in this paper we give sharp upper bounds on the zagreb indices and characterize all trees achieving equality in these bounds. also, we give lower bound on first zagreb coindex of trees.

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

We consider the optimal discrimination of bipartite quantum states and provide an upper bound for maximum success probability local discrimination. also a necessary sufficient condition measurement to realize bound. further establish this be saturated. Finally, we illustrate our results using example.

In this paper we determine the maximum cardinality m of a family A = {A1, ..., Am} of subsets of a set of n elements with the property that for each Ai there are at most s Aj such that |Ai∩Aj | is odd (even). A tight upper bound is given in the case s < c 2n/2 n . In the remaining cases we give an asymptotically tight upper bound. As an application we give a tight upper-bound for the cardinalit...

We provide a new upper bound for traveling salesman problem (TSP) in cubic graphs, i. e. graphs with maximum vertex degree three, and prove that the problem for an n-vertex graph can be solved inO(1.2553) time and in linear space. We show that the exact TSP algorithm of Eppstein, with some minor modifications, yields the stated result. The previous best known upper bound O(1.251) was claimed by...

The inverse tangent function can be bounded by different inequalities, for example by Shafer’s inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent function. In particular, we sharpen Shafer’s inequality and calculate the best corresponding constants. The maximum relative errors of the obtained bounds are ap...

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

We consider the problem of determining the size of a maximum clique in a graph, also known as the clique number. Given any method that computes an upper bound on the clique number of a graph, we present a sequential elimination algorithm which is guaranteed to improve upon that upper bound. Computational experiments on DIMACS instances show that, on average, this algorithm can reduce the gap be...

For bipartite graphs the NP-completeness is proved for the problem of existence of maximum matching which removal leads to a graph with given lower(upper) bound for the cardinality of its maximum matching.