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.

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 ...

In this paper we derive the sharp long time stability and error estimates of nite element approximations for parabolic integro di erential equations First the exponential decay of the solution as t is studied and then the semi discrete and fully discrete approximations are considered using the Ritz Volterra projection Other related problems are studied as well The main feature of our analysis i...

Much work paralleling the standard theory of linear di erential equations has been done recently for dynamic equations on time scales, providing a uni ed treatment of the continuous and discrete analysis in this area. One area which is less developed is the theory of series solutions, partly due to the lack of suÆcient di erentiability in a general time scale, and also due to the lack of an ana...

Collocation schemes are presented for solving linear fourth order di erential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalen...

The semi-implicit Euler discretization method is studied for abstract evolution equations in a Hilbert space H, like _ u = f(t; u; u) ; t 2 (0; T ] ; u(0) = u0, where f(t; ; v) is one-sided Lipschitz and R(I hf(t; ; v)) = H for h > 0 su ciently small, and f(t; u; ) is Lipschitz-continuous. Extension to Banach spaces is then pointed out. Ordinary and partial , di erential and integro-di erential...

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 round Data Encryption Standard DES It is shown that the success of such attacks on an r round cipher depend...

We consider di erent situations of blowup in sup norm for hyper bolic equations For scalar conservation laws with a source the asymptotic pro le of the solution close to a blowup point is described in detail Based on an example of Je rey we next show how blowup for ordinary di erential equations can be used to construct examples of blowup for systems of hy perbolic equations Finally we outline ...

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...

The vebrane worldvolume theory in eleven dimensions is known to contain BPS threebrane solitons which can also be interpreted as a vebrane whose worldvolume is wrapped around a Riemann surface. By considering con gurations of intersecting vebranes and hence intersecting threebrane solitons, we determine the Bogomol'nyi equations for more general BPS con gurations. We obtain di erential equation...