We present a tight bound on the exact maximum complexity of Minkowski sums of polytopes in R. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2, . . . ,mk facets respectively is bounded from above by

The subject of this thesis is the theory of nonholomorphic modular forms of non-integral weight, and its applications to arithmetical functions involving Dedekind sums and Kloosterman sums. As was discovered by Andre Weil, automorphic forms of non-integral weight correspond to invariant funtions on Metaplectic groups. We thus give an explicit description of Meptaplectic groups corresponding to ...

in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...

Let A be a finite, nonempty subset of an abelian group. We show that if every element is sum two other elements, then has zero-sum subset. That is, (finite, nonempty) sum-full group not zero-sum-free.

Given a network and a set of source destination pairs (connections), we consider the problem of maximizing the sum of the flow under proportional delay constraints. In this paper, the delay for crossing a link is proportional to the total flow crossing this link. If a connection supports non-zero flow, then the sum of the delay along any path corresponding to that connection must be lower than ...

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...