We construct an example of a torus T over a field K for which the Galois symbol K(K;T, T )/nK(K; T, T ) → H(K,T [n] ⊗ T [n]) is not injective for some n. Here K(K; T, T ) is the Milnor K-group attached to T introduced by Somekawa. We show also that the motive M(T×T ) gives a counterexample to another generalization of the Milnor-BlochKato conjecture (proposed by Beilinson).

Strategic market games model strategic exchange economies as noncooperative simultaneous moves games. A recent paper by Bloch and Ghosal (J. Econ. Theory, 74 (1997), 368{384.) has shown that strategic market games might exhibit a rather counterintuitive comparative statics property: an increase in the number of traders on the own side of the market might increase the equilibrium utility for any...

This is a sequel to [FJ]. It will give a more natural framework for constructing elements in the Hopf algebra χF of framed mixed Tate motives according to Bloch and Křiž [BK]. This framework allows us to extend the results of [FJ] to interpret all multiple zeta values (including the divergent ones) and the multiple polylogarithms in one variable as elements of χF . It implies that the pro-unipo...

We study point-sphere and point-plane incidences in three-dimensional space. In particular, for 1 < k < n, we say that a set of spheres (resp., planes) is k-non-degenerate if no circle is contained in k spheres of the set (resp., if no line is contained in k planes of the set). We prove that, for every ε > 0, the number of incidences between a set of m points and a k-non-degenerate set of n sph...

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We present a reformulation of the plane-wave pseudopotential method for insulators. This new approach allows us to perform density-functional calculations by solving directly for ‘‘nonorthogonal generalized Wannier functions’’ rather than extended Bloch states. We outline the theory on which our method is based and present test calculations on a variety of systems. Comparison of our results wit...

In this paper we will prove Goncharov’s 22-term relations (see [A.B. Goncharov, Geometry of configurations, polylogarithms and motivic cohomology, Adv. Math. 114 (1995) 179–319. [G1]]) in the linearized version of Bloch’s higher Chow group CH3(F,5) using linear fractional cycles of Bloch, Kriz and Totaro under the Beilinson–Soulé vanishing conjecture that CH2(F,n)= 0 for n 4. © 2006 Elsevier In...

The objective of this work was to analyze the degree physical activity university teachers before and during Covid-19 pandemic, in context social isolation. present study adopts a quantitative cross-sectional approach. sample determined randomly, made up 129 professors from Faculty Physical Culture Sciences Autonomous University Chihuahua, aged between 18 74 years. results show that 50.39% pand...

Subject of research: the state tourist and recreational sphere Nizhnevartovsk region Khanty-Mansiysk Autonomous Okrug Yugra.&#x0D; Purpose to develop promising areas for sustainable development tourism industry in northern territory face reduced competition from foreign operators closure external destinations.&#x0D; Methods objects statistical, comparative, strategic analysis were used as main ...