A graph G is called a sum graph if there is a so-called sum labeling of G, i.e. an injective function l : V (G) → N such that for every u, v ∈ V (G) it holds that uv ∈ E(G) if and only if there exists a vertex w ∈ V (G) such that l(u) + l(v) = l(w). We say that sum labeling l is minimal if there is a vertex u ∈ V (G) such that l(u) = 1. In this paper, we show that if we relax the conditions (ei...

We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=sum_{i=1}^n |eta_i|, where eta_i=zeta_i-frac{2m}{n} and where zeta_1,zeta_2,ldots,zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if sum_{i=1}^n |eta_i|=sum_{i=1}^n |zeta_i|. Conditions ...

Abstract: In this paper, with the help of the Hardy and Dedekind sums we will give many properties of the sum B1(h, k), which was defined by Cetin et al. Then we will give the connections of this sum with the other well-known finite sums such as the Dedekind sums, the Hardy sums, the Simsek sums Y(h, k) and the sum C1(h, k). By using the Fibonacci numbers and two-term polynomial relation, we wi...

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.

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...