Green's function for a Schroedinger operator and some related summation formulas

Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem that arises in connection with integral equations. The new approach introduced in this paper may be useful for the construction of wider classes of generating function.Comment: 14 page

Generating mice with targeted mutations.

Journal ArticleMutational analysis is one of the most informative approaches available for the study of complex biological processes. It has been particularly successful in the analysis of the biology of bacteria, yeast, the nematode worm Caenorhabditis elegans and the fruit fly Drosophila melanogaster. Extension of this approach to the mouse, through informative, was far less successful relative to what has been achieved with these simpler model organisms. This is because it is not numerically practical in mice to use random mutagenesis to isolate mutations that affect a specified biological process of interest. Nonetheless, biological phenomena such as a sophisticated immune response, cancer, vascular disease or higher-order cognitive function, to mention just a few, must analyzed in organisms that show such phenomena, and for this reason geneticists and other researchers have turned to the mouse. Gene targeting, the means for creating mice with designed mutations in almost any gene, was developed as an alternative to the impractical use of random mutgenesis for pursing genetic analysis in the mouse. Now gene targeting has advanced the genomic manipulations possible in mice to a level that can be matched only in far simple organisms such as bacteria and yeast

Postnatal development and progression of renal dysplasia in cyclooxygenase-2 null mice

BACKGROUND: Genetic ablation of cyclooxygenase-2 (COX-2) resulted in cystic renal dysplasia and early death in adult mice. The ontologic development of the renal pathology and the biochemical and physiological abnormalities associated with the dysplasia are unknown. METHODS: Mice homozygous for a targeted deletion of COX-2 (-/-) were compared with wild-type littermates (+/+). Somatic and kidney growth and renal histology were studied at the day of birth and at a number of postnatal ages. Systolic blood pressure, urinalysis, urine osmolality, serum and urine chemistries, and inulin clearance were evaluated in adult animals. RESULTS: Beginning at postnatal day 10 (PN10), kidney growth was suppressed in -/- animals, while somatic growth and heart growth were unaffected. By PN10, -/- kidneys had thin nephrogenic cortexes and crowded, small, subcapsular glomeruli. The pathology increased with age with progressive outer cortical dysplasia, cystic subcapsular glomeruli, loss of proximal tubular mass, and tubular atrophy and cyst formation. Adult -/- kidneys had profound diffuse tubular cyst formation, outer cortical glomerular hypoplasia and periglomerular fibrosis, inner cortical nephron hypertrophy, and diffuse interstitial fibrosis. The glomerular filtration rate was reduced by more than 50% in -/- animals (6.82 +/- 0.65 mL/min/kg) compared with wild-type controls (14.7 +/- 1.01 mL/min/kg, P < 0. 001). Plasma blood urea nitrogen and creatinine were elevated in null animals compared with controls. Blood pressure, urinalysis, urine osmolality, and other plasma chemistries were unaffected by the deletion of COX-2. CONCLUSIONS: Deficiency of COX-2 results in progressive and specific renal architectural disruption and functional deterioration beginning in the final phases of nephrogenesis. Tissue-specific and time-dependent expression of COX-2 appears necessary for normal postnatal renal development and the maintenance of normal renal architecture and function

THE FREQUENCIES OF HAPTOGLOBIN TYPES IN FIVE POPULATIONS *

Haptoglobin types have been determined by starch gel electrophoresis of blood from five populations. The gene frequencies obtained for allele Hp 1 were as follows: American whites, 043; American Negroes, 0.59; African Negroes, 0.72; Apaches, 0.59; and Asiatic Indians, 0.18. In tribes of the Ivory Coast and Liberia, there was a suggestion of a cline which parallels that for haemoglobin S. Evidence is presented that the condition of ahaptoglobinemia is under genetic control but not by a gene allelic to the Hp 1 -Hp 2 series. The importance of the ahaptoglobinemic individuals for genetic studies and the possibility of selection in the maintenance of the genetic polymorphism are discussed. The authors wish to acknowledge the excellent assistance of Alojzia Sandor, who carried out the electrophoretic separations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66263/1/j.1469-1809.1958.tb01460.x.pd

An overview of adakite, tonalite-trondhjemite-granodiorite (TTG), and sanukitoid; relationships and some implications for crustal evolution.

