Three schemes for linearizing the transconductance of the basic di erential pair in subthreshold CMOS are examined: 1) multiple asymmetric di erential pairs, 2) source degeneration via symmetric di usors, and 3) source degeneration via a single di usor. Using a maximally at optimizing criterion, the linear range of the basic di erential pair can be increased by four-to-eight times.

An action system framework is a predicate transformer based method for modelling and analysing distributed and reactive systems. The actions are statements in Dijkstra's guarded command language, and their semantics is given by predicate transformers. We extend conventional action systems with a di erential action consisting of a di erential equation and an evolution guard. The semantics is giv...

We introduce and study the Koszul complex for a Hecke R-matrix. Its cohomologies, called the Berezinian, are used to de ne quantum superdeterminant for a Hecke R-matrix. Their behaviour with respect to Hecke sum of R-matrices is studied. Given a Hecke R-matrix in n-dimensional vector space, we construct a Hecke R-matrix in 2n-dimensional vector space commuting with a di erential. The notion of ...

We consider the di?erential equation f<sup>''</sup> +A(z)f<sup>'</sup> +B(z)f = 0, where A(z) and B(z) are entire complex functions. improve various restrictions on coe?cients prove that all non-trivial solutions of in?nite order.

1. Stochastic Integration on Hilbert spaces 2 1.1. Gaussian measures on Hilbert spaces 2 1.2. Wiener processes on Hilbert spaces 6 1.3. Martingales on Banach spaces 7 1.4. Stochastic integration 8 1.5. Appendix: Stochastic integration w.r.t. cylindrical Wiener processes 12 2. Stochastic Di erential Equations on Hilbert spaces 13 2.1. Mild, weak and strong solutions 13 2.2. Existence and uniquen...

The aim of this lecture is to study numerical algorithms for the integration of stochastic di erential equations. I will derive an algorithmwhich exactly integrates the SDE, using a generalization of a Taylor series in the presence of stochastic forces. Given the complexity, we will nd that this algorithm, although \exact", it is not particularly fast or, in general, the most convenient in a di...

dae and pdae are systems of ordinary and partial di erential-algebraic equations with constraints. They occur frequently in applications such as constrained multibody mechanics, space-craft control and incompressible uid dynamics. A dae has di erential index r if a minimum of r+1 di erentiations of it are required before no new constraints are obtained. While dae of low di erential index (0 or ...

This paper considers the security of iterated block ciphers against the di erential cryptanalysis introduced by Biham and Shamir. Di erential cryptanalysis is a chosen-plaintext attack on secret-key block ciphers that are based on iterating a cryptographically weak function r times (e.g., the 16-round Data Encryption Standard (DES) ). It is shown that the success of such attacks on an r-round c...

We have studied two person stochastic di erential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero sum case we have proved the existence of a Nash equilibrium.

We present an introduction to mathematical Finance Theory for math ematicians The approach is to start with an abstract setting and then introduce hypotheses as needed to develop the theory We present the basics of European call and put options and we show the connection between American put options and backwards stochastic di erential equations