Search results for: non-linear exponential (NLINEX) loss function

Authors: Sarika Bahadure

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Sustainability starts with conserving resources for future generations. Since human’s existence on this earth, he has been consuming natural resources. The resource consumption pace in the past was very slow, but industrialization in 18^th century brought a change in the human lifestyle. New inventions and discoveries upgraded the human workforce to machines. The mass manufacture of goods provided easy access to products. In the last few decades, the globalization and change in technologies brought consumer oriented market. The consumption of resources has increased at a very high scale. This overconsumption pattern brought economic boom and provided multiple opportunities, but it also put stress on the natural resources. This paper tries to put forth the facts and figures of the population growth and consumption of resources with examples. This is explained with the help of the mathematical expression of doubling known as exponential growth. It compares the carrying capacity of the earth and resource consumption of humans’ i.e. ecological footprint and bio-capacity. Further, it presents the need to conserve natural resources and re-examine sustainable resource use approach for sustainability.

Keywords: consumption, exponential growth, population, resources, sustainability

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Authors: Kasirga Yildirak, Ismail Gur

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We propose a model to measure hail risk of an Agricultural Insurance portfolio. Hail is one of the major catastrophic event that causes big amount of loss to an insurer. Moreover, it is very hard to predict due to its strange atmospheric characteristics. We make use of parcel based claims data on apricot damage collected by the Turkish Agricultural Insurance Pool (TARSIM). As our ultimate aim is to compute the loadings assigned to specific parcels, we build a portfolio risk model that makes use of PD and the severity of the exposures. PD is computed by Spherical-Linear and Circular –Linear regression models as the data carries coordinate information and seasonality. Severity is mapped into integer brackets so that Probability Generation Function could be employed. Individual regressions are run on each clusters estimated on different criteria. Loss distribution is constructed by Panjer Recursion technique. We also show that one risk-one crop model can easily be extended to the multi risk–multi crop model by assuming conditional independency.

Keywords: hail insurance, spherical regression, circular regression, spherical clustering

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Authors: Padmini S. Navalgund, Manasi Naik, Ujwala Patil

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Road hump is a semi-cylindrical elevation on the road made across specific locations of the road. The vehicle needs to maneuver the hump by reducing the speed to avoid car damage and pass over the road hump safely. Road Humps on road surfaces, if identified in advance, help to maintain the security and stability of vehicles, especially in adverse visibility conditions, viz. night scenarios. We have proposed a deep learning architecture adaptation by implementing the MISH activation function and developing a new classification loss function called "Effective Focal Loss" for Indian road humps detection in adverse light scenarios. We captured images comprising of marked and unmarked road humps from two different types of cameras across South India to build a heterogeneous dataset. A heterogeneous dataset enabled the algorithm to train and improve the accuracy of detection. The images were pre-processed, annotated for two classes viz, marked hump and unmarked hump. The dataset from these images was used to train the single-stage object detection algorithm. We utilised an algorithm to synthetically generate reduced visible road humps scenarios. We observed that our proposed framework effectively detected the marked and unmarked hump in the images in clear and ad-verse light environments. This architectural adaptation sets up an option for early detection of Indian road humps in reduced visibility conditions, thereby enhancing the autonomous driving technology to handle a wider range of real-world scenarios.

Keywords: Indian road hump, reduced visibility condition, low light condition, adverse light condition, marked hump, unmarked hump, YOLOv9

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Authors: Jiheon Park, Taekwang Kim, Kwang Ryel Ryu

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Electric automated guided vehicles (AGVs) are becoming popular in many automated container terminals nowadays because they are pollution-free and environmentally friendly vehicles for transporting the containers within the terminal. Since efficient operation of AGVs is critical for the productivity of the container terminal, the replacement of batteries of the AGVs must be conducted in a strategic way to minimize undesirable transportation interruptions. While a too frequent replacement may lead to a loss of terminal productivity by delaying container deliveries, missing the right timing of battery replacement can result in a dead AGV that causes a severer productivity loss due to the extra efforts required to finish post treatment. In this paper, we propose a strategy for battery replacement based on a scoring function of multiple criteria taking into account the current battery level, the distances to different battery stations, and the progress of the terminal job operations. The strategy is optimized using a genetic algorithm with the objectives of minimizing the total time spent for battery replacement as well as maximizing the terminal productivity.

