scholarly journals On an oscillatory integral involving a homogeneous form

2020 ◽  
Vol 62 (1) ◽  
pp. 21-58
Author(s):  
Shuntaro Yamagishi
Keyword(s):  
Oscillatory Integral ◽  
Homogeneous Form

STUDIES ON THE AROMATISATION OF NEUTRAL STEROIDS IN PREGNANT WOMEN

1970 ◽  
Vol 65 (1) ◽  
pp. 69-83 ◽  
Author(s):  
H. Vokal ◽  
D. F. Archer ◽  
N. Wiqvist ◽  
E. Diczfalusy
Keyword(s):  
Pregnant Women ◽  
Placental Perfusion ◽  
Homogeneous Form ◽  
Urine Specimens

ABSTRACT The following steroids, [7α-3H]5-androstene-3β,16α,17β-triol and [4-14C] 5-androstene-3β,16β,17β-triol were biosynthesized and their metabolism was studied in two subjects at midgestation, following placental perfusion in situ. Among the metabolites isolated in a radiochemically homogeneous form, exclusively 3H-labelled 16α,17β-dihydroxy-4-androsten-3-one was isolated from the extracts of placentas and perfusates. Exclusively 14C-labelled 16β,17β-dihydroxy-4-androsten-3-one was isolated from the placentas and perfusates and 16-epioestriol (1,3,5(10)-oestratriene-3,16β,17β-triol) from the placentas, perfusates and urine specimens. The following compounds contained both 3H and 14C-label: oestriol (placentas and urine specimens) and 5β-androstane-3α,16α,17β-triol (urine specimens). The 3H/14C-ratio of oestriol isolated from the urine specimens was much lower than that of urinary 5β-androstane-3α,16α,17β-triol, or that of the oestriol isolated from the placentas. The 3H/14C-ratio of the oestriol isolated from the urine 2–4 days following the perfusion was lower than that of the perfused material. It is concluded that a considerable amount of the 16-epioestriol secreted by the placenta is gradually converted to oestriol by the maternal organism. A limited conversion occurs also in the placenta.

STUDIES ON THE METABOLISM OF C-19 STEROIDS IN THE HUMAN FOETO-PLACENTAL UNIT.

1967 ◽  
Vol 55 (2) ◽  
pp. 263-277 ◽  
Author(s):  
E. Lamb ◽  
S. Mancuso ◽  
S. Dell' Acqua ◽  
N. Wiqvist ◽  
E. Diczfalusy
Keyword(s):  
Isotope Ratios ◽  
Arterial Supply ◽  
Homogeneous Form

ABSTRACT Dehydroepiandrosterone sulphate (DHAS) labelled with 3H and dehydroepiandrosterone (DHA) labelled with 14C were simultaneously administered into the arterial supply of four placentas perfused in situ immediately following the removal of the foetus at midpregnancy. From the perfused placentas testosterone (T), androstenedione (A), oestrone (OE1) and 17β-oestradiol (OE2) derived from the metabolism of both DHA and DHAS were isolated in a radiochemically homogeneous form. In addition DHA derived from DHAS was isolated. No labelled 19-hydroxy-androst-4-ene-3,17-dione, or 3β,19-dihydroxy-androst-5-en-17-one was detected. From the perfusates the same steroids were isolated as from the placentas. They contained so small amounts of 3H that their radiochemical homogeneity could be established only on the basis of the 14C label. The 3H/14C ratio of the A isolated from each placenta was higher than that of DHA and OE1 isolated from the same source, indicating a higher contribution of DHAS to A than to DHA or OE1 However, no conjugated or unconjugated intermediates between DHAS and A other than DHA were detected. One possible explanation for the differences in isotope ratios based on the existence of two hypothetical placental compartments, is discussed.

Efficient evaluation of the earth return mutual impedance of overhead conductors over a horizontally multilayered soil

2014 ◽  
Vol 33 (4) ◽  
pp. 1379-1395 ◽  
Author(s):  
Jae-bok Lee ◽  
Jun Zou ◽  
Benliang Li ◽  
Munno Ju
Keyword(s):  
Unit Length ◽  
Oscillatory Integral ◽  
Electromagnetic Transients ◽  
Closed Form Expression ◽  
Computational Time ◽  
Horizontal Distance ◽  
Content Type ◽  
Mutual Impedance ◽  
The Earth ◽  
Highly Oscillatory

Purpose – The per-unit-length earth return mutual impedance of the overhead conductors plays an important role for analyzing electromagnetic transients or couplings of multi-conductor systems. It is impossible to have a closed-form expression to evaluate this kind of impedance. The purpose of this paper is to propose an efficient numerical approach to evaluate the earth return mutual impedance of the overhead conductors above horizontally multi-layered soils. Design/methodology/approach – The expression of the earth return mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts intentionally, i.e. the definite and the tail integral, respectively. The definite integral is calculated using the proposed moment functions after fitting the integrand into the piecewise cubic spline functions, and the tail integral is replaced by exponential integrals with newly developed asymptotic integrands. Findings – The numerical examples show the proposed approach has a satisfactory accuracy for different parameter combinations. Compared to the direct quadrature approach, the computational time of the proposed approach is very competitive, especially, for the large horizontal distance and the low height of the conductors. Originality/value – The advantage of the proposed approach is that the calculation of the highly oscillatory integral is completely avoided due to the fact that the moment function can be evaluated analytically. The contribution of the tail integral is well included by means of the exponential integral, though in an asymptotic way. The proposed approach is completely general, and can be applied to calculate the earth return mutual impedance of overhead conductors above a soil structure with an arbitrary number of horizontal layers.

