Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...

Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in R the corresponding set is also a convex set in R. The iterative optimization approach start...

The logistic loss function is often advocated in machine learning and statistics as a smooth and strictly convex surrogate for the 0-1 loss. We investigate the question of whether these smoothness and convexity properties make the logistic loss preferable to other widely considered options such as the hinge loss. We show that in contrast to known asymptotic bounds, as long as the number of pred...

In this paper we intend to examine the application of Kullback-Leibler, Hellinger and LINEX loss function in Dynamic Linear Model using the real price of oil for 106 years of data from 1913 to 2018 concerning the asymmetric problem in filtering and forecasting. We use DLM form of the basic Hoteling Model under Quadratic loss function, Kullback-Leibler, Hellinger and LINEX trying to address the ...

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

We show that the class of two layer neural networks with bounded fan-in is eeciently learn-able in a realistic extension to the Probably Approximately Correct (PAC) learning model. In this model, a joint probability distribution is assumed to exist on the observations and the learner is required to approximate the neural network which minimizes the expected quadratic error. As special cases, th...

in this article, a multi-objective function for placement of distributed generation (dg) and capacitors with thetap setting of under load tap changer (ultc) transformer is introduced. most of the recent articles have paidless attention to dg, capacitor placement and ultc effects in the distribution network simultaneously. insimulations, a comparison between different modes was carried out with,...

Extreme learning machines (ELMs) have recently attracted significant attention due to their fast training speeds and good prediction effect. However, ELMs ignore the inherent distribution of original samples, they are prone overfitting, which fails at achieving generalization performance. In this paper, based on expectile penalty correntropy, an asymmetric C-loss function (called AC-loss) is pr...