Search results for: nonlinear filter generator

Authors: Daljinder Singh, J.S.Dhillon, Balraj Singh

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According to no free lunch theorem, a single search technique cannot perform best in all conditions. Optimization method can be attractive choice to solve optimization problem that may have exclusive advantages like robust and reliable performance, global search capability, little information requirement, ease of implementation, parallelism, no requirement of differentiable and continuous objective function. In order to synergize between exploration and exploitation and to further enhance the performance of Bat algorithm, the paper proposed a modified bat algorithm that adds additional search procedure based on bat’s previous experience. The proposed algorithm is used for solving the economic load dispatch (ELD) problem. The practical constraint such valve-point loading along with power balance constraints and generator limit are undertaken. To take care of power demand constraint variable elimination method is exploited. The proposed algorithm is tested on various ELD problems. The results obtained show that the proposed algorithm is capable of performing better in majority of ELD problems considered and is at par with existing algorithms for some of problems.

Keywords: bat algorithm, economic load dispatch, penalty method, variable elimination method

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Abdou Khafor Ndiaye

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The article examines clean water and sanitation in Saint-Louis region schools. It finds that 59% have clean water, with disparities between departments, urban/rural areas, and school types. Podor and Dagana lack water due to distance and costs. 70% have sanitation, but rural schools lack it due to low investment. Podor and Dagana suffer the most. Many sanitation facilities need renovation. Wastewater treatment is effective, reducing pollutants and nitrogen, but adjustments are needed for nitrates. Treated water meets Senegalese standards and can be used for irrigation but needs monitoring for strict standards. In conclusion, the wastewater system is good for regions with limited water. Meeting stricter European standards and monitoring for health and environmental standards are needed.

Keywords: water, constructed wetland, sanitation, hygiene

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Authors: Baptiste Bouvier

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While we are constantly flooded with stimuli in daily life, attention allows us to select the ones we specifically process and ignore the others. Some salient stimuli may sometimes pass this filter independently of our will, in a "bottom-up" way. The role of the acoustic properties of the timbre of a sound on its salience, i.e., its ability to capture the attention of a listener, is still not well understood. We implemented a paradigm called the "additional singleton paradigm", in which participants have to discriminate targets according to their duration. This task is perturbed (higher error rates and longer response times) by the presence of an irrelevant additional sound, of which we can manipulate a feature of our choice at equal loudness. This allows us to highlight the influence of the timbre features of a sound stimulus on its salience at equal loudness. We have shown that a stimulus that is brighter than the others but not louder leads to an attentional capture phenomenon in this framework. This work opens the door to the study of the influence of any timbre feature on salience.

Keywords: attention, audition, bottom-up attention, psychoacoustics, salience, timbre

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Authors: Roza Afarin, Saeed Mozaffari

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The aim of this paper is image encryption using Genetic Algorithm (GA). The proposed encryption method consists of two phases. In modification phase, pixels locations are altered to reduce correlation among adjacent pixels. Then, pixels values are changed in the diffusion phase to encrypt the input image. Both phases are performed by GA with binary chromosomes. For modification phase, these binary patterns are generated by Local Binary Pattern (LBP) operator while for diffusion phase binary chromosomes are obtained by Bit Plane Slicing (BPS). Initial population in GA includes rows and columns of the input image. Instead of subjective selection of parents from this initial population, a random generator with predefined key is utilized. It is necessary to decrypt the coded image and reconstruct the initial input image. Fitness function is defined as average of transition from 0 to 1 in LBP image and histogram uniformity in modification and diffusion phases, respectively. Randomness of the encrypted image is measured by entropy, correlation coefficients and histogram analysis. Experimental results show that the proposed method is fast enough and can be used effectively for image encryption.

Keywords: correlation coefficients, genetic algorithm, image encryption, image entropy

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Authors: Dib Djalel, Mordjaoui Mourad

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The current trend towards the exploitation of various renewable energy resources has become indispensable, so it is important to improve the efficiency and reliability of the GPV photovoltaic systems. Maximum Power Point Tracking (MPPT) plays an important role in photovoltaic power systems because it maximize the power output from a PV system for a given set of conditions. This paper presents a new fuzzy logic control based MPPT algorithm for solar panel. The solar panel is modeled and analyzed in Matlab/Simulink. The Solar panel can produce maximum power at a particular operating point called Maximum Power Point(MPP). To produce maximum power and to get maximum efficiency, the entire photovoltaic panel must operate at this particular point. Maximum power point of PV panel keeps on changing with changing environmental conditions such as solar irradiance and cell temperature. Thus, to extract maximum available power from a PV module, MPPT algorithms are implemented and Perturb and Observe (P&O) MPPT and fuzzy logic control FLC, MPPT are developed and compared. Simulation results show the effectiveness of the fuzzy control technique to produce a more stable power.

