This paper investigates the impact of electric vehicle (EV) aggregator with communication time delay on stability regions and margins a single-area load frequency control (LFC) system. Primarily, graphical method characterizing boundary locus is implemented. For given delay, computes all stabilizing pro-portional-integral (PI) controller gains, which constitutes region in parameter space PI con...

Iterated Hopf Ore extensions (IHOEs) over an algebraically closed base field $\Bbbk$ of positive characteristic $p$ are studied. We show that every IHOE satisfies a polynomial identity (PI), with PI-degree power $p$, and it is filtered deformation commutative ring. classify all $2$-step IHOEs $\Bbbk$, thus generalising the classification $2$-dimensional connected unipotent algebraic groups $\Bb...

We extend the Wermer’s theorem, to describe the polynomial hull of compact sets lying on the boundary of a smooth strictly convex domain of Cn. We also extend the result to polynomial p-hulls and apply it to get properties of pluriharmonic or p.s.h. positive currents. RÉSUMÉ. Nous décrivons à la suite des travaux de Wermer, l’enveloppe polynomiale des ensembles compacts contenus dans le bord d’...

Abstract In this work, we prove a version of the Sylvester–Gallai theorem for quadratic polynomials that takes us one step closer to obtaining deterministic polynomial time algorithm testing zeroness $\Sigma ^{[3]}\Pi \Sigma \Pi ^{[2]}$ circuits. Specifically, that, if finite set irreducible ${\mathcal {Q}}$ satisfies every two $Q_1,Q_2\in {\mathcal there is subset {K}}\subset such $Q_1,Q_2 \no...

The paper attacks absolute phase estimation with a two-step approach: the first step applies an adaptive local denoising scheme to the modulo-2 pi noisy phase; the second step applies a robust phase unwrapping algorithm to the denoised modulo-2 pi phase obtained in the first step. The adaptive local modulo-2 pi phase denoising is a new algorithm based on local polynomial approximations. The zer...

We investigate the complexity of integration and derivative for multivariate polynomials in the standard computation model. The integration is in the unit cube [0, 1] for a multivariate polynomial, which has format f(x1, · · · , xd) = p1(x1, · · · , xd)p2(x1, · · · , xd) · · · pk(x1, · · · , xd), where each pi(x1, · · · , xd) = ∑d j=1 qj(xj) with all single variable polynomials qj(xj) of degree...

We show that there exist Po > 0 ar>d P\, ■■■ , Pn nonnegative integers, such that 0 < p(x) = Po + Pi cosx + • ■ • + Pn cos Nx and po -C s1/3 for .s = J2'J=oPj < improving on a result of Odlyzko who showed the existence of such a polynomial p that satisfies Po < (.slogs)1/3 . Our result implies an improvement of the best known estimate for a problem of Erdos and Szekeres. As our method is noncon...

In recent years, Alexandersson and others proved combinatorial formulas for the Schur function expansion of horizontal-strip LLT polynomial \(G_{\boldsymbol\lambda}(\boldsymbol x;q)\) in some special cases. We associate a weighted graph \(\Pi\) to \(\boldsymbol\lambda\) we use it express linear relation among polynomials. apply this prove an explicit Schur-positive whenever is triangle-free. al...

Given a set r of permutations of an n-set, let G be the group of permutations generated by f. If p is a prime, a Sylow p-subgroup of G is a subgroup whose order is the largest power of p dividing IGI. For more than 100 years it has been known that a Sylow p-subgroup exists, and that for any two Sylow p-subgroups PI, P, of G there is an element go G such that Pz = g-‘PI g. We present polynomial-...

For a graph G and a collection of vertex pairs {(s1, t1), . . . , (sk, tk)}, the k disjoint paths problem is to find k vertex-disjoint paths P1, . . . , Pk, where Pi is a path from si to ti for each i = 1, . . . , k. In the corresponding optimization problem, the shortest disjoint paths problem, the vertex-disjoint paths Pi have to be chosen such that a given objective function is minimized. We...