On the solvability of a subclass of the surányi reduction class

1963 ◽  
Vol 28 (3) ◽  
pp. 237-244
Author(s):  
Richard Goldberg
Keyword(s):  
Present Note ◽  
Direct Proof ◽  
Finite Domain ◽  
Reduction Class

In [1] Dreben showed that the subclass K′ (described below) of the Suranyi reduction class is recursively solvable by showing that the subclass is finitely controllable; that is, by showing that any member S of K′ is satisfiable only if it is finitely satisfiable. Dreben's argument is very complex, but much of the complexity is due to his proving not merely solvability, but the deeper property of finite controllability. In the present note, by exploiting certain features of Dreben's technique, a simpler, direct proof of the solvability of K′ is obtained — that is, a proof in which the question of satisfiability in a finite domain plays no role.

scholarly journals Proof of the Combinatorial Nullstellensatz over Integral Domains, in the Spirit of Kouba

10.37236/463 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Peter Heinig
Keyword(s):  
General Result ◽  
Duality Theory ◽  
Integral Domain ◽  
Present Note ◽  
Direct Proof ◽  
Vector Spaces ◽  
Combinatorial Nullstellensatz ◽  
Integral Domains ◽  
Sole Purpose ◽  
Cramer’S Rule

It is shown that by eliminating duality theory of vector spaces from a recent proof of Kouba [A duality based proof of the Combinatorial Nullstellensatz, Electron. J. Combin. 16 (2009), #N9] one obtains a direct proof of the nonvanishing-version of Alon's Combinatorial Nullstellensatz for polynomials over an arbitrary integral domain. The proof relies on Cramer's rule and Vandermonde's determinant to explicitly describe a map used by Kouba in terms of cofactors of a certain matrix. That the Combinatorial Nullstellensatz is true over integral domains is a well-known fact which is already contained in Alon's work and emphasized in recent articles of Michałek and Schauz; the sole purpose of the present note is to point out that not only is it not necessary to invoke duality of vector spaces, but by not doing so one easily obtains a more general result.

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

Evaluation of Second- and Third-Level Variance Proportions in Multilevel Designs With Completely Observed Populations: A Note on a Latent Variable Modeling Procedure

2021 ◽  
pp. 001316442110086
Author(s):  
Tenko Raykov ◽  
Natalja Menold ◽  
Jane Leer
Keyword(s):  
Latent Variable ◽  
Large Scale ◽  
Present Note ◽  
Interval Estimation ◽  
Psychological Research ◽  
Latent Variable Modeling ◽  
Model Choice ◽  
Modeling Methodology ◽  
Level 3 ◽  
Level 2

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity of large-scale studies in these and cognate disciplines. The present note discusses a readily applicable procedure for point-and-interval estimation of the proportions of second- and third-level variances in such multilevel settings, which may also be employed in model choice considerations regarding ensuing analyses for response variables of interest. The method is developed within the framework of the latent variable modeling methodology, is readily utilized with widely used software, and is illustrated with an example.

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