scholarly journals From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1328 ◽  
Author(s):  
Octav Olteanu
Keyword(s):  
Direct Proof ◽  
Positive Cone ◽  
Small Subset ◽  
Extension Theorems ◽  
Domain Space ◽  
Simplicial Set ◽  
Topological Version ◽  
Arbitrary Convex ◽  
Markov Moment ◽  
New Applications

The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the following problems: (1) pointing out a previously published sandwich theorem of the type f ≤ h ≤ g, where f, −g are convex functionals and h is an affine functional, over a finite-simplicial set X, and proving a topological version for this result; (2) characterizing isotonicity of convex operators over arbitrary convex cones; giving a sharp direct proof for one of the generalizations of Hahn–Banach theorem applied to the isotonicity; (3) extending inequalities assumed to be valid on a small subset, to the entire positive cone of the domain space, via Krein–Milman or Carathéodory’s theorem. Thus, we point out some earlier, as well as new applications of the Hahn–Banach type theorems, emphasizing the topological versions of these applications.

scholarly journals On Markov Moment Problem and Related Results

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 986
Author(s):  
Octav Olteanu
Keyword(s):  
Moment Problem ◽  
Quadratic Forms ◽  
Polynomial Solution ◽  
Positive Cone ◽  
Linear Operators ◽  
Moment Conditions ◽  
Domain Space ◽  
Markov Moment ◽  
Vector Valued ◽  
Multidimensional Moment Problem

We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued functions on a compact subset or an space, where is a positive moment determinate measure on a closed unbounded set. The existence and uniqueness of the operator solution are proved. Our solutions satisfy the interpolation moment conditions and are between two given linear operators on the positive cone of the domain space. The norm controlling of the solution is emphasized. The most part of the results are stated and proved in terms of quadratic forms. This type of result represents the first aim of the paper. Secondly, we construct a polynomial solution for a truncated multidimensional moment problem.

scholarly journals Subdifferential calculus for invariant linear ordered vector space-valued operators and applications

2016 ◽  
Vol 12 (4) ◽  
pp. 6160-6170
Author(s):  
Antonio Boccuto
Keyword(s):  
Vector Space ◽  
Vector Lattice ◽  
Direct Proof ◽  
Extension Theorems ◽  
Subdifferential Calculus ◽  
Partially Ordered ◽  
Ordered Vector Space ◽  
Partially Ordered Vector Space ◽  
Sandwich Type ◽  
Linear Invariant

We give a direct proof of sandwich-type theorems for linear invariant partially ordered vector space operators in the setting of convexity. As consequences, we deduce equivalence results between sandwich, Hahn-Banach, separation and Krein-type extension theorems, Fenchel duality, Farkas and Kuhn-Tucker-type minimization results and subdifferential formulas in the context of invariance. As applications, we give Tarski-type extension theorems and related examples for vector lattice-valued invariant probabilities, defined on suitable kinds of events.

1250-kilovolt scanning transmission electron microscope

1984 ◽  
Vol 42 ◽  
pp. 624-625
Author(s):  
T. Imura ◽  
S. Maruse ◽  
K. Mihama ◽  
M. Iseki ◽  
M. Hibino ◽  
...  
Keyword(s):  
High Voltage ◽  
Electron Probe ◽  
Scanning Transmission Electron Microscope ◽  
Pressure Vessels ◽  
Practical Applications ◽  
Voltage Generator ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
New Applications ◽  
High Voltage Generator

Ultra high voltage STEM has many inherent technical advantages over CTEM. These advantages include better signal detectability and signal processing capability. It is hoped that it will explore some new applications which were previously not possible. Conventional STEM (including CTEM with STEM attachment), however, has been unable to provide these inherent advantages due to insufficient performance and engineering problems. Recently we have developed a new 1250 kV STEM and completed installation at Nagoya University in Japan. It has been designed to break through conventional engineering limitations and bring about theoretical advantage in practical applications.In the design of this instrument, we exercised maximum care in providing a stable electron probe. A high voltage generator and an accelerator are housed in two separate pressure vessels and they are connected with a high voltage resistor cable.(Fig. 1) This design minimized induction generated from the high voltage generator, which is a high frequency Cockcroft-Walton type, being transmitted to the electron probe.

