Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A second fourth-order ordinary differential equation for the general Fourier coefficent is derived from an integral representation of the coefficient, and both differential equations are shown to be equivalent. Series solutions for the various Fourier coefficients are also given, mostly in terms of Legendre functions and Bessel/Hankel functions. These are derived from the closed form hypergeometric solutions or an integral representation, or both. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented

Perspective: Dietary Biomarkers of Intake and Exposure - Exploration with Omics Approaches

While conventional nutrition research has yielded biomarkers such as doubly labeled water for energy metabolism and 24-h urinary nitrogen for protein intake, a critical need exists for additional, equally robust biomarkers that allow for objective assessment of specific food intake and dietary exposure. Recent advances in high-throughput MS combined with improved metabolomics techniques and bioinformatic tools provide new opportunities for dietary biomarker development. In September 2018, the NIH organized a 2-d workshop to engage nutrition and omics researchers and explore the potential of multiomics approaches in nutritional biomarker research. The current Perspective summarizes key gaps and challenges identified, as well as the recommendations from the workshop that could serve as a guide for scientists interested in dietary biomarkers research. Topics addressed included study designs for biomarker development, analytical and bioinformatic considerations, and integration of dietary biomarkers with other omics techniques. Several clear needs were identified, including larger controlled feeding studies, testing a variety of foods and dietary patterns across diverse populations, improved reporting standards to support study replication, more chemical standards covering a broader range of food constituents and human metabolites, standardized approaches for biomarker validation, comprehensive and accessible food composition databases, a common ontology for dietary biomarker literature, and methodologic work on statistical procedures for intake biomarker discovery. Multidisciplinary research teams with appropriate expertise are critical to moving forward the field of dietary biomarkers and producing robust, reproducible biomarkers that can be used in public health and clinical research

Asymptotic waveforms in propeller acoustics

SIGLEAvailable from British Library Document Supply Centre- DSC:D063009 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Normative Functional Fitness Standards and Trends of Portuguese Older Adults: Cross-Cultural Comparisons

This cross-sectional study was designed to develop normative functional fitness standards for the Portuguese older adults, to analyze age and gender patterns of decline, to compare the fitness level of Portuguese older adults with that of older adults in other countries, and to evaluate the fitness level of Portuguese older adults relative to recently published criterion fitness standards associated with maintaining physical independence. A sample of 4,712 independent-living older adults, age 65-103 yr, was evaluated using the Senior Fitness Test battery. Age-group normative fitness scores are reported for the 10th, 25th, 50th, 75th, and 90th percentiles. Results indicate that both women and men experience age-related losses in all components of functional fitness, with their rate of decline being greater than that observed in other populations, a trend which may cause Portuguese older adults to be at greater risk for loss of independence in later years. These newly established normative standards make it possible to assess individual fitness level and provide a basis for implementing population-wide health strategies to counteract early loss of independence