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Deep Learning is an effective technique and used in various fields of natural language processing, computer vision, image processing and machine vision. Deep fakes uses deep learning technique to synthesis and manipulate image of a person in which human beings cannot distinguish the fake one. By using generative adversarial neural networks (GAN) deep fakes are generated which may threaten the public. Detecting deep fake image content plays a vital role. Many research works have been done in detection of deep fakes in image manipulation. The main issues in the existing techniques are inaccurate, consumption time is high. In this work we implement detecting of deep fake face image analysis using deep learning technique of fisherface using Local Binary Pattern Histogram (FF-LBPH). Fisherface algorithm is used to recognize the face by reduction of the dimension in the face space using LBPH. Then apply DBN with RBM for deep fake detection classifier. The public data sets used in this work are FFHQ, 100K-Faces DFFD, CASIA-WebFace.

This study introduces an enhanced self-adaptive wild goose algorithm (SAWGA) for solving economical-environmental-technical optimal power flow (OPF) problems in traditional and modern energy systems. Leveraging adaptive search strategies and robust diversity capabilities, SAWGA distinguishes itself from classical WGA by incorporating four potent optimizers. The algorithm's application to optimize an OPF model on the different IEEE 30-bus and 118-bus electrical networks, featuring conventional thermal power units alongside solar photovoltaic (PV) and wind power (WT) units, addresses the rising uncertainties in operating conditions, particularly with the integration of renewable energy sources (RESs). The inherent complexity of OPF problems in electrical networks, exacerbated by the inclusion of RESs like PV and WT units, poses significant challenges. Traditional optimization algorithms struggle due to the problem's high complexity, susceptibility to local optima, and numerous continuous and discrete decision parameters. The study's simulation results underscore the efficacy of SAWGA in achieving optimal solutions for OPF, notably reducing overall fuel consumption costs in a faster and more efficient convergence. Noteworthy attributes of SAWGA include its remarkable capabilities in optimizing various objective functions, effective management of OPF challenges, and consistent outperformance compared to traditional WGA and other modern algorithms. The method exhibits a robust ability to achieve global or nearly global optimal settings for decision parameters, emphasizing its superiority in total cost reduction and rapid convergence. [ABSTRACT FROM AUTHOR]

In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).