Keywords: MPPT, photovoltaic panel, fuzzy logic control, modeling, solar power

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Authors: Wael M. Bazzi, Amir Rastegarnia, Azam Khalili

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In this paper we consider the issue of reliability of measurements in distributed adaptive estimation problem. To this aim, we assume a sensor network with different observation noise variance among the sensors and propose new estimation method based on incremental distributed least mean-square (IDLMS) algorithm. The proposed method contains two phases: I) Estimation of each sensors observation noise variance, and II) Estimation of the desired parameter using the estimated observation variances. To deal with the reliability of measurements, in the second phase of the proposed algorithm, the step-size parameter is adjusted for each sensor according to its observation noise variance. As our simulation results show, the proposed algorithm considerably improves the performance of the IDLMS algorithm in the same condition.

Keywords: adaptive filter, distributed estimation, sensor network, IDLMS algorithm

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: Ali Y Al-Attraqchi, P. Rajeev, M. Javad Hashemi, Riadh Al-Mahaidi

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This paper presents a probabilistic incremental dynamic analysis (IDA) of a full reinforced concrete building subjected to column loss scenario for the assessment of progressive collapse. The IDA is chosen to explicitly account for uncertainties in loads and system capacity. Fragility curves are developed to predict the probability of progressive collapse given the loss of one or more columns. At a broader scale, it will also provide critical information needed to support the development of a new generation of design codes that attempt to explicitly quantify structural robustness.

Keywords: fire, nonlinear incremental dynamic analysis, progressive collapse, structural engineering

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Authors: Hisham M. Soliman, Hassan Yousef

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This manuscript presents new results on design saturated power system stabilizers (PSS) to assign system poles within a desired region for achieving good dynamic performance. The regional pole placement is accomplished against model uncertainties caused by different load conditions. The design is based on a sufficient condition in the form of linear matrix inequalities (LMI) which forces the saturated nonlinear controller to lie within the linear zone. The controller effectiveness is demonstrated on a single machine infinite bus system.

Keywords: power system stabilizer, saturated control, robust control, regional pole placement, linear matrix inequality (LMI)

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Authors: Wilfred Fritz

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Grid connected solar PV inverters need to be compliant to standard regulations regarding unwanted harmonic generation. This paper gives an introduction to harmonics, solar PV inverter voltage regulation and balancing through compensation and investigates the behaviour of harmonic generation at different power levels. Practical measurements of harmonics and power levels with a power quality data logger were made, on a test network at a university in Germany. The test setup and test results are discussed. The major finding was that between the morning and afternoon load peak windows when the PV inverters operate under low solar insolation and low power levels, more unwanted harmonics are generated. This has a huge impact on the power quality of the grid as well as capital and maintenance costs. The design of a single-tuned harmonic filter towards harmonic mitigation is presented.

Keywords: harmonics, power quality, pulse width modulation, total harmonic distortion

Procedia PDF Downloads 239

Authors: B. Sellami, Y. Laskri, M. Belloufi

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Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, a new family of conjugate gradient method is proposed for unconstrained optimization. This method includes the already existing two practical nonlinear conjugate gradient methods, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the Wolfe conditions. The numerical experiments are done to test the efficiency of the new method, which implies the new method is promising. In addition the methods related to this family are uniformly discussed.

Keywords: conjugate gradient method, global convergence, line search, unconstrained optimization

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Authors: Thomas Paris, Vincent Bruyere, Patrick Namy

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A numerical model is developed to simulate gas blowdowns through a thin tube and a filter (porous media), separating a high pressure gas filled reservoir to low pressure ones. Based on a previous work, a one-dimensional approach is developed by using the finite element method to solve the transient compressible flow and to predict the pressure and temperature evolution in space and time. Mass, momentum, and energy conservation equations are solved in a fully coupled way in the reservoirs, the pipes and the porous media. Numerical results, such as pressure and temperature evolutions, are firstly compared with experimental data to validate the model for different configurations. Couplings between porous media and pipe flow are then validated by checking mass balance. The influence of the porous media and the nature of the gas is then studied for different initial high pressure values.

