The galactic gamma-ray distribution: Implications for galactic structure and the radial cosmic ray gradient

The radial distribution of gamma ray emissivity in the Galaxy was derived from flux longitude profiles, using both the final SAS-2 results and the recently corrected COS-B results and analyzing the northern and southern galactic regions separately. The recent CO surveys of the Southern Hemisphere, were used in conjunction with the Northern Hemisphere data, to derive the radial distribution of cosmic rays on both sides of the galactic plane. In addition to the 5 kpc ring, there is evidence from the radial asymmetry for spiral features which are consistent with those derived from the distribution of bright HII regions. Positive evidence was also found for a strong increase in the cosmic ray flux in the inner Galaxy, particularly in the 5 kpc region in both halves of the plane

Pulsar and diffuse contributions to the observed galactic gamma radiation

With the acquisition of satellite data on the energy spectrum of galactic gamma-radiation, it is clear that such radiation has a multicomponent nature. A calculation of the pulsar gamma ray emission spectrum is used together with a statistical analysis of recent data on 328 known pulsars to make a new determination of the pulsar contribution to galactic gamma ray emission. The contributions from diffuse interstellar cosmic ray induced production mechanisms to the total emission are then reexamined. It is concluded that pulsars may account for a significant fraction of galactic gamma ray emission

The multi-disciplinary design study: A life cycle cost algorithm

The approach and results of a Life Cycle Cost (LCC) analysis of the Space Station Solar Dynamic Power Subsystem (SDPS) including gimbal pointing and power output performance are documented. The Multi-Discipline Design Tool (MDDT) computer program developed during the 1986 study has been modified to include the design, performance, and cost algorithms for the SDPS as described. As with the Space Station structural and control subsystems, the LCC of the SDPS can be computed within the MDDT program as a function of the engineering design variables. Two simple examples of MDDT's capability to evaluate cost sensitivity and design based on LCC are included. MDDT was designed to accept NASA's IMAT computer program data as input so that IMAT's detailed structural and controls design capability can be assessed with expected system LCC as computed by MDDT. No changes to IMAT were required. Detailed knowledge of IMAT is not required to perform the LCC analyses as the interface with IMAT is noninteractive

Approximation of Rough Functions

For given $p\in\lbrack1,\infty]$ and $g\in L^{p}\mathbb{(R)}$, we establish the existence and uniqueness of solutions $f\in L^{p}(\mathbb{R)}$, to the equation $$f(x)-af(bx)=g(x),$$ where $a\in\mathbb{R}$, $b\in\mathbb{R} \setminus \{0\}$, and $\left\vert a\right\vert \neq\left\vert b\right\vert ^{1/p}$. Solutions include well-known nowhere differentiable functions such as those of Bolzano, Weierstrass, Hardy, and many others. Connections and consequences in the theory of fractal interpolation, approximation theory, and Fourier analysis are established.Comment: 16 pages, 3 figure

convicted by the holy spirit: the rhetoric of fundamental Baptist conversion

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136400/1/ae.1987.14.1.02a00100.pd

Least square smoothing by linear combination

The problem of fitting a polynomial to a set of observational data so that the sum of the squared residuals is a minimum has been frequently investigated. A.C. Aitken, in an appendix to his paper, "On the Graduation of Data by the Orthogonal Polynomials of Least Squares ", (Proc. Roy. Soc. Edin. Vol. LIII (1933) pp. 77 -78,) provides a list of the more important papers on this subject. Tchebychef and Gram were the first to expound, more than fifty years ago, the method of fitting my means of orthogonal polynomials. Their work has been followed up in more recent times by several writers, including Jordan, R.A. Fisher and A.C. Aitken. W.F. Sheppard and C.W.M. Sherriff develop the equivalent method of linear combination of data. However, in the latter method, the fitted value of the central observation only is considered in detail, and an odd number of data is therefore required.It has been shown by W.F. Sheppard, and recently, with much more conciseness by G.J. Lidstone that the methods of Least Square Fitting and Linear Combination of Minimal Reduction Co-efficient lead to identical results.It is proposed, in the following investigation, to express all the fitted values as linear combinations of the observed values. The data considered are either odd or even in number, equidistant, unweighted and uncorrelated.In Chapter I we shall investigate the form of the matrix and its properties, and shall give examples of its construction and practical use.The corresponding matrices of co-efficients, obtained in this way, of lower and lower order, are discussed in Chapter II, and appropriate examples given. The properties of these matrices are very similar to, and often identical with those of the matrix C Chapter III contains alternative methods of fitting, with simple checks on accuracy of working. Examples of each method are given.The appendix consists of tables of the numerical values of the matrices connecting observed and fitted values, for numbers of data equal to 4, 5, 6, 7 - - - 15, and for fitted polynomials of degree 0, 1, 2, 3, 4, 5, together with the corresponding matrices connecting the differences. There is also a short bibliography.Methods of fitting involving the matrices discussed here are particularly suitable for rapid calculation with a machine. Indeed the use of a machine is taken for granted.The same example is used throughout to simplify the comparison of the various methods