The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.

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...

Teachers can often readily identify students who demonstrate high or low motivation in a certain task. Motivated students engage in the task with intensity and feeling, whereas unmotivated students procrastinate and indicate in other ways that they would rather do something else. These differences exemplify the quantitative dimension of motivation, ranging from high to low. Teachers can often a...

A central tenet of economics is that individuals respond to incentives. For psychologists and sociologists, in contrast, rewards and punishments are often counterproductive, because they undermine “intrinsic motivation”. We reconcile these two views, showing how performance incentives offered by an informed principal (manager, teacher, parent) can adversely impact an agent’s (worker, child) per...