Keywords: AGV operation, automated container terminal, battery replacement, electric AGV, strategy optimization

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Authors: Pejman Daryabor, Kamal Mohammadi

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In the present work, the study of vibration characteristics of a functionally graded thick hollow cylinder is investigated. The cylinder natural frequencies are obtained using Galerkin finite element method. The functionally graded cylinder is assumed to be made from many subcylinders. Each subcylinder is considered as an isotropic layer. Material’s properties in each layer are constant and functionally graded properties result by exponential function of layer radius in multilayer cylinder. To validate the FE results code, plane strain model of functionally graded cylinder are also modeled in ABAQUS. Analytical results are validated for both models. Also, a good agreement is found between the present results and those reported in the literature.

Keywords: natural frequency, functionally graded material, finite element method, thick cylinder

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Authors: Ceren Kaya, Okan Erkaymaz, Orhan Ayar, Mahmut Özer

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Diabetes Mellitus (Diabetes) is a disease based on insulin hormone disorders and causes high blood glucose. Clinical findings determine that diabetes can be diagnosed by electrophysiological signals obtained from the vital organs. 'Diabetic Retinopathy' is one of the most common eye diseases resulting on diabetes and it is the leading cause of vision loss due to structural alteration of the retinal layer vessels. In this study, features of horizontal and vertical Video-Oculography (VOG) signals have been used to classify non-proliferative and proliferative diabetic retinopathy disease. Twenty-five features are acquired by using discrete wavelet transform with VOG signals which are taken from 21 subjects. Two models, based on multi-layer perceptron and radial basis function, are recommended in the diagnosis of Diabetic Retinopathy. The proposed models also can detect level of the disease. We show comparative classification performance of the proposed models. Our results show that proposed the RBF model (100%) results in better classification performance than the MLP model (94%).

Keywords: diabetic retinopathy, discrete wavelet transform, multi-layer perceptron, radial basis function, video-oculography (VOG)

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Authors: Hussein Shaman, Faris Almansour

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This paper proposes a modified optimum bandstop filter with ultra-wideband stopband. The filter consists of three shunt open-circuited stubs and two non-redundant unit elements. The proposed bandstop filter is designed with unequal electrical lengths of the open-circuited stubs at the mid-stopband. Therefore, the filter can exhibit a quasi-elliptic function response that improves the selectivity and enhances the rejection bandwidth. The filter is designed to exhibit a fractional bandwidth of about 114% at a mid-stopband frequency of 3.0 GHz. The filter is successfully realized in theory, simulated, fabricated and measured. An excellent agreement is obtained between calculated, simulated and measured. The fabricated filter has a compact size with a low insertion loss in the passbands, high selectivity and good attenuation level inside the desired stopband

Keywords: microstrip filter, bandstop filter, UWB filter, transmission line filter

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Authors: Jihene Jebeniani

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We proposed an approach combining both the techniques of experimental economy and the flexibility of discrete choice models in order to test the loss aversion. Our main objective was to test the loss aversion of the Cumulative Prospect Theory (CPT). We developed an experimental laboratory in the context of the financial investments that aimed to analyze the attitude towards the risk of the investors. The study uses the lotteries and is basing on econometric modeling. The estimated model was the ordered probit.

Keywords: risk aversion, behavioral finance, experimental economic, lotteries, cumulative prospect theory

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Authors: Ying-Pin Chang

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This paper presents a method for combining a particle swarm optimization with nonlinear time-varying evolution and orthogonal arrays (PSO-NTVEOA) in the planning of harmonic filters for the high speed railway traction system with specially connected transformers in unbalanced three-phase power systems. The objective is to minimize the cost of the filter, the filters loss, the total harmonic distortion of currents and voltages at each bus simultaneously. An orthogonal array is first conducted to obtain the initial solution set. The set is then treated as the initial training sample. Next, the PSO-NTVEOA method parameters are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments would have an effect that approximates the full factorial experiments. This PSO-NTVEOA method is then applied to design optimal harmonic filters in Taiwan High Speed Rail (THSR) traction system, where both rectifiers and inverters with IGBT are used. From the results of the illustrative examples, the feasibility of the PSO-NTVEOA to design an optimal passive harmonic filter of THSR system is verified and the design approach can greatly reduce the harmonic distortion. Three design schemes are compared that V-V connection suppressing the 3rd order harmonic, and Scott and Le Blanc connection for the harmonic improvement is better than the V-V connection.

