A Direct Proof of Pitot’s Theorem

2021 ◽  
pp. 1-2
Quang Hung Tran
M.L.A. Dass ◽  
T.A. Bielicki ◽  
G. Thomas ◽  
T. Yamamoto ◽  
K. Okazaki

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.

1962 ◽  
Vol 41 (3) ◽  
pp. 474-480 ◽  
Otto Wegelius ◽  
E. J. Jokinen

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.

Claude Carlet ◽  
Kwang Ho Kim ◽  
Sihem Mesnager

2021 ◽  
pp. 2003714
Hyeonseok Moon ◽  
Kwang‐Ho Ha ◽  
Yuwon Park ◽  
Jungho Lee ◽  
Mi‐Sook Kwon ◽  

Swen Lang ◽  
Michael Dyballa ◽  
Yvonne Traa ◽  
Deven Estes ◽  
Elias Klemm ◽  

2006 ◽  
Vol 243 (13) ◽  
pp. 3221-3225 ◽  
Jiří Čech ◽  
Seamus A. Curran ◽  
Donghui Zhang ◽  
James L. Dewald ◽  
Aditya Avadhanula ◽  

Fractals ◽  
2011 ◽  
Vol 19 (02) ◽  
pp. 221-226 ◽  

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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