In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores

the textit{commutativity degree}, $pr(g)$, of a finite group $g$ (i.e. the probability that two (randomly chosen) elements of $g$ commute with respect to its operation)) has been studied well by many authors. it is well-known that the best upper bound for $pr(g)$ is $frac{5}{8}$ for a finite non--abelian group $g$. in this paper, we will define the same concept for a finite non--abelian textit{...

In this paper we derive high probability lower and upper bounds on the excess risk of stochastic optimization of exponentially concave loss functions. Exponentially concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, and negative logarithm loss in portfolio management. We demonstrate an O(d...

The problem of attitude stabilization of a fighter aircraft is investigated in this paper. The practical aspects of a real physical system like existence of external disturbance with unknown upper bound and actuator saturation are considered in the process of controller design of this aircraft. In order to design a robust autopilot in the presence of the actuator saturation, the Composite Nonli...

In this paper we obtain an upper bound and also a lower bound for maximum edges of strongly 2 multiplicative graphs of order n. Also we prove that triangular ladder the graph obtained by duplication of an arbitrary edge by a new vertex in path and the graphobtained by duplicating all vertices by new edges in a path and some other graphs are strongly 2 multiplicative

In 15], Keliher et al. present a new method for upper bounding the maximum average linear hull probability (MALHP) for SPNs, a value which is required to make claims about provable security against linear cryptanalysis. Application of this method to Rijndael (AES) yields an upper bound of UB = 2 ?75 when 7 or more rounds are approximated, corresponding to a lower bound on the data complexity of...