Keywords: harmonic filters, particle swarm optimization, nonlinear time-varying evolution, orthogonal arrays, specially connected transformers

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Authors: Benniche Omar

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We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.

Keywords: abstract differential equation, graph, tangency condition, viability

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Authors: S. N. Derrar, M. Sekkal-Rahal

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The Nonlinear optics (NLO) technique is widely used in the field of biological imaging. In fact, grafting biological entities with a high NLO response on tissues and cells enhances the NLO responses of these latter, and ameliorates, consequently, their biological imaging quality. In this optics, we carried out a theoretical study, in the aim of analyzing the peptide bonds created between alanine amino acid and both unnatural amino acids: L-Dopa and Azatryptophan, respectively. Ramachandran plots have been performed for these systems, and their structural parameters have been analyzed. The NLO responses of these peptides have been reported by calculating the first hyperpolarizability values of all the minima found on the plots. The use of such unnatural amino acids as endogenous probing molecules has been investigated through this study. The Density Functional Theory (DFT) has been used for structural properties, while the Second-order Møller-Plesset Perturbation Theory (MP2) has been employed for the NLO calculations.

Keywords: biological imaging, hyperpolarizability, nonlinear optics, probing molecule

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Authors: Geeta Partap, Nitika Chugh

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The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: microstretch, deflection, exponential load, Laplace transforms, residue theorem, simply supported

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Authors: Karen E. Supan

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Thermal degradation kinetics of switchgrass (Panicum virgatum) from the field, as well as in a pellet form, are presented. Thermogravimetric analysis tests were performed at heating rates of 10-40 K min⁻¹ in an inert atmosphere. The activation energy and the pre-exponential factor were calculated using the Ozawa/Flynn/Wall method as suggested by the ASTM Standard Test Method for Decomposition Kinetics by Thermogravimetry. Four stages were seen in the degradation: dehydration, active pyrolysis of hemicellulose, active pyrolysis of cellulose, and passive pyrolysis. The derivative mass loss peak for active pyrolysis of cellulose in the field-dried sample was much higher than the pelletized. The range of activation energy in the 0.15 – 0.70 conversion interval was 191 – 242 kJ mol⁻¹ for the field-dried and 130-192 kJ mol⁻¹ for the pellets. The highest activation energies were achieved at 0.50 conversion and were 242 kJ mol⁻¹ and 192 kJ mol⁻¹ for the field-dried and pellets, respectively. The thermal degradation and activation energies were comparable to switchgrass and other biomass reported in the literature.

Keywords: biomass, switchgrass, thermal degradation, thermogravimetric analysis

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Authors: Abdelkarim M. Ertiame, D. W. Yu, D. L. Yu, J. B. Gomm

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In this paper, a new robust fault detection and isolation (FDI) scheme is developed to monitor a multivariable nonlinear chemical process called the Chylla-Haase polymerization reactor when it is under the cascade PI control. The scheme employs a radial basis function neural network (RBFNN) in an independent mode to model the process dynamics and using the weighted sum-squared prediction error as the residual. The recursive orthogonal Least Squares algorithm (ROLS) is employed to train the model to overcome the training difficulty of the independent mode of the network. Then, another RBFNN is used as a fault classifier to isolate faults from different features involved in the residual vector. The several actuator and sensor faults are simulated in a nonlinear simulation of the reactor in Simulink. The scheme is used to detect and isolate the faults on-line. The simulation results show the effectiveness of the scheme even the process is subjected to disturbances and uncertainties including significant changes in the monomer feed rate, fouling factor, impurity factor, ambient temperature and measurement noise. The simulation results are presented to illustrate the effectiveness and robustness of the proposed method.

