868,274 research outputs found
Refinement Derivatives and Values of Games
A definition of set-wise differentiability for set functions is given through refining the partitions of sets. Such a construction is closely related to the one proposed by Rosenmuller (1977) as well as that studied by Epstein (1999) and Epstein and Marinacci (2001). We present several classes of TU games which are differentiable and study differentiation rules. The last part of the paper applies refinement derivatives to the calculation of value of games. Following Hart and Mas-Colell (1989), we define a value operator through the derivative of the potential of the game. We show that this operator is a truly value when restricted to some appropriate spaces of games. We present two alternative spaces where this occurs: the spaces pM( ) and POT2. The latter space is closely related to Myerson's balanced contribution axiom.TU games; large games; non-additive set functions; value; derivatives
Local identification in nonseparable models
Conditions are derived under which there is local nonpara
metric identification of values of structural functions and of their derivatives in potentially nonlinear nonseparable models. The attack on this problem is via conditional quantile functions and exploits local quantile independence conditions. The identification conditions include local analogues of the order and rank conditions familiar in the analysis of linear simultaneous equations models. The derivatives whose identification is sought are derivatives of structural equations at a point defined by values of covariates and quantiles of the distributions of the stochastic drivers of the system. These objects convey information about the distribution of the exogenous impact of changes in variables potentially endogenous in the data generating process. The identification conditions point directly to analogue estimators of derivatives of structural functions which are functionals of quantile regression function estimators
Existence of Hilbert cusp forms with non-vanishing -values
We give a derivative version of the relative trace formula on PGL(2) studied
in our previous work, and obtain a formula of an average of central values
(derivatives) of automorphic -functions for Hilbert cusp forms. As an
application, we prove existence of Hilbert cusp forms with non-vanishing
central values (derivatives) such that the absolute degrees of their Hecke
fields are sufficiently large
Derivatives of tangent function and tangent numbers
In the paper, by induction, the Fa\`a di Bruno formula, and some techniques
in the theory of complex functions, the author finds explicit formulas for
higher order derivatives of the tangent and cotangent functions as well as
powers of the sine and cosine functions, obtains explicit formulas for two Bell
polynomials of the second kind for successive derivatives of sine and cosine
functions, presents curious identities for the sine function, discovers
explicit formulas and recurrence relations for the tangent numbers, the
Bernoulli numbers, the Genocchi numbers, special values of the Euler
polynomials at zero, and special values of the Riemann zeta function at even
numbers, and comments on five different forms of higher order derivatives for
the tangent function and on derivative polynomials of the tangent, cotangent,
secant, cosecant, hyperbolic tangent, and hyperbolic cotangent functions.Comment: 17 page
Global stabilization of multiple integrators by a bounded feedback with constraints on its successive derivatives
In this paper, we address the global stabilization of chains of integrators
by means of a bounded static feedback law whose p first time derivatives are
bounded. Our construction is based on the technique of nested saturations
introduced by Teel. We show that the control amplitude and the maximum value of
its p first derivatives can be imposed below any prescribed values. Our results
are illustrated by the stabilization of the third order integrator on the
feedback and its first two derivatives
Recommended from our members
Branch points, m. Fractions, and rational functions matching both derivatives and values
- …