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In this paper, we present an analytical approach in obtaining the probability density function (pdf) of the random decision variable Y, which is formed at the output of the power-cubic all-optical nonlinear preprocessor followed by the photodetector, with applications in ultrafast optical time-division multiplexing and optical code-division multiple-access systems. Our approach can be used to accurately evaluate the performance of ultrafast pulse detection in the presence of Gaussian noise. Through rigorous Monte Carlo simulation, the accuracy of the widely used Gaussian approximation of decision variable Y is refuted. However, in this paper, we show that the so-called log-Pearson type-3... 

In this paper, an accurate model for the probability density function (pdf) of the random decision variable Y in an ultrafast digital lightwave communication system, utilizing power-cubic all-optical nonlinear preprocessor is presented. The proposed model can replace the prevalent Gaussian approximation, as the accuracy of the latter is discredited by Monte-Carlo simulation. The Log-Pearson type-3 probability density function (LP3 pdf) is shown to appropriately represents the random decision variable Y. Three characteristic parameters of the LP3 pdf are also obtained through the three moments of the decision variable Y. Finally, the system error probability is revisited using the obtained... 

In this paper, a spectral-phase-encoded ultrashort light pulse optical code division multiple access (SPE-OCDMA) system employing a novel nonlinear power-cubic optical preprocessor at its receiver's front end is theoretically investigated. The system's mathematical model and the statistical distribution of the decision variable Y, prior to the decision module of the receiver, are discussed. The first three moments of the random decision variable Y are obtained in the context of the above OCDMA system and subsequently used in an appropriate Log-Pearson type 3 (LP3) distribution to represent the random decision variable $Y$. Multiple access interference (MAI) and amplified spontaneous emission... 

In the restructured power markets, price of electricity has been the key of all activities in the power market. Accurately and efficiently forecasting electricity price becomes more and more important. Therefore in this paper, an Artificial Neural Network (ANN) model is designed for short term price forecasting of electricity in the environment of restructured power market. The proposed ANN model is a four-layered perceptron neural network, which consists of, input layer, two hidden layers and output layer. Instead of conventional back propagation (BP) method, Levenberg- Marquardt BP (LMBP) method has been used for the ANN training to increase the speed of convergence. Matlab is used for... 

With increasing the presence of co-and tri-generating units, energy hub operators are encouraged to optimally schedule the available energy resources in an economic way. This scheduling needs to be run in an online manner due to the uncertainties in energy prices and demands. In this paper, the real-time scheduling problem of energy hubs is formulated in a dynamic pricing market. The energy hubs interaction is modeled as an exact potential game to optimize each energy hub’s payments to the electricity and gas utilities, as well as the customers’ satisfaction from energy consumption. The potential game approach enables us to study the existence and uniqueness of the Nash equilibrium (NE) and... 

With increasing the presence of co- and tri-generating units, energy hub operators are encouraged to optimally schedule the available energy resources in an economic way. This scheduling needs to be run in an online manner due to the uncertainties in energy prices and demands. In this paper, the real-time scheduling problem of energy hubs is formulated in a dynamic pricing market. The energy hubs interaction is modeled as an exact potential game to optimize each energy hub's payments to the electricity and gas utilities, as well as the customers' satisfaction from energy consumption. The potential game approach enables us to study the existence and uniqueness of the Nash equilibrium and to... 

The main purpose of this article is to generalize a recent result about isometries of Lipschitz spaces. Botelho, Fleming and Jamison [2] described surjective linear isometries between vector-valued Lipschitz spaces under certain conditions. In this article, we extend the main result of [2] by removing the quasi-sub-reflexivity condition from Banach spaces  

The main purpose of this article is to generalize a characterization of constant functions to the context of metric-measure spaces. In fact, we approximate a measurable function, in terms of a certain integrability condition, by Lipschitz functions. Then, similar to Brezis (2002) [2], we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be constant a.e. Also, we provide a different proof for the main result of Pietruska-Pałuba (2004) [7] in the setting of Dirichlet forms  

The main purpose of this article is to generalize a theorem of Stepanov which provides a necessary and sufficient condition for almost everywhere differentiability of functions over Euclidean spaces. We state and prove an Lp-type generalization of the Stepanov theorem and then we extend it to the context of Orlicz spaces. Then, this generalized Rademacher-Stepanov type theorem is applied to the Sobolev and bounded variation maps with values into a metric space. It is shown that several generalized differentiability type theorems are valid for the Sobolev maps from a Lipschitz manifold into a metric space. As a byproduct, it is shown that the Sobolev spaces of Korevaar-Schoen and Reshetnyak... 

Let f : M {long rightwards arrow} over(M, -) be an isometric immersion between Riemannian manifolds. For certain conditions on M and over(M, -) in terms of curvatures and external diameter, we extend the non-embedding theorem of Chern and Kuiper to the isometric immersions of non-compact manifolds. Also, our results generalize and improve the main results of Jorge and Koutroufiotis [L. Jorge, D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (4) (1981) 711-725] and Veeravalli [A. R. Veeravalli, A sharp lower bound for the Ricci curvature of bounded hypersurfaces in space forms, Bull. Austral. Math. Soc. 62 (1) (2000) 165-170]. © 2008 Elsevier B.V.... 

The main purpose of this article is to generalize a characterization of Lipschitz functions in the context of metric-measure spaces. The results are established in the class of metric-measure spaces which satisfy a strong version of the doubling (Bishop-Gromov regularity) condition. Indeed, we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be essentially Lipschitzian. © 2019 Elsevier Inc  

In this article, we describe isometries over the Lipschitz spaces under certain conditions. Indeed, we provide a unified proof for the main results of and in a more general setting. Finally, we extend our results for some other functions spaces like the space of vector-valued little Lipschitz maps and pointwise Lipschitz maps. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  

The purpose of this paper is to describe a simple proof for a result originally presented by H. Brezis in [B], with roots in J. Bourgain, H. Brezis and P. Mironescu [BBM]. © 2020 University of Houston  

The purpose of this article is to study the isometries between vector-valued absolutely continuous function spaces, over compact subsets of the real line. Indeed, under certain conditions, it is shown that such isometries can be represented as a weighted composition operator. © 2020 Alireza Ranjbar-Motlagh  

The purpose of this paper is to generalize the Liouville theorem for functions which are defined on the complete Riemannian manifolds. Then, we apply it to the isometric immersions between complete Riemannian manifolds in order to obtain an estimate for the size of the image of immersions in terms of the supremum of the length of their mean curvature vector in a quite general setting. The proofs are based on the Calabi's generalization of maximum principle for functions which are not necessarily differentiable. © 2007 Elsevier B.V. All rights reserved  

This article characterizes the isometries between spaces of all differentiable functions from a compact interval of the real line into a strictly convex Banach space. © 2021 Alireza Ranjbar-Motlagh