Technical applications are often modeled by systems of differential algebraic equations. The systems may include parameters that involve some uncertainties. We arrange a stochastic model for uncertainty quantification in the case of linear systems of differential algebraic equations. The generalized polynomial chaos yields a larger linear system of differential algebraic equations, whose soluti...

This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a0 +a1x+a2x2 +···+an−1xn−1. The coefficients aj (j = 0,1,2, . . . ,n−1) are assumed to be independent normal random variables with nonidentical means. Previous results aremainly for identically distributed coefficients. Our result remains valid when the means of the coefficients are...

We give an eecient algorithm for factoring polynomials over nite algebraic extensions of the p-adic numbers. This algorithm uses ideas of Chistov's random polynomial-time algorithm, and is suitable for practical implementation.

We solve two computational problems concerning plane algebraic curves over nite elds: generating an (approximately) uniform random point, and nding all points deterministically in amortized polynomial time (over a prime eld, for non-exceptional curves).

We give an efficient algorithm for factoring polynomials over finite algebraic extensions of the p-adic numbers. This algorithm uses ideas of Chistov’s random polynomial-time algorithm, and is suitable for practical implementation.

In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the num...

The Polynomial Freiman-Ruzsa conjecture is one of the central open problems in additive combinatorics. It speculates tight quantitative bounds between combinatorial and algebraic notions of approximate subgroups. In this note, we restrict our attention to subsets of Euclidean space. In this regime, the original conjecture considers approximate algebraic subgroups as the set of lattice points in...