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《Indagationes Mathematicae》2022,33(4):801-815
We consider the irreducibility of polynomial where is a negative integer. We observe that the constant term of vanishes if and only if . Therefore we assume that where is a non-negative integer. Let and more general polynomial, let where with are integers such that . Schur was the first to prove the irreducibility of for . It has been proved that is irreducible for . In this paper, by a different method, we prove: Apart from finitely many explicitly given possibilities, either is irreducible or is linear factor times irreducible polynomial. This is a consequence of the estimate whenever has a factor of degree and . This sharpens earlier estimates of Shorey and Tijdeman and Nair and Shorey. 相似文献
3.
Generalized quantum measurements with two outcomes are fully characterized by two real parameters, dubbed as sharpness parameter and biasedness parameter and they can be linked with different aspects of the experimental setup. It is known that sharpness parameter characterizes precision of the measurements and decreasing sharpness parameter of the measurements reduces the possibility of probing quantum features like quantum mechanical (QM) violation of local-realism (LR) or macro-realism (MR). Here we investigate the effect of biasedness together with that of sharpness of measurements and find a trade-off between those two parameters in the context of probing QM violations of LR and MR. Interestingly, we also find that the above mentioned trade-off is more robust in the latter case. 相似文献
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Francis Jordan Sam B. Nadler Jr. 《Proceedings of the American Mathematical Society》2001,129(4):1219-1228
It is shown that a continuum that is an space in the sense of Michael must be hereditarily decomposable. This improves known results, thereby providing more evidence that such continua must be dendrites.
6.
Beniamino Cappelletti Montano Antonio De Nicola 《Journal of Geometry and Physics》2007,57(12):2509-2520
We present a compared analysis of some properties of 3-Sasakian and 3-cosymplectic manifolds. We construct a canonical connection on an almost 3-contact metric manifold which generalises the Tanaka–Webster connection of a contact metric manifold and we use this connection to show that a 3-Sasakian manifold does not admit any Darboux-like coordinate system. Moreover, we prove that any 3-cosymplectic manifold is Ricci-flat and admits a Darboux coordinate system if and only if it is flat. 相似文献
7.
Jan Andres Tom Fürst Karel Pastor 《Journal of Mathematical Analysis and Applications》2008,340(2):1132-1144
A full analogy of the celebrated Sharkovsky cycle coexistence theorem is established for lower semicontinuous (multivalued) maps on metrizable linear continua. This result is further extended to triangular maps. 相似文献
8.
Toupin's early theory for an elastic dielectric is called upon to describe main events in an active damper. 相似文献
9.
On potentially negative space time covariances obtained as sum of products of marginal ones 总被引:1,自引:0,他引:1
P. Gregori E. Porcu J. Mateu Z. Sasvári 《Annals of the Institute of Statistical Mathematics》2008,60(4):865-882
Most of the literature on spatio-temporal covariance models proposes structures that are positive in the whole domain. However,
problems of physical, biological or medical nature need covariance models allowing for negative values or oscillations from
positive to negative values. In this paper, we propose an easy-to-implement and interpretable class of models that admits
this type of covariances. We show particular analytical examples that may be of interest in the biometrical context.
Work partially funded by grants GV04A724 (Generalitat Valenciana) and MTM2004-06231 (Spanish Ministry of Science and Education). 相似文献
10.
戴天民 《应用数学和力学(英文版)》2007,28(2):163-172
Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories. 相似文献