Continuous system dynamics can be described by possibly large systems of di erential equations These can be either ordinary di erential equations ODEs or contain algebraic constraints as well to form di erential and algebraic equations DAEs Complex systems such as aircraft often operate in di erent modes of continuous operation and when mode changes occur the continuous dynamics change abruptly...

We propose a method to represent solid objects as multiple combinations of globally deformed supershapes. Our approach handles primitives that have both parametric and implicit representations. An implicit equation with guaranteed di erential properties is obtained by combinations of the primitives' implicit representations using R-functions. The surface corresponding to the zero-set of the imp...

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 ...

We present a scheme for the determination of control Lyapunov functions which can be used as a basis for numerical computations. Under the assumption of local asymptotic nullcontrollability we de ne the domain of asymptotic nullcontrollability. On this set a control Lyapunov function is de ned via an optimal control problem. It is then shown that this function can be characterized as the unique...

We reformulate the self-dual Einstein equation as a trio of di erential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2D sigma models valued in in nite-dimensional group, which was shown by Park and Husain earlier. We also derive other eld theories including the 2D Higgs bundle equation. This formulation elucidates the relation among thos...

Thickeners for solid±liquid separation are still designed and controlled empirically in the mining industry. Great e€orts are being made to develop mathematical models that will change this situation. Starting from the basic principles of continuum mechanics, the authors developed a phenomenological theory of sedimentation for ̄occulated suspensions which takes the compressibility of the ̄ocs u...

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 ...

There are three di erent actions of the unimodular Lie group SL on a two dimensional space In every case we show how an ordinary di erential equation admitting SL as a symmetry group can be reduced in order by three and the solution recovered from that of the reduced equation via a pair of quadratures and the solution to a linear second order equation A particular example is the Chazy equation ...