In [2, Chapter VII (p. 133)], Ritt shows an example of two irreducible differential variety of differential dimension 2 in U whose intersection consists of a single point: the origin. The details below follow Ritt’s exposition using more modern language and notation. The first part is taken from my tutorial paper [3], with some change in notation. That paper provides the basic background needed...

In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...

Generalized Order-Value Optimization (GOVO) problems involve functions whose evaluation depends on order relations on some representation functional set. Examples will be given of GOVO problems that may be analyzed in the context of Piecewise-Smooth Optimization. Generalizations of algorithms that have been proved to be effective for proving special classes of GOVO problems will be introduced. ...

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of comp...

in this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. we use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. finally, one example is given to illustrate our results.

this paper proposes a new method for parameter estimation of distorted single phase signals, through an improved demodulation-based phase tracking incorporated with a frequency adaptation mechanism. the simulation results demonstrate the superiority of the proposed method compared to the conventional sogi (second-order generalized integrator)-based approach, in spite of the dc-offset and harmon...