Keywords: compressible flow, fluid mechanics, heat transfer, porous media

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Authors: Frie Ayalew, Seada Hussen

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Ethio-telecom holds a variety of telecom devices that needs a consistent power source to be operational. The company got this power mainly from the national grid and used this power source alone or with a generator and/or batteries as a backup. In addition, for off-grid or remote areas, the company commonly uses generators and batteries. But unstable diesel prices, huge expenses of fuel and transportation, and high carbon emissions are the main problems associated with fuel energy. So, the design of solar power with battery backup is a highly recommended and advantageous source for the next coming years. This project designs the AC and DC standalone photovoltaic supply to Ethio-telecom access layer devices for the case of multi-service access gateway in Adama. The design is done by using Homer software for both AC and DC loads. The project shows that the design of a solar based microgrid is the best option for the designed area.

Keywords: solar power, battery, inverter, Ethio-telecom, solar radiation

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Authors: Bachir Bentouati, Lakhdar Chaib, Saliha Chettih, Gai-Ge Wang

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The problem of economic dispatch (ED) is the basic problem of power framework, its main goal is to find the most favorable generation dispatch to generate each unit, reduce the whole power generation cost, and meet all system limitations. A heuristic algorithm, recently developed called Stud Krill Herd (SKH), has been employed in this paper to treat non-convex ED problems. The proposed KH has been modified using Stud selection and crossover (SSC) operator, to enhance the solution quality and avoid local optima. We are demonstrated SKH effects in two case study systems composed of 13-unit and 40-unit test systems to verify its performance and applicability in solving the ED problems. In the above systems, SKH can successfully obtain the best fuel generator and distribute the load requirements for the online generators. The results showed that the use of the proposed SKH method could reduce the total cost of generation and optimize the fulfillment of the load requirements.

Keywords: stud krill herd, economic dispatch, crossover, stud selection, valve-point effect

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Authors: Ilkay Turk Cakir, Murat Altinli, Zekeriya Uysal, Abdulkadir Senol, Olcay Bolukbasi Yalcinkaya, Ali Yilmaz

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The Higgs boson was discovered by the ATLAS and CMS experimental groups in 2012 at the Large Hadron Collider (LHC). Production and decay properties of the Higgs boson, Standard Model (SM) couplings, and limits on effective scale of the Higgs boson’s couplings with other bosons are investigated at particle colliders. Deviations from SM estimates are parametrized by effective Lagrangian terms to investigate Higgs couplings. This is a model-independent method for describing the new physics. In this study, sensitivity to neutral gauge boson anomalous couplings with the Higgs boson is investigated using the parameters of the Large Hadron electron Collider (LHeC) and the Future Circular electron-hadron Collider (FCC-eh) with a model-independent approach. By using MadGraph5_aMC@NLO multi-purpose event generator with the parameters of LHeC and FCC-eh, the bounds on the anomalous Hγγ, HγZ and HZZ couplings in e− p → e− q H process are obtained. Detector simulations are also taken into account in the calculations.

Keywords: anomalos couplings, FCC-eh, Higgs, Z boson

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Authors: Roswati Md. Amin, Nurul Asmera Mudiman, Muhammad Faisal Abd. Rahman, Md-Suffian Idris, Noor Hazwani Mohd Azmi

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Distribution of picophytoplankton from two genera, Synechococcus and Prochlorococcus at the surface water (0.5m) were observed from coastal to offshore area of the southeastern coast of Peninsular Malaysia, for a six day cruise in August 2014 during SouthWest monsoon. The picophytoplankton was divided into two different size fractions (0.7-2.7μm and <0.7 μm) by filtering through GF/D (2.7 μm) and GF/F (0.7 μm) filter papers and counted by using flow cytometer. Synechococcus and Prochlorococcus contribute higher at 0.7-2.7μm size range (ca. 90% and 95%, respectively) compared to <0.7 μm (ca. 10% and 5%, respectively). Synechococcus (>52%) dominated the total picophytoplankton compared to Prochlorococcus (<26%) for both size fractions in southeastern coast of Peninsular Malaysia. Total density (<2.7 μm) of Synechococcus was ranging between 1.72 x104 and 12.57 x104 cells ml-1, while Prochlorococcus varied from 1.50 x104 to 8.62 x104. Both Synechococcus and Prochlorococcus abundance showed a decreasing trend from coastal to offshore.

