In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [5, 16, 7, 9] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994, see [3]. In the present paper, we show that the answe...

We explicitly construct a convex entropy function for a hyperbolic system with relaxation. This entropy is deened in the sense of Chen, Levermore and Liu 2], which resembles Boltzman's H-Theorem for kinetic equations. This construction follows the idea of Suliciu's energy function for a rate-type mixed hyperbolic-elliptic system 10]. Such an entropy will be useful in proving the entropy propert...

in this paper, we prove that every metric line in the poincare ball model of hyperbolic geometry is exactly a classical line of itself. we also proved nonexistence of periodic lines in the poincare ball model of hyperbolic geometry.

in arid and semi-arid environments, groundwater plays a significant role in the ecosystem. in the last decades, groundwater levels have decreased due to the increasing demand for water, weak irrigation management and soil damage. for the effective management of groundwater, it is important to model and predict fluctuations in groundwater levels. in this study, groundwater table in kashan plain ...

Neural networks have a wide range of applications in analog and digital signal processing Nonlinear activation function is one of the main building blocks of artificial neural networks. Hyperbolic tangent and sigmoid are the most used nonlinear activation functions of NN.This project proposes a knowledge-based neural network (KBNN) modeling approach with new hyperbolic tangent function . The KB...

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [5,18,9,13] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994, see [3]. In the present paper, we show that the answer ...

This paper studies corporate governance when a ̄rm faces imperfect competition. We derive ̄rms' decisions from utility maximisation by individuals. This reduces the usual monopoly distortion. We ̄nd that corporate governance can e®ect the equilibrium in the product (or input) markets. This enables us to endogenise the objective function of the ̄rm. If the ̄rm cannot commit not to change its con...

For a conformally compact manifold that is hyperbolic near infinity and of dimension n + 1, we complete the proof of the optimal O(r) upper bound on the resonance counting function, correcting a mistake in the existing literature. In the case of a compactly supported perturbation of a hyperbolic manifold, we establish a Poisson formula expressing the regularized wave trace as a sum over scatter...

In this paper, we explore more applications of the hyperbolic function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations (PDES), to special discrete nonlinear equations. Some exact travelling wave solution of the discrete sine-Gordon equation are obtained in terms of hyperbolic fun...