Convergent-bceam diffraction studies on lead zirconate titanate Ceramics

1986 ◽  
Vol 44 ◽  
pp. 482-483
Author(s):  
M.L.A. Dass ◽  
T.A. Bielicki ◽  
G. Thomas ◽  
T. Yamamoto ◽  
K. Okazaki
Keyword(s):  
Lead Zirconate Titanate ◽  
Direct Proof ◽  
Lead Zirconate ◽  
Subsolidus Phase ◽  
Pzt Ceramics ◽  
Subsolidus Phase Diagram ◽  
Zirconate Titanate ◽  
Two Phases ◽  
Cbd Method ◽  
Titanate Ceramics

Lead zirconate titanate, Pb(Zr,Ti)O3 (PZT), ceramics are ferroelectrics formed as solid solutions between ferroelectric PbTiO3 and ant iferroelectric PbZrO3. The subsolidus phase diagram is shown in figure 1. PZT transforms between the Ti-rich tetragonal (T) and the Zr-rich rhombohedral (R) phases at a composition which is nearly independent of temperature. This phenomenon is called morphotropism, and the boundary between the two phases is known as the morphotropic phase boundary (MPB). The excellent piezoelectric and dielectric properties occurring at this composition are believed to.be due to the coexistence of T and R phases, which results in easy poling (i.e. orientation of individual grain polarizations in the direction of an applied electric field). However, there is little direct proof of the coexistence of the two phases at the MPB, possibly because of the difficulty of distinguishing between them. In this investigation a CBD method was found which would successfully differentiate between the phases, and this was applied to confirm the coexistence of the two phases.

IN-BEAM NUCLEAR MAGNETIC RESONANCE OF β-ACTIVE NUCLEI PRODUCED BY CAPTURE OF POLARIZED NEUTRONS - SOME NEW APPLICATIONS

1982 ◽  
Vol 43 (C7) ◽  
pp. C7-305-C7-308
Author(s):  
H. Ackermann ◽  
B. Bader ◽  
P. Freiländer ◽  
P. Heitjans ◽  
G. Kiese ◽  
...  
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Polarized Neutrons ◽  
New Applications ◽  
Nuclear Magnetic

WHO WHO'S STRATEGY IN THE NATIONAL MEDICINE SECTOR FOR 2013-2023 AND NEW APPLICATIONS OF PHYTOTIC PRODUCTION IN THE CARPATHIANS

Fitoterapia ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 74-75
Author(s):  
O. I. Voloshуn ◽  
◽  
M. M. Stovpyuk ◽  
O. V. Hyndych ◽  
L. O. Voloshina ◽  
...  
Keyword(s):  
The Carpathians ◽  
New Applications

THE HEXOSAMINE CONTENT OF THE ORBIT IN RELATION TO ANTI-THYROTROPHIN ANTIBODY TITRES IN SERA OF THYROTROPHIN-TREATED RABBITS WITH AND WITHOUT CORTISONE ADMINISTRATION

1962 ◽  
Vol 41 (3) ◽  
pp. 474-480 ◽  
Author(s):  
Otto Wegelius ◽  
E. J. Jokinen
Keyword(s):  
Connective Tissue ◽  
Guinea Pigs ◽  
Antibody Formation ◽  
Direct Proof ◽  
Significant Rise ◽  
Extraocular Muscles ◽  
Concomitant Treatment ◽  
Antibody Titres ◽  
Hexosamine Content ◽  
Synergetic Action

ABSTRACT In all previous investigations on experimental exophthalmos, heterologous thyrotrophic pituitary extracts have been used. These protein hormones stimulate antihormone formation in the test animals. Cortisone has been reported to effectively block antibody formation. In addition, it has been shown to potentiate TSH-induced exophthalmos in guinea-pigs. With rabbits as test animals, the hexosamine content of the orbital tissues was determined and used as an index of exophthalmos development and at the same time the antibody titres in the sera were followed. TSH injections for six weeks led to a highly significant accumulation of hexosamine in the retrobulbar connective tissue and in the extraocular muscles, i. e. an increase of up to 400% as compared with the control animals. At the same time a significant rise in antihormonal titres was detectable in the sera. Concomitant treatment with cortisone brought about an equal or higher accumulation of hexosamine but significantly lower antibody titres. The known opposite peripheral actions of TSH and cortisone can be reconciled with the synergy in producing experimental exophthalmos by attributing the synergetic action of cortisone to the blocking of antihormone formation. If less antihormones are produced, the effect of TSH is enhanced. Our experiments do not provide direct proof for this hypothesis. High hexosamine values in the orbit and low antihormone titres in the serum are, however, concomitant phenomena.

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