scholarly journals The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Jean-Pierre Magnot
Keyword(s):  
Lebesgue Measure ◽  
Infinite Product ◽  
Mean Value ◽  
Uniform Limit ◽  
Infinite Products ◽  
Infinite Dimensional ◽  
The Mean ◽  
Invariant Means ◽  
Lebesgue Measures ◽  
Dimensional Lebesgue Measure

One of the goals of this article is to describe a setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure and of the concentration property on metric measured spaces, inspired from classical examples of means. In some cases, we get a linear extension of the limit at infinity. Then, the mean value on an infinite product is defined, first for cylindrical functions and secondly taking the uniform limit. Finally, the mean value for the heuristic Lebesgue measure on a separable infinite dimensional topological vector space (e.g., on a Hilbert space) is defined. This last object, which is not the classical infinite dimensional Lebesgue measure but its “normalized” version, is shown to be invariant under translation, scaling, and restriction.

scholarly journals Randomizes hamiltonian mechanics

2019 ◽  
Vol 486 (6) ◽  
pp. 653-658
Author(s):  
Yu. N. Orlov ◽  
V. Zh. Sakbaev ◽  
O. G. Smolyanov
Keyword(s):  
Hamiltonian System ◽  
Quantum System ◽  
Open Quantum System ◽  
Hamiltonian Function ◽  
Mean Value ◽  
Hamiltonian Mechanics ◽  
Infinite Dimensional ◽  
The Mean ◽  
Random Hamiltonian ◽  
Infinite Dimensional Hamiltonian System

Randomized Hamiltonian mechanics is the Hamiltonian mechanics which is determined by a time-dependent random Hamiltonian function. Corresponding Hamiltonian system is called random Hamiltonian system. The Feynman formulas for the random Hamiltonian systems are obtained. This Feynman formulas describe the solutions of Hamilton equation whose Hamiltonian is the mean value of random Hamiltonian function. The analogs of the above results is obtained for a random quantum system (which is a random infinite dimensional Hamiltonian system). This random quantum Hamiltonians are the part of Hamiltonians of open quantum system.

scholarly journals Characterizations of the lebesgue measure and product measures related to holomorphic functions having non-negative imaginary or real part

2020 ◽  
Vol 31 (12) ◽  
pp. 2050102
Author(s):  
Mitja Nedic
Keyword(s):  
Lebesgue Measure ◽  
Fourier Coefficients ◽  
Holomorphic Functions ◽  
Special Role ◽  
Borel Measures ◽  
Study Product ◽  
Nevanlinna Functions ◽  
Product Measures ◽  
Lebesgue Measures ◽  
Dimensional Lebesgue Measure

In this paper, we study a class of Borel measures on [Formula: see text] that arises as the class of representing measures of Herglotz-Nevanlinna functions. In particular, we study product measures within this class where products with the Lebesgue measures play a special role. Hence, we give several characterizations of the [Formula: see text]-dimensional Lebesgue measure among all such measures and characterize all product measures that appear in this class of measures. Furthermore, analogous results for the class of positive Borel measures on the unit poly-torus with vanishing mixed Fourier coefficients are also presented, and the relation between the two classes of measures with regard to the obtained results is discussed.

scholarly journals Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Claudio Asci
Keyword(s):  
Banach Space ◽  
Lebesgue Measure ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Change Of Variables ◽  
Infinite Dimensional Banach Space ◽  
Dimensional Lebesgue Measure

We study, for some subsets I of N*, the Banach space E of bounded real sequences {xn}n∈I. For any integer k, we introduce a measure over (E,B(E)) that generalizes the k-dimensional Lebesgue measure; consequently, also a theory of integration is defined. The main result of our paper is a change of variables' formula for the integration.

A harmonic quadrature formula characterizing open strips

1993 ◽  
Vol 113 (1) ◽  
pp. 147-151 ◽  
Author(s):  
D. H. Armitage ◽  
C. S. Nelson
Keyword(s):  
Harmonic Function ◽  
Lebesgue Measure ◽  
Quadrature Formula ◽  
Open Subset ◽  
Harmonic Functions ◽  
Mean Value ◽  
Open Ball ◽  
Mean Value Property ◽  
Image Position ◽  
Dimensional Lebesgue Measure

Let γn denote n-dimensional Lebesgue measure. It follows easily from the well-known volume mean value property of harmonic functions that if h is an integrable harmonic function on an open ball B of centre ξ0 in ℝn, where n ≥ 2, thenA converse of this result is due to Kuran [8]: if D is an open subset of ℝn such that γn(D) < + ∞ and if there exists a point ξo∈D such thatfor every integrable harmonic function h on D, then D is a ball of centre ξ0. Armitage and Goldstein [2], theorem 1, showed that the same conclusion holds under the weaker hypothesis that (1·2) holds for all positive integrable harmonic functions h on D.

Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables

Integers ◽  
2012 ◽  
Vol 12 (5) ◽  
Author(s):  
Noboru Ushiroya
Keyword(s):  
Infinite Product ◽  
Prime Numbers ◽  
Mean Value ◽  
Arithmetic Functions ◽  
Mean Value Theorems ◽  
Several Variables ◽  
The Mean ◽  
Multiplicative Arithmetic

Abstract.Letif this limit exists. We first generalize the Wintner theorem and then consider the multiplicative case by expressing the mean-value as an infinite product over all prime numbers. In addition, we study the mean-value of a function of the form

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

Detection of Soluble Fibrin Monomer Complexes in Blood by Means of Protamine Sulphate Test

1968 ◽  
Vol 20 (01/02) ◽  
pp. 044-049 ◽  
Author(s):  
B Lipiński ◽  
K Worowski
Keyword(s):  
Human Subjects ◽  
Coronary Thrombosis ◽  
Mean Value ◽  
Healthy Human ◽  
Protamine Sulphate ◽  
Soluble Fibrin ◽  
Fibrin Monomer ◽  
Dog Plasma ◽  
The Mean ◽  
Precipitable Protein

SummaryIn the present paper described is a simple test for detecting soluble fibrin monomer complexes (SFMC) in blood. The test consists in mixing 1% protamine sulphate with diluted oxalated plasma or serum and reading the optical density at 6190 Å. In experiments with dog plasma, enriched with soluble fibrin complexes, it was shown that OD read in PS test is proportional to the amount of fibrin recovered from the precipitate. It was found that SFMC level in plasma increases in rabbits infused intravenously with thrombin and decreases after injection of plasmin with streptokinase. In both cases PS precipitable protein in serum is elevated indicating enhanced fibrinolysis. In healthy human subjects the mean value of OD readings in plasma and sera were found to be 0.30 and 0.11, while in patients with coronary thrombosis they are 0.64 and 0.05 respectively. The origin of SFMC in circulation under physiological and pathological conditions is discussed.

Detection of Circulating Tissue Factor and Factor VII in a Normal Population

1996 ◽  
Vol 75 (05) ◽  
pp. 772-777 ◽  
Author(s):  
Sybille Albrecht ◽  
Matthias Kotzsch ◽  
Gabriele Siegert ◽  
Thomas Luther ◽  
Heinz Großmann ◽  
...  
Keyword(s):  
Tissue Factor ◽  
Normal Population ◽  
Mean Value ◽  
Factor Vii ◽  
Significant Difference ◽  
Age Dependent ◽  
The Mean ◽  
Highly Correlated ◽  
And Gender

SummaryThe plasma tissue factor (TF) concentration was correlated to factor VII concentration (FVIIag) and factor VII activity (FVIIc) in 498 healthy volunteers ranging in age from 17 to 64 years. Immunoassays using monoclonal antibodies (mAbs) were developed for the determination of TF and FVIIag in plasma. The mAbs and the test systems were characterized. The mean value of the TF concentration was 172 ± 135 pg/ml. TF showed no age- and gender-related differences. For the total population, FVIIc, determined by a clotting test, was 110 ± 15% and the factor VIlag was 0.77 ± 0.19 μg/ml. FVII activity was significantly increased with age, whereas the concentration demonstrated no correlation to age in this population. FVII concentration is highly correlated with the activity as measured by clotting assay using rabbit thromboplastin. The ratio between FVIIc and FVIIag was not age-dependent, but demonstrated a significant difference between men and women. Between TF and FVII we could not detect a correlation.

Determination of Plasminogen in Clots and Thrombi

1966 ◽  
Vol 16 (01/02) ◽  
pp. 038-050 ◽  
Author(s):  
Ulla Hedner ◽  
Inga Marie Nilsson ◽  
B Robertson
Keyword(s):  
Mean Value ◽  
Main Mechanism ◽  
Clot Lysis ◽  
Post Mortem ◽  
Digestion Time ◽  
Normal Volunteers ◽  
Casein Solution ◽  
The Mean

SummaryThe plasminogen content was determined by a casein method in plasma and serum from 20 normal volunteers. The mean plasminogen content was found to be 10.1 ACU (the arbitrary caseinolytic unit defined in such a way that using a 3% casein solution and a digestion time of 20 min. at 37°C, 10 ACU gave an extinction of 0.300). No difference between serum and plasma regarding the plasminogen content was found.Plasminogen was determined in drained and drained plus washed clots prepared from 2 ml plasma. The highest values found in the drained clots were 0.9 ACU/clot and 0.2 ACU/clot in the drained plus washed clots.Plasminogen was also determined in drained and drained plus washed clots prepared from plasma with added purified plasminogen. The plasminogen was recovered in the washing fluid. According to these tests, then, purified added plasminogen is washed out of the clots.The plasminogen content of 20 thrombi obtained post mortem was also determined. The mean value was found to be 0.7 ACU/cm thrombus. Judging from our results, the “intrinsic clot lysis theory” is not the main mechanism of clot dissolution.

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