The problem of learning qualitative models of physical systems from observations of its behaviour has been addressed by several researchers in recent years. Most current techniques limit themselves to learning a single qualitative di erential equation to model the entire system. However, many systems have several qualitative differential equations underlying them. In this paper, we present an a...

The transformation which assigns to a linear operator L the recurrence satis ed by coe cient se quences of the polynomial series in its kernel is shown to be an isomorphism of the corresponding operator algebras We use this fact to help factoring q di erence and recurrence operators and to nd nice power series solutions of linear di erential equations In particular we characterize generalized h...

A q-di erence analog of the sixth Painlev e equation is presented. It arises as the condition for preserving the connection matrix of linear q-di erence equations, in close analogy with the monodromy preserving deformation of linear di erential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed. Mathematical Subject Classi cations (19...

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...

in this work, we have applied elzaki transform and he's homotopy perturbation method to solvepartial dierential equation (pdes) with time-fractional derivative. with help he's homotopy per-turbation, we can handle the nonlinear terms. further, we have applied this suggested he's homotopyperturbation method in order to reformulate initial value problem. some illustrative examples...

Alternative Best-E ort (ABE) is a novel service for IP networks which o ers applications the choice between receiving a lower end-to-end delay and receiving more overall throughput. Every best e ort packet is marked as either green or blue. Green packets receive a low, bounded queueing delay. To ensure blue packets do not su er as a result, green ows receive less throughput during bouts of cong...

of a Delay-Di erential Equation Tom a s Gedeon1 Department of Mathematical Sciences, Montana State University, Bozeman,MT 59717 [email protected] Gwendolen Hines2 Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588 [email protected] In this paper, we consider a discrete delay problem with negative feedback _ x(t) = f(x(t); x(t 1)) along with a ce...

We investigate the derivation and the mathematical properties of a Saint-Venant model with an energy equation and with temperature-dependent transport coe±cients. These equations model shallow water °ows as well as thin viscous sheets over °uid substrates like oil slicks, atlantic waters in the Strait of Gilbraltar or °oat glasses. We exhibit an entropy function for the system of partial di®ere...

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...