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Constant Functions (constant + function)

Distribution by Scientific Domains

Mathematics and Statistics	33%
Business, Economics, Finance and Accounting	33%

Selected Abstracts

Accurate motion-produced distance and direction under systematically distorted perception

JAPANESE PSYCHOLOGICAL RESEARCH, Issue 3 2005
NAOFUMI FUJITA
Abstract:, We report the visually directed actions of soccer players. After perceiving the location of a target on their left side at the starting point and traveling toward the ball without seeing the target, the players could kick the ball accurately (Experiment 2). In contrast, if they were verbally asked the direction of the target in a similar situation, the perceived direction was systematically distorted (Experiment 3). Our major concern in explaining the distorted perception was whether the egocentric distance before locomotion was perceived accurately or not, and whether the updating of the target location during locomotion was accurate or not. Combining these two possibilities, there should be four hypotheses, each of which assumes either: (1) accurate egocentric distance and accurate updating, (2) inaccurate egocentric distance and accurate updating, (3) accurate egocentric distance and inaccurate updating, or (4) inaccurate egocentric distance and inaccurate updating. Based on these hypotheses, we conducted four simulations, which revealed that the combination of the perception of the accurate egocentric distance and the distorted updating that substituted the constant function for the sine function produced not only a good r2, but also three kinds of interactions obtained in Experiment 3. Why did the players, based on their distorted perception, perform accurately? We would like to suggest that through perceptual learning they might acquire a perceptual-motor relation as the inverse function of the physical-perceptual relation. [source]

Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2008
Tobias H. Colding
We show that for a Schrödinger operator with bounded potential on a manifold with cylindrical ends, the space of solutions that grows at most exponentially at infinity is finite dimensional and, for a dense set of potentials (or, equivalently, for a surface for a fixed potential and a dense set of metrics), the constant function 0 is the only solution that vanishes at infinity. Clearly, for general potentials there can be many solutions that vanish at infinity. One of the key ingredients in these results is a three circles inequality (or log convexity inequality) for the Sobolev norm of a solution u to a Schrödinger equation on a product N × [0, T], where N is a closed manifold with a certain spectral gap. Examples of such N's are all (round) spheres ,,n for n , 1 and all Zoll surfaces. Finally, we discuss some examples arising in geometry of such manifolds and Schrödinger operators.© 2007 Wiley Periodicals, Inc. [source]

The Limits of ex post Implementation

ECONOMETRICA, Issue 3 2006
Philippe Jehiel
The sensitivity of Bayesian implementation to agents' beliefs about others suggests the use of more robust notions of implementation such as ex post implementation, which requires that each agent's strategy be optimal for every possible realization of the types of other agents. We show that the only deterministic social choice functions that are ex post implementable in generic mechanism design frameworks with multidimensional signals, interdependent valuations, and transferable utilities are constant functions. In other words, deterministic ex post implementation requires that the same alternative must be chosen irrespective of agents' signals. The proof shows that ex post implementability of a nontrivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of differential equations that are not satisfied by generic valuation functions. [source]

A rational approach to mass matrix diagonalization in two-dimensional elastodynamics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
E. A. Paraskevopoulos
Abstract A variationally consistent methodology is presented, which yields diagonal mass matrices in two-dimensional elastodynamic problems. The proposed approach avoids ad hoc procedures and applies to arbitrary quadrilateral and triangular finite elements. As a starting point, a modified variational principle in elastodynamics is used. The time derivatives of displacements, the velocities, and the momentum type variables are assumed as independent variables and are approximated using piecewise linear or constant functions and combinations of piecewise constant polynomials and Dirac distributions. It is proved that the proposed methodology ensures consistency and stability. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Invariance and factorial models

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2000
P. McCullagh
Two factors having the same set of levels are said to be homologous. This paper aims to extend the domain of factorial models to designs that include homologous factors. In doing so, it is necessary first to identify the characteristic property of those vector spaces that constitute the standard factorial models. We argue here that essentially every interesting statistical model specified by a vector space is necessarily a representation of some algebraic category. Logical consistency of the sort associated with the standard marginality conditions is guaranteed by category representations, but not by group representations. Marginality is thus interpreted as invariance under selection of factor levels (I -representations), and invariance under replication of levels (S -representations). For designs in which each factor occurs once, the representations of the product category coincide with the standard factorial models. For designs that include homologous factors, the set of S -representations is a subset of the I -representations. It is shown that symmetry and quasi-symmetry are representations in both senses, but that not all representations include the constant functions (intercept). The beginnings of an extended algebra for constructing general I -representations is described and illustrated by a diallel cross design. [source]

First-Order Schemes in the Numerical Quantization Method

MATHEMATICAL FINANCE, Issue 1 2003
V. Bally
The numerical quantization method is a grid method that relies on the approximation of the solution to a nonlinear problem by piecewise constant functions. Its purpose is to compute a large number of conditional expectations along the path of the associated diffusion process. We give here an improvement of this method by describing a first-order scheme based on piecewise linear approximations. Main ingredients are correction terms in the transition probability weights. We emphasize the fact that in the case of optimal quantization, many of these correcting terms vanish. We think that this is a strong argument to use it. The problem of pricing and hedging American options is investigated and a priori estimates of the errors are proposed. [source]