Keywords: Peninsular Malaysia, prochlorococcus, South China Sea, synechococcus

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Authors: M. Akhlaque Ahmed, Maliha Afshan Siddiqui

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A study has been carried out to see the prospect of wind power potential of southern Sindh namely Karachi, Hawksbay, Norriabad, Hyderabad, Ketibander and Shahbander using local wind speed data. The monthly average wind speed for these area ranges from 4.5m/sec to 8.5m/sec at 30m height from ground. Extractable wind power, wind energy and Weibul parameter for above mentioned areas have been examined. Furthermore, the power output using fast and slow wind machine using different blade diameter along with the 4Kw and 20 Kw aero-generator were examined to see the possible use for deep well pumping and electricity supply to remote villages. The analysis reveals that in this wind corridor of southern Sindh Hawksbay, Ketibander and Shahbander belongs to wind power class-3 Hyderabad and Nooriabad belongs to wind power class-5 and Karachi belongs to wind power class-2. The result shows that the that higher wind speed values occur between June till August. It was found that considering maximum wind speed location, Hawksbay,Noriabad are the best location for setting up wind machines for power generation.

Keywords: wind energy generation, Southern Sindh, seasonal change, Weibull parameter, wind machines

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Authors: Md. Abud Darda

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Different options for natural gas production in wide geographic areas may be described through diffusion of innovation models. This type of modeling approach provides an indirect estimate of an ultimately recoverable resource, URR, capture the quantitative effects of observed strategic interventions, and allow ex-ante assessments of future scenarios over time. In order to ensure a sustainable energy policy, it is important to forecast the availability of this natural resource. Considering a finite life cycle, in this paper we try to investigate the natural gas production of Myanmar and Algeria, two important natural gas provider in the world energy market. A number of homogeneous and heterogeneous diffusion models, with convenient extensions, have been used. Models validation has also been performed in terms of prediction capability.

Keywords: diffusion models, energy forecast, natural gas, nonlinear production

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Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

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Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: decentralized, optimal control, output, singular perturb

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Authors: Javier Menéndez, Jorge Loredo

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Large scale energy storage systems (LSESS) such as pumped-storage hydro-power (PSH) are required in the current energy transition towards a low carbon economy by using green energies that produce low levels of greenhouse gas (GHG) emissions. Coal mines are currently being closed in the European Union and their underground facilities may be used to build PSH plants. However, the development of this projects requires the excavation of a network of tunnels and a large cavern that would be used as a powerhouse to install the Francis turbine and motor-generator. The technical feasibility to excavate the powerhouse cavern has been analyzed in the North of Spain. Three-dimensional numerical models have been conducted to analyze the stability considering shale and sandstone rock mass. Total displacements and thickness of plastic zones were examined considering different support systems. Systematic grouted rock bolts and fibre reinforced shotcrete were applied at the cavern walls and roof. The results obtained show that the construction of the powerhouse is feasible applying proper support systems.

Keywords: closed mines, mine water, numerical model, pumped-storage, renewable energies

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Authors: Harsh Vikram Singh, Ankur Rai, Anand Mohan

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In this paper, we propose secure and robust data hiding algorithm based on DCT by Arnold transform and chaotic sequence. The watermark image is scrambled by Arnold cat map to increases its security and then the chaotic map is used for watermark signal spread in middle band of DCT coefficients of the cover image The chaotic map can be used as pseudo-random generator for digital data hiding, to increase security and robustness .Performance evaluation for robustness and imperceptibility of proposed algorithm has been made using bit error rate (BER), normalized correlation (NC), and peak signal to noise ratio (PSNR) value for different watermark and cover images such as Lena, Girl, Tank images and gain factor .We use a binary logo image and text image as watermark. The experimental results demonstrate that the proposed algorithm achieves higher security and robustness against JPEG compression as well as other attacks such as addition of noise, low pass filtering and cropping attacks compared to other existing algorithm using DCT coefficients. Moreover, to recover watermarks in proposed algorithm, there is no need to original cover image.