Keywords: Robust fault detection, cascade control, independent RBF model, RBF neural networks, Chylla-Haase reactor, FDI under closed-loop control

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Authors: Shangerganesh Lingeshwaran

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In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: Brahmi Brahim, Mohammad Habibur Rahman, Maarouf Saad, Cristóbal Ochoa Luna

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A repetitive training movement is an efficient method to improve the ability and movement performance of stroke survivors and help them to recover their lost motor function and acquire new skills. The ETS-MARSE is seven degrees of freedom (DOF) exoskeleton robot developed to be worn on the lateral side of the right upper-extremity to assist and rehabilitate the patients with upper-extremity dysfunction resulting from stroke. Practically, rehabilitation activities are repetitive tasks, which make the assistive/robotic systems to suffer from repetitive/periodic uncertainties and external perturbations induced by the high-order dynamic model (seven DOF) and interaction with human muscle which impact on the tracking performance and even on the stability of the exoskeleton. To ensure the robustness and the stability of the robot, a new nonlinear backstepping control was implemented with designed tests performed by healthy subjects. In order to limit and to reject the periodic/repetitive disturbances, an iterative estimator was integrated into the control of the system. The estimator does not need the precise dynamic model of the exoskeleton. Experimental results confirm the robustness and accuracy of the controller performance to deal with the external perturbation, and the effectiveness of the iterative estimator to reject the repetitive/periodic disturbances.

Keywords: backstepping control, iterative control, Rehabilitation, ETS-MARSE

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Authors: Hasliza A. Rahim, Fareq Malek, Nur A. M. Affendi, Azuwa Ali, Norshafinash Saudin, Latifah Mohamed

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This paper presents the experimental investigation of on-body channel fading at 2.45 GHz considering two effects of the user body movement; stationary and mobile. A pair of body-worn antennas was utilized in this measurement campaign. A statistical analysis was performed by comparing the measured on-body path loss to five well-known distributions; lognormal, normal, Nakagami, Weibull and Rayleigh. The results showed that the average path loss of moving arm varied higher than the path loss in sitting position for upper-arm-to-left-chest link, up to 3.5 dB. The analysis also concluded that the Nakagami distribution provided the best fit for most of on-body static link path loss in standing still and sitting position, while the arm movement can be best described by log-normal distribution.

Keywords: on-body channel communications, fading characteristics, statistical model, body movement

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Authors: Y. Bhatt, N. Ghosh, N. Tiwari

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Acreage response function are modeled taking account of expected harvest prices, weather related variables and other non-price variables allowing for partial adjustment possibility. At the outset, based on the literature on price expectation formation, we explored suitable formulations for estimating the farmer’s expected prices. Assuming that farmers form expectations rationally, the prices of food and biofuel crops are modeled using time-series methods for possible ARCH/GARCH effects to account for volatility. The prices projected on the basis of the models are then inserted to proxy for the expected prices in the acreage response functions. Food crop acreages in different growing states are found sensitive to their prices relative to those of one or more of the biofuel crops considered. The required percentage improvement in food crop yields is worked to offset the acreage loss.

Keywords: acreage response function, biofuel, food security, sustainable development

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Authors: David C. Ni

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In the previous efforts, we constructed N-Body Systems by an extended Blaschke product (EBP), which represents a non-temporal and nonlinear extension of Lorentz transformation. In this construction, we rely only on two parameters, nonlinear degree, and relative momentum to characterize the systems. We further explored root computation via iteration with an algorithm extended from Jenkins-Traub method. The solution sets demonstrate a form of σ+ i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various canonical distributions. In this paper, we correlate the convergent sets in the original domain with solution sets, which demonstrating large-deviation distributions in the codomain. We proceed to compare our approach with the formula or principles, such as Donsker-Varadhan and Wentzell-Freidlin theories. The deterministic model based on this construction allows us to explore applications in the areas of finance and statistical mechanics.

Keywords: nonlinear Lorentz transformation, Blaschke equation, iteration solutions, root computation, large deviation distribution, deterministic model

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Authors: Pavle Dakić, Dimitrije Kotur, Zoran Stojanović

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This paper presents the results of the study in which the excitation system fault of synchronous generator is simulated. In a case of excitation system fault (loss of field), distance relay is used to prevent further damage. Loss-of-field relay calculates complex impedance using measured voltage and current at the generator terminals. In order to obtain phasors from sampled measured values, discrete Fourier transform is used. All simulations are conducted using Matlab and Simulink software package. The analysis is conducted on the two machine system which supplies equivalent load. While simulating loss of excitation on one generator in different conditions (at idle operation, weakly loaded, and fully loaded), diagrams of active power, reactive power, and measured impedance are analyzed and monitored. Moreover, in the simulations, the effect of generator load on relay tripping time is investigated. In conclusion, the performed tests confirm that the fault in the excitation system can be detected by measuring the impedance.

