A Sharp Double Inequality for the Inverse Tangent Function

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 approximately smaller than 0.27% and 0.23% for the lower and upper bound, respectively. Furthermore, we determine an upper bound on the relative errors of the proposed bounds in order to describe their tightness analytically. Moreover, some important properties of the obtained bounds are discussed in order to describe their behavior and achieved accuracy.Comment: Submitted to the Transactions on Information Theor

Semiparametric Estimation of Stochastic Frontiers A Bayesian Penalized Approach

Almost all previous approaches to estimating semiparametric frontier models, where the functional form for the production (cost) function is unknown, have been local nonparametric (ie. kernel) approaches. In this paper we use a penalized (ie. spline) approach. We show how this approach can be applied to a variety of frontier models, including panel models with fixed and random effects, within a Bayesian framework. We also apply our approach to different multivariate settings, including additive and additive with interaction models. The latter is a promising model because it is very flexible and does not suffer the severe curse of dimensionality problem common with fully nonparametric functions. We illustrate our method using a simulated example.

An Application of Joint Spectral Radius in Power Control Problem for Wireless Communications

Resource management, including power control, is one of the most essential functionalities of any wireless telecommunication system. Various transmitter power-control methods have been developed to deliver a desired quality of service in wireless networks. We consider two of these methods: Distributed Power Control and Distributed Balancing Algorithm schemes. We use the concept of joint spectral radius to come up with conditions for convergence of the transmitted power in these two schemes when the gains on all the communications links are assumed to vary at each time-step.Comment: 4 page

Hybrid dynamic modeling of 4-CBA hydrogenation fixed-bed catalytic reactor of PTA production plant

In this paper, a dynamic hybrid model of 4-carboxybenzaldehyde (4-CBA) hydrogenation fixed-bed catalytic reactor of Purified Terephthalic Acid (PTA) production plant has been developed. At the first step, the deactivation model of the reaction system has been predicted by using artificial neural network (ANN) technique. Then, the deactivation model estimated by ANN as black box incorporated to first principle model (FPM) as white box. Therefore, the established hybrid model has been utilized to model the hydrogenation reactor of PTA plant. Finally, the simulated results have been compared with the industrial reactor data. It has been concluded that hybrid model is more precise than a FPM model