In this article, standard bases of a finitely generated vector space over a linearly ordered commutative incline are studied. We obtain that if a standard basis exists, then it is unique. In particular, if the incline is solvable or multiplicatively-declined or multiplicatively-idempotent (i.e....
Further, we describe hUi in this case: as a valued K-vector space, it is uniquely determined by the valued F -vector space F U (Proposition 4.3). Moreover, its components are just the subspaces generated by the corresponding components of U (Proposition 3.10), and its value set is ...
& Herz, A. V. M. Connecting multiple spatial scales to decode the population activity of grid cells. Sci. Adv. 1, e1500816 (2015). Article ADS PubMed PubMed Central Google Scholar Sarel, A., Finkelstein, A., Las, L. & Ulanovsky, N. Vectorial representation of spatial goals in ...
Probing the periodic lattice deformation in the reciprocal space. (a) Rock-salt type crystal structure of CoO. (b) HR-TEM image of CoO showing the interface with the sapphire substrate. The inset image shows a large-scale bright-field image of the CoO thin film. (c) EDP showing the crys...
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Just like many scientific giants, Issac Newton (1643–1727) was also a weirdo. He was anti-social and aggressive, unique in thinking as well as actions, at the same time refusing to yield to authority. Born in the county of Lincolnshire, he later moved t
This chapter has proposed an overview of set-functions valued on a totally ordered scale, with emphasis on the simplest of such set-functions, found in possibility theory. The corresponding relations on a power set describing the relative confidence of events have been studied. It has been shown...
__m128d _mm_cmpord_sd (__m128d a, __m128d b) CMPSD xmm, xmm/m64, imm8(7) C# 复制 public static System.Runtime.Intrinsics.Vector128<double> CompareScalarOrdered (System.Runtime.Intrinsics.Vector128<double> left, System.Runtime.Intrinsics.Vector128<double> right); Parameters left ...
Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a spatial coordinate system. However, irregularities in the grid pattern as well as responses of grid cells in contexts other than spatial navigation have
Introduction If F is an ordered field, an F-metric space is a set X together with a metric p : X x X —> F. This concept appears to be an interesting generalization of the classical real metric space. An example of a nonclassi-cal F-metric space is the hyperreal field *R studied...