Keywords: loss-of-excitation, synchronous generator, distance protection, Fourier transformation

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Authors: Abderraouf Gaaloul, Faouzi Msahli

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The use of standard sliding mode controller, usually, leads to the appearing of an undesirable chattering phenomenon affecting the control signal. Such problem can be overcome using a higher-order sliding mode controller (HOSMC) which preserves the main properties of the standard sliding mode and deliberately increases the control smoothness. In this paper, we propose a new HOSMC for a class of uncertain multi-input multi-output nonlinear systems. Based on high gain and integral sliding mode paradigms, the established control scheme removes theoretically the chattering phenomenon and provides the stability of the control system. Numerical simulations are developed to show the effectiveness of the proposed controller when applied to solve a control problem of two water levels into a quadruple-tank process.

Keywords: nonlinear systems, sliding mode control, high gain, higher order

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Authors: Ridha Fethi Mechlouch, Ahlem Ayadi, Ammar Ben Brahim

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Given the importance of the preservation of polyphenols and carotenoids during thermal processing, we attempted in this study to investigate the variation of these two parameters in faba beans during microwave treatment using different power densities (1; 2; and 3W/g), then to perform a mathematical modeling by using non-linear regression analysis to evaluate the models constants. The variation of the carotenoids and polyphenols ratio of faba beans and the models are tested to validate the experimental results. Exponential models were found to be suitable to describe the variation of caratenoid ratio (R²= 0.945, 0.927 and 0.946) for power densities (1; 2; and 3W/g) respectively, and polyphenol ratio (R²= 0.931, 0.989 and 0.982) for power densities (1; 2; and 3W/g) respectively. The effect of microwave power density Pd(W/g) on the coefficient k of models were also investigated. The coefficient is highly correlated (R² = 1) and can be expressed as a polynomial function.

Keywords: microwave treatment, power density, carotenoid, polyphenol, modeling

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Authors: Dong Sang Yoo

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We consider nonlinear uncertain systems such that a priori information of the uncertainties is not available. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound and design a continuous robust control which renders nonlinear uncertain systems ultimately bounded.

Keywords: adaptive control, estimation, Fredholm integral, uncertain system

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Authors: Magdy Roman, Mostafa Shoeib, Mostafa Rostom

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Global vision, whether provided by overhead fixed cameras, on-board aerial vehicle cameras, or satellite images can always provide detailed information on the environment around mobile robots. In this paper, an intelligent vision-based method of path planning and obstacle avoidance for mobile robots is presented. The method integrates visual perception with a new proposed field-based path-planning method to overcome common path-planning problems such as local minima, unreachable destination and unnecessary lengthy paths around obstacles. The method proposes an exponential angle deviation field around each obstacle that affects the orientation of a close robot. As the robot directs toward, the goal point obstacles are classified into right and left groups, and a deviation angle is exponentially added or subtracted to the orientation of the robot. Exponential field parameters are chosen based on Lyapunov stability criterion to guarantee robot convergence to the destination. The proposed method uses obstacles' shape and location, extracted from global vision system, through a collision prediction mechanism to decide whether to activate or deactivate obstacles field. In addition, a search mechanism is developed in case of robot or goal point is trapped among obstacles to find suitable exit or entrance. The proposed algorithm is validated both in simulation and through experiments. The algorithm shows effectiveness in obstacles' avoidance and destination convergence, overcoming common path planning problems found in classical methods.

Keywords: path planning, collision avoidance, convergence, computer vision, mobile robots

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Authors: Hocine Hammoum, Karima Bouzelha, Lounis Ziani, Lounis Hamitouche

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In this paper, we study a complex structure which is an apartment building surmounted by a reinforced concrete water tank. The tank located on the top floor of the building is a container with capacity of 1000 m³. The building is complex in its design, its calculation and by its behavior under earthquake effect. This structure located in Algiers and aged of 53 years has been subjected to several earthquakes, but the earthquake of May 21^st, 2003 with a magnitude of 6.7 on the Richter scale that struck Boumerdes region at 40 Kms East of Algiers was fatal for it. It was downgraded after an investigation study because the central core sustained serious damage. In this paper, to estimate the degree of its damages, the seismic performance of the structure will be evaluated taking into account the hydrodynamic effect, using a static equivalent nonlinear analysis called pushover.

