Tobin's average q has usually been well above 1, but fell below 1 during 1974-1984. Our model explains this pattern and reconciles it with unchanging aggregate investment. The stock market value in the numerator of q reflects ownership of physical capital and knowledge, but the denominator measures just physical capital. Therefore, q is usually above 1. Periodic arrivals of important new technologies, such as the microprocessor in the 1970's, suddenly render old knowledge and capital obsolete, causing the stock market to drop. National accounts measures of physical capital miss this rapid obsolescence. Then q appears to drop below 1. (JEL E44, O3, O41)

In this paper we develop the method of finding sharp estimates by using a Bellman function. In such a form the method appears in the proofs of the classical John-Nirenberg inequality and L p estimations of BMO functions. In the present paper we elaborate a method of solving the boundary value problem for the homogeneous Monge-Ampère equation in a parabolic strip for sufficiently smooth boundary conditions. In such a way, we have obtained an algorithm for constructing an exact Bellman function for a large class of integral functionals on the BMO space.

Let {T 1 , . . . , T l } be a collection of differential operators with constant coefficients on the torus T n . Consider the Banach space X of functions f on the torus for which all functions T j f , j = 1, . . . , l, are continuous. Extending the previous work of the first two authors, we analyse the embeddability of X into some space C(K) as a complemented subspace. We prove the following. Fix some pattern of mixed homogeneity and extract the senior homogeneous parts (relative to the pattern chosen) {τ 1 , . . . , τ l } from the initial operators {T 1 , . . . , T l }. Let N be the dimension of the linear span of {τ 1 , . . . , τ l }. If N 2, then X is not isomorphic to a complemented subspace of C(K) for any compact space K.The main ingredient of the proof of this fact is a new Sobolev-type embedding theorem. In general, we use the mapping t → e 2πit to parametrise the unit circle; so, the trigonometric system is {e 2πikt } k∈Z , t ∈ [0, 1), and the (multiple) Fourier series are handled accordingly.

We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of martingales and an extremal problem on this class, which is dual to the minimization problem for locally concave functions.

This paper develops a dynamic model with transaction costs to determine the equilibrium resale pattern in a market for a durable good. The key result is that the probability of resale is nonmonotonic in the age of the good. Trade volume is relatively low in the very beginning and in the middle of a good's life. This result helps explain observed variations of resale rates across vintages for the U.S. market of used cars.

This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12-15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's 60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves. Contents: R. Lazarsfeld, Some remarks on the work of Lawrence Ein; A. Calabri and C. Ciliberto, Contractible curves on a rational surface; F. Catanese, On the canonical map of some surfaces isogenous to a product; C. Ciliberto, F. Flamini, C. Galati, and A. L. Knutsen, Degeneration of differentials and moduli of nodal curves on 3 surfaces; I. Coskun and J. Huizenga, Weak Brill-Noether for rational surfaces; R. Datta and K. E. Smith, Excellence in prime characteristic; M. González Villa, A. Libgober, and L. Maxim, Motivic zeta functions and infinite cyclic covers; C. Hacon, M. Popa, and C. Schnell, Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun; S. Ishii and W. Niu, A strongly geometric general residual intersection; J. Kollár, Quadratic solutions of quadratic forms; S. J Kovács, Non-Cohen-Macaulay canonical singularities; N. Mok, Full cones swept out by minimal rational curves on irreducible Hermitian symmetric spaces as examples of varieties underlying geometric substructures; M. Mustaţă and Y. Nakamura, A boundedness conjecture for minimal log discrepancies on a fixed germ; E. Sernesi, The Wahl map of one-nodal curves on K3 surfaces; Y.-T. Siu, Skoda's ideal generation from vanishing theorem for semipositive Nakano curvature and Cauchy-Schwarz inequality for tensors; C. Voisin, Hyper-Kähler compactification of the intermediate Jacobian fibration of a cubic fourfold: The twisted case.

We construct key household and individual economic variables using a panel micro data set from the Russia Longitudinal Monitoring Survey (RLMS) for [1994][1995][1996][1997][1998][1999][2000][2001][2002][2003][2004][2005]. We analyze cross-sectional income and consumption inequality and find that inequality decreased during the 2000-2005 economic recovery. The decrease appears to be driven by falling volatility of transitory income shocks. The response of consumption to permanent and transitory income shocks becomes weaker later in the sample, consistent with greater self-insurance against permanent shocks and greater smoothing of transitory shocks. Finally, expenditure and income inequality in Russia are not far apart.

In this paper we develop the method of finding sharp estimates by using a Bellman function. In such a form the method appears in the proofs of the classical John-Nirenberg inequality and L p estimations of BMO functions. In the present paper we elaborate a method of solving the boundary value problem for the homogeneous Monge-Ampère equation in a parabolic strip for sufficiently smooth boundary conditions. In such a way, we have obtained an algorithm for constructing an exact Bellman function for a large class of integral functionals on the BMO space.