It is shown that complexity of implementation of prefix sums of m variables (i.e. functions x1 ◦ . . . ◦ xi, 1 ≤ i ≤ m) by circuits of depth dlog2 me in the case m = 2n is exactly 3.5 · 2 − (8.5 + 3.5(n mod 2))2bn/2c + n + 5. As a consequence, for an arbitrary m an upper bound (3.5 − o(1))m holds. In addition, an upper bound ( 3 3 11 − o(1) ) m for complexity of the minimal depth prefix circuit...

In 1985, Chor et al 2] conjectured that the only 1-resilient symmetric functions are the exclusive-or of all n variables and its negation. In this note the existence of symmetric resilient functions is shown to be equivalent to the existence of a solution to a simultaneous subset sum problem. Then, using arithmetic properties of certain binomial coeecients, an innnite class of counterexamples t...

entrepreneurship has been known as a method of identifying new opportunities, allocating resources in the situation of uncertainty and creating an organization to manage resources. this paper describes religious learning approaches in which entrepreneurship is beneficial to society and individuals through its economic advantages. the benefits are gained through innovation, productivity and new ...

in this paper we study finding the $(k,l)$-core problem on a tree which the vertices have positive or negative weights. let $t=(v,e)$ be a tree. the $(k,l)$-core of $t$ is a subtree with at most $k$ leaves and with a diameter of at most $l$ which the sum of the weighted distances from all vertices to this subtree is minimized. we show that, when the sum of the weights of vertices is negative, t...

In this paper we study finding the $(k,l)$-core problem on a tree which the vertices have positive or negative weights. Let $T=(V,E)$ be a tree. The $(k,l)$-core of $T$ is a subtree with at most $k$ leaves and with a diameter of at most $l$ which the sum of the weighted distances from all vertices to this subtree is minimized. We show that, when the sum of the weights of vertices is negative, t...