local Distribution Companies (LDCs) to forecast their customers\u27 natural gas demand accurately. A significant error on a single very cold day can cost the customers of the LDC millions of dollars. This paper looks at the financial implication of forecasting natural gas, the nature of natural gas forecasting, the factors that impact natural gas consumption, and describes a survey of mathematical techniques and practices used to model natural gas demand. Many of the techniques used in this paper currently are implemented in a software GasDayTM, which is currently used by 24 LDCs throughout the United States, forecasting about 20% of the total U.S. residential, commercial, and industrial consumption. Results of GasDay\u27sTM forecasting performance also is presented

Set & Drift: Aid and Assistance to Developing Nations

In recent years questions relating to U.S. involvement in the developing world have been both illuminated and overshadowed by international events

Defense Systems Analysis… One More Time

[There] has been a tendency on the part of some staff people to use systems analysis as a cover for what is really subjective judgment .... I am determined not to let what is essentially a helpful tool, and systems analysis can be a helpful tool, become the overriding force in driving decisions, particularly in the dark. -The Honorable W. Graham Claytor, Jr., Secretary of the Navy, Keynote Address of the Naval War College Current Strategy Forum, 27 March 1978. What is this helpful tool? What may we ask of it? What must we not ask of it