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In this work, we propose a new method to enhance text in document-image. Firstly, we introduce a classical model and a way to solve it by means of a non-convex optimization problem. So, a simoultaneaous estimation of the reflectance and the luminance is obtained when the non uniform illumination (also called luminance) is a smooth function and the reflectance is a function of bounded variation. We give an analyse of this problem and some conditions of existence and unicity. Then, we consider the "log" of the classical model. A new pde's model is proposed. This method is based on the resolution of an original partial differential equation (PDE) estimating the log of the luminance. We assume that the luminance is enough smooth and is the solution of a non classical second order's PDE.Then we deduce the reflectance from the estimated luminance and the acquired image. The effectiveness and the robustness of the proposed process are shown on numerical examples in real-world situation (images acquired from cameraphones). Then, we illustrate the ability of this method to improve an Optical Character Recognition (OCR) in text recognition.

In this paper, we present an intelligent combination of partition of unity (PU) and finite element (FE) methods for valuing American option pricing problems governed by the Black-Scholes (BS) model. The model is based on a partial differential equation (PDE) from which one can deduce the Black-Scholes formula, which gives a theoretical estimated value of options using current stock prices, expected dividends, the option’s strike price, expected interest rates, time to expiration and expected volatility. Although the finite element method (FEM) seems to be an alternative tool for pricing options with a few applications reported in the literature, this combination called the Partition of Unity Finite Element Method (PUFEM) appears to offer many of the desired properties. The main advantage of the proposed approach is its ability to locally refine the solution by adapting an incorporated specific class of enrichment in the finite element space instead of generating a new fine mesh for the problem under study. Numerical computations are carried out to show a huge reduction in the number of degrees of freedom required to achieve a fixed accuracy which confirms that the PUFE method used is very efficient and gives better accuracy than the conventional FE method.

Mathematical epidemiology is one of the most important research areas, it has contributed to understanding the behavior and the impact also the prediction of infectious disease. One of the fundamental methods intended to see the behavior of the pandemic is the susceptible-infectious-recovered epidemic model. However, the deterministic approach of this model has some limitations in mathematical modeling, for that we propose to add a stochastic variation in SIR equations. In this paper we present a stochastic differential equation with jump-diffusion formula for COVID-19, then we estimate the parameters of our stochastic susceptible-infected-recovered model. Finally, we compare our result with real covid19 spread in Morocco.

The present work proposes an Artificial Neural Network framework for calculating the price and delta hedging of American put option. We consider a sequence of Radial Basis function Neural Network, where each network learns the difference of the price function according to the Gaussian basis function. Based on Black Scholes partial differential equation, we improve the superiority of Artificial Neural Network by comparing the performance and the results achieved used in classic Monte Carlo Least Square simulation with those obtained by Neural networks in one dimension. Thus, numerical result shows that the Artificial Neural Network solver can reduce the computing time significantly as well as the error training.

In this work, we propose a tool to scan a document-image acquired with a cameraphone. Firstly, we try to reduce the noise in the document-image. Then we build a new image by cropping or by perspective rectifying the denoised one. From this step, we can expect the document to a real quadrangle. The new document is analyzed and we try to find images, logo or non text element in the documentimage with the aid of an image segmentation. At this stage, we provide deux parts of the document image: the text part and the "non text" part of the document-image (images, logos, non ...). The text part of the document-image is enhanced by an original pde's based model that we proposed. The "non text" document is enhanced by classical methods such as retinex processing. Then, we merge both parts of the document image by a poisson image editing. The effectiveness and the robustness of the proposed process are shown on numerical examples in real-world situation (images acquired from cameraphones).

This paper aims to study the asymptotic behavior of double barrier American-style put option prices under an uncertain volatility model, which degenerates to a single point. We give an approximation of the double barrier American-style option prices with a small volatility interval, expressed by the Black–Scholes–Barenblatt equation. Then, we propose a novel representation for the early exercise boundary of American-style double barrier options in terms of the optimal stopping boundary of a single barrier contract.

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