in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

In this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice Banach spaces. Also, we give some results about simultaneous approximations of normal sets.

In this paper, we present a new degree-based estimator for the size of maximum matching in bounded arboricity graphs. When graph is by $$\alpha $$ , gives +2$$ factor approximation size. For planar graphs, show does better and returns 3.5 Using estimator, get results approximating graphs streaming distributed models computation. particular, vertex-arrival streams, randomized $$O\left( \frac{\sq...

We describe deterministic algorithms which for a given depth-2 circuit $F$ approximate the probability that on a random input $F$ outputs a specific value $\alpha$. Our approach gives an algorithm which for a given $GF[2]$ multivariate polynomial $p$ and given $\varepsilon >0$ approximates the number of zeros of $p$ within a multiplicative factor $1+ \varepsilon$. The algorithm runs in time $ex...

Given a stable SISO LTI system $G$, we investigate the problem of estimating the $\mathcal{H}_\infty$-norm of $G$, denoted $||G||_\infty$, when $G$ is only accessible via noisy observations. Wahlberg et al. recently proposed a nonparametric algorithm based on the power method for estimating the top eigenvalue of a matrix. In particular, by applying a clever time-reversal trick, Wahlberg et al. ...

We study transport properties in a simple model of two-dimensional roll convection under a slow periodic (period of order 1/ varepsilon >>1) perturbation. The problem is considered in terms of conservation of the adiabatic invariant. It is shown that the adiabatic invariant is well conserved in the system. It results in almost regular dynamics on large time scales (of order approximately vareps...

In $L_2(\mathbb{R}^d;\mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\mathcal{A}_\varepsilon$, $\varepsilon >0$. The coefficients of the $\mathcal{A}_\varepsilon$ are periodic and depend on $\mathbf{x}/\varepsilon$. We study behavior $\mathcal{A}_\varepsilon ^{-1/2}\sin (\tau \mathcal{A}_\varepsilon ^{1/2})$, $\tau\in\mathbb{R}$, in small p...

In convex stochastic optimization, convergence rates in terms of minimizing the objective have been well-established. However, in terms of making the gradients small, the best known convergence rate was $O(\varepsilon^{-8/3})$ and it was left open how to improve it. In this paper, we improve this rate to $\tilde{O}(\varepsilon^{-2})$, which is optimal up to log factors.