Let Xj be smooth varieties over a field k of characteristic zero, for 1 ≤ j ≤ p. Consider a family f of p functions fj : Xj → A 1 k. We shall denote also by fj the function on the product X = ∏ j Xj obtained by composition with the projection. We denote by X0(f) the set of common zeroes in X of the functions fj. Let P ∈ k[y1, . . . , yp] be a polynomial, which we assume to be non-degenerate wit...

In this paper, we present a new type of Gronwall inequality and discuss some particular cases. We apply these results to investigate the uniqueness δ-Ulam–Hyers–Rassias stability mild solutions fractional differential equation with non-instantaneous impulses in Pδ-normed Banach space. sense, an example, order elucidate one discussed.

Let an arbitrarily small positive constant δ less than 1 and a polynomial f with integer coefficients be fixed. We prove unconditionally that f modulo p can be completely factored in deterministic polynomial time if p− 1 has a (ln p)O(1)-smooth divisor exceeding pδ. We also address the issue of factoring f modulo p over finite extensions of the prime field Fp and show that p− 1 can be replaced ...

This paper proposes the stochastic tabu search (STS) for improving the measurement scheme for power system state estimation. If the original measured scheme is not observable, the additional measurements with minimum number of measurements are added into the system by STS so that there is no critical measurement pair. The random bit flipping and bit exchanging perturbations are used for generat...

We report our Monte Carlo results on the critical and multicritical behavior of the ±J Ising model [with a random-exchange probability P (Jxy) = pδ(Jxy−J)+(1−p)δ(Jxy +J)], in two and three dimensions. We study the transition line between the paramagnetic and ferromagnetic phase, which extends from p = 1 to a multicritical (Nishimori) point. By a finitesize scaling analysis, we provide strong nu...

This paper proposes the stochastic tabu search (STS) for improving the measurement scheme for power system state estimation. If the original measured scheme is not observable, the additional measurements with minimum number of measurements are added into the system by STS so that there is no critical measurement pair. The random bit flipping and bit exchanging perturbations are used for generat...