Keywords: performance analysis, building, reinforced concrete tank, seismic analysis, nonlinear analysis, hydrodynamic, pushover

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Authors: A. Oukaci, R. Toufouti, D. Dib, l. Atarsia

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This article presents a multitude of alternative techniques to control the vector control, namely the nonlinear control and sliding mode control. Moreover, the implementation of their control law applied to the high-performance to the induction motor with the objective to improve the tracking control, ensure stability robustness to parameter variations and disturbance rejection. Tests are performed numerical simulations in the Matlab/Simulink interface, the results demonstrate the efficiency and dynamic performance of the proposed strategy.

Keywords: Induction Motor (IM), Non-linear Control (NLC), Sliding Mode Control (SMC), nonlinear sliding surface

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Authors: Ceren Vardar Acar, Mine Caglar

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In finance, the price of a volatile asset can be modeled using fractional Brownian motion (fBm) with Hurst parameter H>1/2. The Black-Scholes model for the values of returns of an asset using fBm is given as, 〖Y_t=Y_0 e^((r+μ)t+σB)〗_t^H, 0≤t≤T where Y_0 is the initial value, r is constant interest rate, μ is constant drift and σ is constant diffusion coefficient of fBm, which is denoted by B_t^H where t≥0. Black-Scholes model can be constructed with some Markov processes such as Brownian motion. The advantage of modeling with fBm to Markov processes is its capability of exposing the dependence between returns. The real life data for a volatile asset display long-range dependence property. For this reason, using fBm is a more realistic model compared to Markov processes. Investors would be interested in any kind of information on the risk in order to manage it or hedge it. The maximum possible loss is one way to measure highest possible risk. Therefore, it is an important variable for investors. In our study, we give some theoretical bounds on the distribution of maximum possible loss of fBm. We provide both asymptotical and strong estimates for the tail probability of maximum loss of standard fBm and fBm with drift and diffusion coefficients. In the investment point of view, these results explain, how large values of possible loss behave and its bounds.

Keywords: maximum drawdown, maximum loss, fractional brownian motion, large deviation, Gaussian process

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Authors: L. Foudia, K. Haddadi, M. Reffas

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First principles study of structural, elastic, electronic and optical properties of the monoclinic perovskite type ScRhO₃ has been reported using the pseudo-potential plane wave method within the local density approximation. The calculated lattice parameters, including the lattice constants and angle β, are in excellent agreement with the available experimental data, which proving the reliability of the chosen theoretical approach. Pressure dependence up to 20 GPa of the single crystal and polycrystalline elastic constants has been investigated in details using the strain-stress approach. The mechanical stability, ductility, average elastic wave velocity, Debye temperature and elastic anisotropy were also assessed. Electronic band structure and density of states (DOS) demonstrated its semiconducting nature showing a direct band gap of 1.38 eV. Furthermore, several optical properties, such as absorption coefficient, reflectivity, refractive index, dielectric function, optical conductivity and electron energy loss function, have been calculated for radiation up to 40 eV.

Keywords: ab-initio, perovskite, DFT, band gap

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Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Yosra Baaziz, Moez Labidi

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Given limited research on monetary policy rules in revolutionary countries, this paper challenges the suitability of the Taylor rule in characterizing the monetary policy behavior of the Tunisian Central Bank (BCT), especially in turbulent times. More specifically, we investigate the possibility that the Taylor rule should be formulated as a threshold process and examine the validity of such nonlinear Taylor rule as a robust rule for conducting monetary policy in Tunisia. Using quarterly data from 1998:Q4 to 2013:Q4 to analyze the movement of nominal short-term interest rate of the BCT, we find that the nonlinear Taylor rule improves its performance with the advent of special events providing thus a better description of the Tunisian interest rate setting. In particular, our results show that the adoption of an appropriate nonlinear approach leads to a reduction in the errors of 150 basis points in 1999 and 2009, and 60 basis points in 2011, relative to the linear approach.

Keywords: policy rule, central bank, exchange rate, taylor rule, nonlinearity

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