Let X1, . . . , XN be independent random vectors uniformly distributed on an isotropic convex body K ⊂ Rn, and let KN be the symmetric convex hull of Xi’s. We show that with high probability LKN ≤ C √ log(2N/n), where C is an absolute constant. This result closes the gap in known estimates in the range Cn ≤ N ≤ n1+δ. Furthermore, we extend our estimates to the symmetric convex hulls of vectors ...

Where Z∗ is OPT, we know Z∗ = 3x1 + 2x ∗ 2 + 8x ∗ 3, for some x ∗ 1, x ∗ 2, x ∗ 3 ∈ P . By adding two of the inequalities, we arrive at 2x1 + x2 + x3 ≥ 15. Since x1, x2, x3 ≥ 0, we know that Z∗ ≥ 15. But we aren’t limited to addition, multiplication is another way the equations can be combined. So how is this new formulation bouned? This is done by using the dual formulation, D of the minimizat...

The eddy viscosity is the tensor in the equation that governs the transport of the large-scale (modulational) perturbations of small-scale stationary flows. As an approximation to eddy viscosity the effective tensor, that arises in the limit as the ratio between the scales ε → 0, can be considered. We are interested here in the accuracy of this approximation. We present results of computational...

Znajdziemy teraz wzór na odleg lość punktu (x0, y0) od prostej, wspó lrze↪dne punktów której spe lniaja↪ równanie ax+by+c = 0 . Oczywíscie po to, by to równanie przedstawia lo prosta↪ trzeba za lożyć, że wektor [a, b] nie jest wektorem zerowym, czyli że [a, b] 6= [0, 0] . Odleg lość punktów (x1, y1) i (x2, y2) to √ (x1 − x2) + (y1 − y2) . Wynika to natychmiast z twierdzenia Pitagorasa zastosowa...

We consider the risk premium π demanded by a decision maker with present wealth x in order to be indifferent between obtaining a new level of wealth y1 with certainty, or to participate in a lottery which either results in unchanged wealth x or a level of wealth y2 > y1. We then define the relative risk premium λ as the quotient between π and the increase in wealth y1−x which the decision maker...

If a and b are positive integers with a ≤ b and a ≡ a mod b, then the set Ma,b = {x ∈ N : x ≡ a mod b or x = 1} is a multiplicative monoid known as an arithmetical congruence monoid (or ACM). For any monoid M with units M× and any x ∈ M \M× we say that t ∈ N is a factorization length of x if and only if there exist irreducible elements y1, . . . , yt of M and x = y1 · · · yt. Let L(x) = {t1, . ...

Our main interest in this paper is approximation of a continuous function, on a finite interval, which changes convexity finitely many times by algebraic polynomials which are coconvex with it. This topic has received much attention in recent years, and the purpose of this paper is to give final answers to open questions concerning the validity of Jackson type estimates involving the weighted D...