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In this paper, we prove the following differential analog of the Noether normalization lemma: for every d-dimensional differential algebraic variety over differentially closed field of zero characteristic there exists a surjective map on to the d-dimensional affine space. Equivalently, for every integral differential algebra A over differential field of zero characteristic there exist differentially independent b1, . . . , bd such that A is differentially algebraic over subalgebra B differentially generated by b1, . . . , bd, and whenever p ⊂ B is a prime differential ideal, there exists a prime differential ideal q ⊂ A such that p = B ∩ q. We also prove the analogous theorem for differential algebraic varieties over the ring of formal power series over an algebraically closed differential field and present some applications to differential equations. [ABSTRACT FROM AUTHOR]

We consider a Landau-Lifshitz-Gilber equation perturbed by a multiplicative space-dependent noise for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere . The regularity of weak solutions is also discussed. Our research is in response to the paper by Kohn et al. “Magnetic elements at finite temperature and large deviation theory.” Journal of Nonlinear Science 15 (2005): 223–53, which calls for the study of stochastic equations with spatially varying magnetization. [ABSTRACT FROM AUTHOR]

In this paper, we study the decay properties of the solutions to Timoshenko beam with a weak non-linear dissipation. [ABSTRACT FROM PUBLISHER]

In this paper, we study the complex version of the Kharitonov theorem without the constant-degree assumption. It is proved that, for a complex-interval polynomial with degree drop, robust Hurwitz stability is equivalent to the Hurwitz stability of the eight Kharitonov polynomials. Furthermore, it is also shown that for a robustly stable complex-interval polynomial, degree drop cannot exceed one and degree drop can only occur at one of the corners of the rectangular region in the complex plane corresponding to the leading coefficient of the uncertain polynomial. [ABSTRACT FROM PUBLISHER]