the stability of learning rate in neural network identifiers and controllers is one of the challenging issues which attracts great interest from researchers of neural networks. this paper suggests adaptive gradient descent algorithm with stable learning laws for modified dynamic neural network (mdnn) and studies the stability of this algorithm. also, stable learning algorithm for parameters of ...

The use of auxiliary functions in nonparametric inference for theM/G/∞ queueinging model is considered. Estimation of the service time distribution G is challenging when only limited information about the busy/idle cycle is available. It is shown, using diagnostic plots of estimators, that a standard auxiliary function aimed at providing numerical stability fails in that regard but that a relia...

This paper reviews the problem of a thin rigid rod sliding on a horizontal surface in the plane, which is commonly cited as an example of the inconsistency of planar rigid-body Newtonian mechanics. We demonstrate the existence of a consistent solution, using Routh's analysis of rigid-body impact. Copyright © 1987 Carnegie-Mel lon University This work was supported under grants from the System D...

We consider the partitioning of a society into coalitions in purely hedonic settings; i.e., where each player's payo is completely determined by the identity of other members of her coalition. We rst discuss how hedonic and non-hedonic settings di er and some su cient conditions for the existence of core stable coalition partitions in hedonic settings. We then focus on a weaker stability condit...

Life on earth drives a continuous exchange of carbon between soils and the atmosphere. Some forms of soil carbon, or organic matter, are more stable and have a longer residence time in soil than others. Relative differences in stability have often been derived from shifts in δ13C (which is bound to a vegetation change from C3 to C4 type) or through 14C-dating (which is bound to small sample num...

We briefly sketch the methods for a numerically stable evaluation of tensor one-loop integrals that have been used in the calculation of the complete electroweak one-loop corrections to e + e − → 4 fermions. In particular, the improvement of the new methods over the conventional Passarino–Veltman reduction is illustrated for some 4-point integrals in the delicate limits of small Gram (and other...

We prove upper bounds for the first eigenvalue of the Laplacian of hypersurfaces of Euclidean space involving anisotropic mean curvatures. Then, we study the equality case and its stability.

A class of linear hyperbolic systems of conservation laws with multiple time scales which are modeled by a perturbation parameter is considered in this paper. By setting the perturbation parameter to zero, two subsystems, the reduced subsystem standing for the slow dynamics and the boundary-layer subsystem representing the fast dynamics, are computed. It is first proved that the exponential sta...