A Direct Proof of De Moivre's Formula

1916 ◽  
Vol 23 (10) ◽  
pp. 366 ◽  
Author(s):  
S. Lefschetz
Keyword(s):  
Direct Proof ◽  
De Moivre’S Formula

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.

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.

scholarly journals A direct proof of APN-ness of the Kasami functions

2021 ◽  
Author(s):  
Claude Carlet ◽  
Kwang Ho Kim ◽  
Sihem Mesnager
Keyword(s):  
Direct Proof

scholarly journals Direct Proof of the Reversible Dissolution/Deposition of Mn 2+ /Mn 4+ for Mild‐Acid Zn‐MnO 2 Batteries with Porous Carbon Interlayers

2021 ◽  
pp. 2003714
Author(s):  
Hyeonseok Moon ◽  
Kwang‐Ho Ha ◽  
Yuwon Park ◽  
Jungho Lee ◽  
Mi‐Sook Kwon ◽  
...  
Keyword(s):  
Porous Carbon ◽  
Direct Proof ◽  
Mild Acid

scholarly journals Direct Proof of Volatile and Adsorbed Hydrocarbons on Solid Catalysts by Complementary NMR Methods 

2021 ◽  
Author(s):  
Swen Lang ◽  
Michael Dyballa ◽  
Yvonne Traa ◽  
Deven Estes ◽  
Elias Klemm ◽  
...  
Keyword(s):  
Direct Proof ◽  
Solid Catalysts ◽  
Nmr Methods

Functionalization of multi-walled carbon nanotubes: Direct proof of sidewall thiolation

2006 ◽  
Vol 243 (13) ◽  
pp. 3221-3225 ◽  
Author(s):  
Jiří Čech ◽  
Seamus A. Curran ◽  
Donghui Zhang ◽  
James L. Dewald ◽  
Aditya Avadhanula ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Direct Proof ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

ON THE ASSOUAD DIMENSION OF GRAPH DIRECTED MORAN FRACTALS

Fractals ◽  
2011 ◽  
Vol 19 (02) ◽  
pp. 221-226 ◽  
Author(s):  
L. OLSEN
Keyword(s):  
Direct Proof ◽  
Open Set Condition ◽  
Open Set ◽  
Assouad Dimension ◽  
Box Dimensions

We give a simple and direct proof of the fact that the Assouad dimension of a graph directed Moran fractal satisfying the Open Set Condition coincides with its Hausdorff and box dimensions.

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