Guidelines for development structured FORTRAN programs

Computer programming and coding standards were compiled to serve as guidelines for the uniform writing of FORTRAN 77 programs at NASA Langley. Software development philosophy, documentation, general coding conventions, and specific FORTRAN coding constraints are discussed

On Lipschitz Retraction of Finite Subsets of Normed Spaces

If $X$ is a metric space, then its finite subset spaces $X(n)$ form a nested sequence under natural isometric embeddings $X = X(1)\subset X(2) \subset \cdots$. It was previously established, by Kovalev when $X$ is a Hilbert space and, by Ba\v{c}\'{a}k and Kovalev when $X$ is a CAT(0) space, that this sequence admits Lipschitz retractions $X(n)\rightarrow X(n-1)$ for all $n\geq 2$. We prove that when $X$ is a normed space, the above sequence admits Lipschitz retractions $X(n)\rightarrow X$, $X(n)\rightarrow X(2)$, as well as concrete retractions $X(n)\rightarrow X(n-1)$ that are Lipschitz if $n=2,3$ and H\"older-continuous on bounded sets if $n>3$. We also prove that if $X$ is a geodesic metric space, then each $X(n)$ is a $2$-quasiconvex metric space. These results are relevant to certain questions in the aforementioned previous work which asked whether Lipschitz retractions $X(n)\rightarrow X(n-1)$, $n\geq 2$, exist for $X$ in more general classes of Banach spaces.Comment: 20 pages, Isr. J. Math. (2019). "$\gamma$ is injective" added in Lemma 6.6(ii), Published in Israel Journal of Mathematic

MHC Restriction of V-V Interactions in Serum IgG

According to Jerne’s idiotypic network hypothesis, the adaptive immune system is regulated by interactions between the variable regions of antibodies, B cells, and T cells. The symmetrical immune network theory is based on Jerne’s hypothesis, and provides a basis for understanding many of the phenomena of adaptive immunity. The theory includes the postulate that the repertoire of serum IgG molecules is regulated by T cells, with the result that IgG molecules express V region determinants that mimic V region determinants present on suppressor T cells. In this paper we describe rapid binding between purified murine serum IgG of H-2b and H-2d mice and serum IgG from the same strain and from MHC-matched mice, but not between serum IgG preparations of mice with different MHC genes. We interpret this surprising finding in terms of a model in which IgG molecules are selected to have both anti-anti-self MHC and anti-anti-anti-self MHC specificity