Stability criteria of the Bendixon type

Summary In this paper we consider a system of two first order differential equations {x′=P(x,y). y′=Q(x,y)}. We usually assume that ∂P/∂x+∂Q/∂y vanish identically in a certain region. A number of conditions are then given to insure boundedness of solutions or asymptotic stability of the zero solution. Entrata in Redazione il 5 gennaio 1972.     

Fixed points and stability of a nonconvolution equation

In this note we consider an equation of the form

and give conditions on and to ensure that the zero solution is asymptotically stable. When applied to the classical case of , these conditions do not require that , nor do they involve the sign of or the sign of any derivative of .

     

Forward selection radial basis function networks applied to bacterial classification based on MALDI-TOF-MS

Forward selection improved radial basis function (RBF) network was applied to bacterial classification based on the data obtained by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS). The classification of each bacterium cultured at different time was discussed and the effect of parameters of the RBF network was investigated. The new method involves forward selection to prevent overfitting and generalized cross-validation (GCV) was used as model selection criterion (MSC). The original data was compressed by using wavelet transformation to speed up the network training and reduce the number of variables of the original MS data. The data was normalized prior training and testing a network to define the area the neural network to be trained in, accelerate the training rate, and reduce the range the parameters to be selected in. The one-out-of-n method was used to split the data set of p samples into a training set of size p−1 and a test set of size 1. With the improved method, the classification correctness for the five bacteria discussed in the present paper are 87.5, 69.2, 80, 92.3, and 92.8%, respectively.     

Stationary measures for randomly chosen maps

A Markov process on a compact metric space,X is given by random transformations.S is a finite set of continuous transformations ofX to itself. A random evolution onX is defined by lettingx inX evolve toT(x) forT inS with probability that depends onx andT but is independent of any other past measurable events. This type of model is often called a place dependent iterated function system. The transformations are assumed to have either monotone or contractive properties. Theorems are given to describe the number and types of ergodic invariant measures. Special emphasis is given to learning models and self-reinforcing random walks.Supported in part by AFOSR Grant No. 91-0215, the Alexander von Humboldt Foundation and SFB 170, University of Göttingen.     

A novel staining technique for studying toughening mechanisms in saturated acrylic rubber-modified polymers

A novel technique which utilizes a two-stage staining approach, (i.e., styrene absorption followed by osmium tetraoxide staining) is introduced for staining saturated polyacrylate rubbers. This novel staining approach, which stains and hardens polyacrylate rubber, is found to be useful for room temperature microtomy of polyacrylate rubber-modified polymers. Therefore, both the morphology and the crack tip toughening mechanisms of polyacrylate rubber-modified systems can be studied. Details concerning staining time, staining media, and use of solvents are discussed.     

Periodic solutions of a forced Liénard equation

This research was carried out under a grant form C.N.R. (Italy) while the author was visiting the University of Firenze in the fall of 1992. That support and the gracious hospitality of that university are gratefully acknowledged.