Abstract Examination of an extensive adakite geochemical database identifies two distinct compositional groups. One consists of high-SiO 2 adakites (HSA) which is considered to represent subducted basaltic slab-melts that have reacted with peridotite during ascent through mantle wedge. The second group consists of low-SiO 2 adakites (LSA) which we interpret to have formed by melting of a peridotitic mantle wedge whose composition has been modified by reaction with felsic slab-melts. The chemical composition of less differentiated (primitive) Archaean tonalite-trondhjemite-granodiorite (TTG) magmas evolved from 4.0 to 2.5 Ga. Mg# (molecular Mg/(Mg+Fe 2+ ), Ni, and Cr contents increased over this period of time and we interpret these changes in terms of changes in the degree to which the TTG magmas interacted with mantle peridotite. Over the same period, concentrations of (CaO+Na 2 O) and Sr also increased, as the amount of plagioclase, residual from basalt melting, decreased in response to increased pressures at the site of slab-melting. In the Early Archaean, it appears that these interactions were very rare or absent thus leading to the conclusion that subduction was typically flat and lacked the development of a mantle wedge. In contrast, the relatively lower heat production by~2.5 Ga meant that slab-melting occurred at greater depth, where plagioclase was no longer stable, and where the development of a thick mantle wedge ensured interaction between the slab-melts and mantle peridotite. Close compositional similarities between HSA and Late Archaean TTG (Tb~3.0 Ga) strongly suggest a petrogenetic analogy. However, an analogy between the older Archaean TTG and HSA is not complete because evidence for mantle wedge interaction is missing in most Early Archaean TTGs. Late Archaean sanukitoids and the compositionally similar Closepet-type granites have compositions significantly different from TTG of all ages. However, they show some affinity with LSA which could be considered as their possible analogue. These magmas are all thought to result from melting of a mantle peridotite whose composition has been modified by reaction with slab-melts. We propose that all these magmas are directly linked to slab-melting. Archaean TTG and HSA represent slab-melts that have interacted with peridotite to varying extent, whereas sanukitoids, Closepet-type granites, and LSA correspond to melts of peridotite previously metasomatised by slab-melt. The changes observed from Early Archaean TTG to Late Archaean TTG and to sanukitoids reflect change in both the nature and efficiency of interaction between slab-melt and mantle wedge peridotite. Comparisons between all of these rocks suggest that ancient styles of subduction that have operated since at least~3.3 Ga persist in a limited way today. The secular changes in the degree and style of these interactions is a direct consequence of the cooling of Earth that modified the thermal and dynamic parameters at the subducted slab-mantle wedge interface.

Greenstone burial–exhumation cycles at the late Archean transition to plate tectonics

Converging lines of evidence suggest that, during the late Archean, Earth completed its transition from a stagnant-lid to a plate tectonics regime,although how and when this transition occurred is debated. The geological record indicates that some form of subduction, a key component of plate tectonics—has operated since the Mesoarchean, even though the tectonic style and timescales of burial and exhumation cycles within ancient convergent margins are poorly constrained.Here, we present a Neoarchean pressure–temperature–time (P–T–t) path from supracrustal rocks of the transpressional Yilgarn orogen (Western Australia), which documents how sea-floor-altered rocks underwent deep burial then exhumation during shortening that was unrelated to the episode of burial. Archean subduction, even if generally short-lived, was capable of producing eclogites along converging lithosphere boundaries, although exhumation processes in those environments were likely less efficient than today, such that return of high-pressure rocks to the surface was rare

Haptoglobin frequencies in Jewish communities *

Haptoglobin and transferrin types have been determined by starch gel electrophoresis on blood from 929 subjects belonging to various Jewish communities. The frequency of the Hp 1 gene in 499 Ashkenazic Jews is 0.29 and does not differ significantly from the value of 0–26 found in 345 Jews of Oriental origin. The Hp 1 frequency of Ashkenazic Jews is significantly lower than that reported for the autochthonous populations of Central and Western Europe. Two small samples collected among Sephardic Jews and among the offspring of intercommunity marriages exhibit somewhat higher frequencies of the Hp 1 gene. The modified 2-1 phenotype was found in a single subject from Baghdad. There were three cases of ahaptoglobinaemia among Ashkenazic Jews and three among the Oriental groups. No ahaptoglobinaemia was discovered in a family sample of ninety-two Jews from Kurdistan among whom thalassaemia minor was common and the majority of whom were affeeted with G-6-P-D deficiency. All transferrins were of type C.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66130/1/j.1469-1809.1962.tb01307.x.pd

Regulation of blood pressure by the type 1A angiotensin II receptor gene.

The renin-angiotensin system plays a critical role in sodium and fluid homeostasis. Genetic or acquired alterations in the expression of components of this system are strongly implicated in the pathogenesis of hypertension. To specifically examine the physiological and genetic functions of the type 1A receptor for angiotensin II, we have disrupted the mouse gene encoding this receptor in embryonic stem cells by gene targeting. Agtr1A(-/-) mice were born in expected numbers, and the histomorphology of their kidneys, heart, and vasculature was normal. AT1 receptor-specific angiotensin II binding was not detected in the kidneys of homozygous Agtr1A(-/-) mutant animals, and Agtr1A(+/-) heterozygotes exhibited a reduction in renal AT1 receptor-specific binding to approximately 50% of wild-type [Agtr1A(+/+)] levels. Pressor responses to infused angiotensin II were virtually absent in Agtr1A(-/-) mice and were qualitatively altered in Agtr1A(+/-) heterozygotes. Compared with wild-type controls, systolic blood pressure measured by tail cuff sphygmomanometer was reduced by 12 mmHg (1 mmHg = 133 Pa) in Agtr1A(+/-) mice and by 24 mmHg in Agtr1A(-/-) mice. Similar differences in blood pressure between the groups were seen when intraarterial pressures were measured by carotid cannulation. These studies demonstrate that type 1A angiotensin II receptor function is required for vascular and hemodynamic responses to angiotensin II and that altered expression of the Agtr1A gene has marked effects on blood pressures

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint