Boundary quasi-orthogonality and sharp inclusion bounds for large Dirichlet eigenvalues

We study eigenfunctions and eigenvalues of the Dirichlet Laplacian on a bounded domain \Omega\subset\RR^n with piecewise smooth boundary. We bound the distance between an arbitrary parameter $E > 0$ and the spectrum $\{E_j \}$ in terms of the boundary $L^2$-norm of a normalized trial solution $u$ of the Helmholtz equation $(\Delta + E)u = 0$. We also bound the $L^2$-norm of the error of this trial solution from an eigenfunction. Both of these results are sharp up to constants, hold for all $E$ greater than a small constant, and improve upon the best-known bounds of Moler--Payne by a factor of the wavenumber $\sqrt{E}$. One application is to the solution of eigenvalue problems at high frequency, via, for example, the method of particular solutions. In the case of planar, strictly star-shaped domains we give an inclusion bound where the constant is also sharp. We give explicit constants in the theorems, and show a numerical example where an eigenvalue around the 2500th is computed to 14 digits of relative accuracy. The proof makes use of a new quasi-orthogonality property of the boundary normal derivatives of the eigenmodes, of interest in its own right.Comment: 18 pages, 3 figure

Space shuttle nonmetallic materials age life prediction

The chemiluminescence from samples of polybutadiene, Viton, Teflon, Silicone, PL 731 Adhesive, and SP 296 Boron-Epoxy composite was measured at temperatures from 25 to 150 C. Excellent correlations were obtained between chemiluminescence and temperature. These correlations serve to validate accelerated aging tests (at elevated temperatures) designed to predict service life at lower temperatures. In most cases, smooth or linear correlations were obtained between chemiluminescence and physical properties of purified polymer gums, including the tensile strength, viscosity, and loss tangent. The latter is a complex function of certain polymer properties. Data were obtained with far greater ease by the chemiluminescence technique than by the conventional methods of study. The chemiluminescence from the Teflon (Halon) samples was discovered to arise from trace amounts of impurities, which were undetectable by conventional, destructive analysis of the sample

Can Diversity Extend to Ways of Knowing? Engaging Cross-Cultural Paradigms

This article briefly outlines three examples of cross-cultural academic programs, each bringing to the table either indigenous knowledge or Chinese medicine, knowledge generally considered to lie beyond the research base of 1862 land-grant institutions. In the process, the gate-keeping function of our research-base is challenged, examined here through a cultural lens. Including diverse ways of knowing as assets within the scope of academic work can enhance engagement outreach, but it asks us to re-examine basic assumptions of our academic culture

Hormone Receptor and ERBB2 Status in Gene Expression Profiles of Human Breast Tumor Samples

The occurrence of large publically available repositories of human breast tumor gene expression profiles provides an important resource to discover new breast cancer biomarkers and therapeutic targets. For example, knowledge of the expression of the estrogen and progesterone hormone receptors (ER and PR), and that of the ERBB2 in breast tumor samples enables choice of therapies for the breast cancer patients that express these proteins. Identifying new biomarkers and therapeutic agents affecting the activity of signaling pathways regulated by the hormone receptors or ERBB2 might be accelerated by knowledge of their expression levels in large gene expression profiling data sets. Unfortunately, the status of these receptors is not invariably reported in public databases of breast tumor gene expression profiles. Attempts have been made to employ a single probe set to identify ER, PR and ERBB2 status, but the specificity or sensitivity of their prediction is low. We enquired whether estimation of ER, PR and ERBB2 status of profiled tumor samples could be improved by using multiple probe sets representing these three genes and others with related expression

Prediction of service life of polymeric sealant compositions for fuel tanks in aerospace structures from measurements of viscoelastic properties Annual report

Prediction of service life of polymeric sealers for fuel tanks from viscoelastic measurement

Full-scale wind tunnel-investigation of the Advanced Technology Light Twin-Engine airplane (ATLIT)

An investigation was conducted to evaluate the aerodynamic performance, stability, and control characteristics of the Advanced Technology Light Twin Engine airplane (ATLIT). Data were measured over an angle of attack range from -4 deg to 20 deg for various angles of sideslip between -5 deg and 15 deg at Reynolds numbers of 0.0000023 and 0.0000035 for various settings of power and flap deflection. Measurements were also made by means of special thrust torque balances to determine the installed propeller characteristics. Part of the investigation was devoted to drag cleanup of the basic airplane and to the evaluation of the effect of winglets on drag and stability

An algorithm for determining program feasibility of a multi-mode PAM commutator telemetry system Technical report no. 10

Algorithm formulation for evaluation of strapping arrangement programs for PAM multimode commutation system of Saturn telemetry syste

The role of purple pens in learning to prescribe.

BACKGROUND: Medical doctors are required to prescribe drugs safely and effectively upon qualification, a skill that many feel poorly prepared to undertake. To better prepare doctors, a whole-task approach that develops knowledge and skills, but that also considers the effect of the complex clinical workplace on prescribing, is optimal. We describe an evaluation of an experiential learning programme that allows senior medical students to gain experience with inpatient prescribing during their hospital assistantship. METHODS: A standard operating procedure (SOP) for medical student transcribing was implemented by the teaching hospitals associated with a single medical school. This included medical student prescriptions being written in purple ink. The evaluation consisted of an audit of transcribing activity and a student survey. We evaluated the usage of the initiative, adherence to the SOP and the propensity for error. RESULTS: The survey was completed by 38 out of a possible 108 fifth-year students. All respondents agreed that the programme was helpful in aiding them to learn about prescribing. A total of 247 prescriptions for 50 patients were audited: 25.1% of the prescriptions written by students required some form of amendment by the supervising doctor or pharmacist; three (1.2%) prescription errors remained unidentified; and none presented a patient safety risk. CONCLUSIONS: The purple-pen scheme affords medical students the opportunity to prescribe in the workplace, where they face authentic challenges when safely contributing to patient care. The identification of prescribing errors, feedback and the learners' own reflections helped the learners to focus on areas for improvement in prescribing prior to qualification

Statistical quality control applied to a telemetry system acceptance prodedure Technical report no. 13

Statistical quality control applied to telemetry system acceptance procedur