A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS

2004 ◽  
Vol 07 (04) ◽  
pp. 507-526 ◽  
Author(s):  
S. ALBEVERIO ◽  
G. GUATTERI ◽  
S. MAZZUCCHI
Keyword(s):  
Phase Space ◽  
Continuous Measurement ◽  
Quantum Particle ◽  
Oscillatory Integral ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Infinite Dimensional ◽  
Feynman Path Integrals ◽  
Characteristics Method ◽  
Stochastic Characteristics

The Belavkin equation, describing the continuous measurement of the momentum of a quantum particle, is studied. The existence and uniqueness of its solution is proved via analytic tools. A stochastic characteristics method is applied. A rigorous representation of the solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the phase space is also given.

scholarly journals A Simpler GMRES Method for Oscillatory Integrals with Irregular Oscillations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qinghua Wu ◽  
Meiying Xiang
Keyword(s):  
Theoretical Analysis ◽  
Matrix Factorization ◽  
Numerical Experiments ◽  
Oscillatory Integral ◽  
Oscillatory Integrals ◽  
New Method ◽  
Gmres Method ◽  
Hessenberg Matrix

A simpler GMRES method for computing oscillatory integral is presented. Theoretical analysis shows that this method is mathematically equivalent to the GMRES method proposed by Olver (2009). Moreover, the simpler GMRES does not require upper Hessenberg matrix factorization, which leads to much simpler program and requires less work. Numerical experiments are conducted to illustrate the performance of the new method and show that in some cases the simpler GMRES method could achieve higher accuracy than GMRES.

scholarly journals Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases

2019 ◽  
Vol 63 (4) ◽  
pp. 771-786
Author(s):  
Danqing He ◽  
Zuoshunhua Shi
Keyword(s):  
Critical Exponents ◽  
Homogeneous Polynomial ◽  
Integral Operators ◽  
Oscillatory Integral ◽  
Sharp Bounds ◽  
Oscillatory Integral Operators ◽  
Several Variables ◽  
Rank One ◽  
Important Notion ◽  
Additional Assumptions

AbstractWe obtain sharp $L^{p}$ bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition that is an important notion introduced by Greenleaf, Pramanik, and Tang. Under certain additional assumptions, we can establish sharp damping estimates with critical exponents to prove endpoint $L^{p}$ estimates.

ACETATE AND CHOLESTEROL METABOLISM IN THE HUMAN FOETO-PLACENTAL UNIT AT MIDGESTATION

1970 ◽  
Vol 63 (1) ◽  
pp. 119-133 ◽  
Author(s):  
G. Telegdy ◽  
J. W. Weeks ◽  
D. F. Archer ◽  
N. Wiqvist ◽  
E. Diczfalusy
Keyword(s):  
Sodium Acetate ◽  
De Novo ◽  
Cholesterol Metabolism ◽  
Human Foetus ◽  
Homogeneous Form ◽  
Per Se ◽  
Hydroxy Progesterone

ABSTRACT Two complete foeto-placental units were perfused at midgestation with 5.0 mCi of uniformly labelled 14C-sodium acetate plus 5.0 mCi of cholesterol-7α-3H and two isolated foetuses were perfused with 2.5 mCi of 14C-labelled sodium acetate plus 2.5 mCi of cholesterol-7α-3H. The perfusions were carried out at 35–36°C for 90 min. The foetal adrenals, livers, testes and perfusates were analyzed and various labelled steroids were isolated in a radiochemically homogeneous form. Major quantities of 14C- and 3H-labelled pregnenolone (3β-hydroxy-pregn-5-en-20-one) and dehydroepiandrosterone (3β-hydroxy-androst-5-en-17-one) were isolated from the foetal perfusates, livers and adrenals. Minor amounts of 14C- and 3H-labelled progesterone (pregn-4-ene-3,20-dione) were isolated from the perfusates and adrenals, and 17α-hydroxy-progesterone (17α-hydroxy-pregn-4-ene-3,20-dione) and androstenedione (androst-4-ene-3,17-dione) from the perfusates. Smaller amounts of exclusively 14C-labelled androstenedione were isolated also from the adrenals. No labelled progesterone, androstenedione or testosterone (17β-hydroxy-androst-4-en-3-one) was detected in the testes. Attempts to isolate 20α-dihydroprogesterone (20α-hydroxy-pregn-4-en-3-one) or 20β-dihydroprogesterone (20β-hydroxy-pregn-4-en-3-one) from the perfusates, adrenals and livers failed. No labelled cortisol (11β,17,21-trihydroxy-pregn-4-ene-3,20-dione) or corticosterone (11β,21-dihydroxy-pregn-4-ene-3,20-dione) was detected in the adrenals, and no testosterone, oestrone (3-hydroxy-oestra-1,3,5(10)-trien-17-one) or 16α-hydroxy-dehydroepiandrosterone (3β,16α-dihydroxy-androst-5-en-17-one) in the perfusates. Pregnenolone and dehydroepiandrosterone (which were present in approximately equal amounts) accounted for as much as 95% of all steroids isolated from all sources. The bulk of these two steroids was isolated from the perfusates. The 14C/3H ratio of the pregnenolone and dehydroepiandrosterone isolated from the conjugated fraction of the perfusates was much higher than that of the unconjugated compounds. It is concluded that the midgestation human foetus is capable per se of carrying out the de novo synthesis of major quantities of pregnenolone and dehydroepiandrosterone. It is suggested that in foetal steroidogenesis acetate is utilized predominantly via a conjugated pathway and circulating cholesterol mainly via an unconjugated pathway.

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