First order neutral di¤erential equations are studied and su‰cient conditions are derived for every solution to be oscillatory. Our approach is to reduce the oscillation of neutral di¤erential equations to the nonexistence of eventually positive solutions of non-neutral di¤erential inequalities. Our results extend and improve several known results in the literature.

This work presents the arguments for the possibility of approximating some discontinuous dynamical systems with continuous or even smooth dynamical systems. The discontinuous di€erential equation, which describes the system, is transformed into a di€erential inclusion and then into a di€erential equation with continuous or smooth right-hand side. As an example a generalization of the equations ...

| Four schemes for linearizing the transconductance of the basic di erential pair in subthreshold CMOS are examined. They are: source degeneration via (1) diode-connected transistors, (2) a single di usor and (3) symmetric di usors, and (4) multiple asymmetric di erential pairs. We derive equations for the di erential output current for each linearizing technique. We apply a maximally at optimi...

In a di erential equations course, one typically studies a few classes of problems for which there are closed form solutions, such as ordinary, linear di erential equations with constant coe cients. Most problems of interest in real world simulation problems are much more complex, however, involving domains of two or more dimensions or nonlinear e ects, yielding partial di erential equations or...

ADi erentially controlled monolithic LC-VCO along with a di erential charge pump are used to implement a di erential PLL for substrate noise immunity. The di erential VCO control is achieved with minimal increase in the power consumption and without sacri cing the tuning range. In a 0.5 m CMOS technology the measured VCO phase noise is -119dBc @1.0MHz and the tuning range is 26% of the 1.25GHz ...

In this paper, the classic straightening out theorem from di erential geometry is used to derive necessary and su cient conditions for locally converting rectangular di erential inclusions to constant rectangular di erential inclusions. Both scalar and coupled di erential inclusions are considered. The results presented in this paper have use in the area of computer aided veri cation of hybrid ...

One of the most important theorems in Ordinary Di↵erential Equations is Picard’s Existence and Uniqueness Theorem for first-order ordinary di↵erential equations. Why is Picard’s Theorem so important? One reason is it can be generalized to establish existence and uniqueness results for higher-order ordinary di↵erential equations and for systems of di↵erential equations. Another is that it is a g...

The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ productivities does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show ...

This paper proposes a method of discovering some kinds of di erential equations with interval coe cients, which characterize or explain numerical data obtained by scienti c observations and experiments. Such numerical data inevitably involve some ranges of errors, and hence they are represented by closed intervals in this paper. Based on these intervals, we design some interval inclusions which...

in this paper, a new and ecient approach based on operational matrices with respect to the gener-alized laguerre polynomials for numerical approximation of the linear ordinary dierential equations(odes) with variable coecients is introduced. explicit formulae which express the generalized la-guerre expansion coecients for the moments of the derivatives of any dierentiable function in terms...