Keywords: data hiding, watermarking, DCT, chaotic sequence, arnold transforms

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Authors: N. Kotabin, Y. Tahara, K. Issakul, O. Chunhachart

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Cadmium (II) (Cd) is one of the major toxic elemental pollutants which is hazardous for humans, animals and plants. γ-Polyglutamic acid (γ-PGA) is an extracellular biopolymer produced by several species of Bacillus which has been reported to be an effective biosorbent for metal ions. The effect of γ-PGA on growth of rice grown under laboratory conditions was investigated. Rice seeds were germinated and then grown at 30±1°C on filter paper soaked with Cd solution and γ-PGA for 7 days. The result showed that Cd significantly inhibited the growth of roots and shoots by reducing root and shoot lengths. Fresh and dry weights also decreased compared with control; however, the addition of 500 mg•L-1 γ-PGA alleviated rice seedlings from the adverse effects of Cd. The analysis of physiological traits revealed that Cd caused a decrease in the total chlorophyll and soluble protein contents and amylase activities in all treatments. The Cd content in seedling tissues increased for the Cd 250 μM treatment (P < 0.05) but the addition of 500 mg•L-1 γ-PGA resulted in a noticeable decrease in Cd (P < 0.05).

Keywords: polyglutamic acid, cadmium, rice, bacillus subtilis

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Authors: Khelil Khadidja

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In this paper, blackness of dark solitons is considered. The exact combination between nonlinearity and dispersion is responsible of solitons stability. Dark solitons get born when dispersion is abnormal and balanced by nonlinearity, at the opposite of brillant solitons which is born by normal dispersion and nonlinearity together. Thanks to their stability, dark solitons are suitable for transmission by optical fibers. Dark solitons which are a solution of Nonlinear Schrodinger equation are simulated with Matlab to discuss the influence of coefficient of blackness. Results show that there is a direct proportion between the coefficient of blackness and the intensity of dark soliton. Those gray solitons are stable and convenient for transmission.

Keywords: abnormal dispersion, nonlinearity, optical fiber, soliton

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Authors: Maryam Ebrahimpour, Amir Ebrahimi

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This paper presents the steady-state amplitude analysis of MOS Colpitts oscillator with short channel device. The proposed method is based on a large signal analysis and the nonlinear differential equations that govern the oscillator circuit behaviour. Also, the short channel effects are considered in the proposed analysis and analytical equations for finding the steady-state oscillation amplitude are derived. The output voltage calculated from this analysis is in excellent agreement with simulations for a wide range of circuit parameters.

Keywords: colpitts oscillator, CMOS, electronics, circuits

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Authors: M. A. Badr, M. N. El Kordy, A. N. Mohib, M. M. Ibrahim

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The basic objective of the research is to study the effect of hybrid wind energy on the cost of generated electricity considering the cost of reduction CO₂ emissions. The system consists of small wind turbine(s), storage battery bank and a diesel generator (W/D/B). Using an optimization software package, different system configurations are investigated to reach optimum configuration based on the net present cost (NPC) and cost of energy (COE) as economic optimization criteria. The cost of avoided CO₂ is taken into consideration. The system is intended to supply the electrical load of a small community (gathering six families) in a remote Egyptian area. The investigated system is not connected to the electricity grid and may replace an existing conventional diesel powered electric supply system to reduce fuel consumption and CO₂ emissions. The simulation results showed that W/D energy system is more economic than diesel alone. The estimated COE is 0.308$/kWh and extracting the cost of avoided CO₂, the COE reached 0.226 $/kWh which is an external benefit of wind turbine, as there are no pollutant emissions through operational phase.

Keywords: hybrid wind turbine systems, remote areas electrification, simulation of hybrid energy systems, techno-economic study

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Authors: Muthana A. M. Jameel Al-Jaboori

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In this paper, we will present a mathematical model to design a system able to generate electricity from ocean-sea waves. We will use the basic principles of the transfer of the energy potential of waves in a chamber to force the air inside a vertical or inclined cylindrical column, which is topped by a wind turbine to rotate the electric generator. The present mathematical model included a high number of variables such as the wave, height, width, length, velocity, and frequency, as well as others for the energy cylindrical column, like varying diameters and heights, and the wave chamber shape diameter and height. While for the wells wind turbine the variables included the number of blades, length, width, and clearance, as well as the rotor and tip radius. Additionally, the turbine rotor and blades must be made from the light and strong material for a smooth blade surface. The variables were too vast and high in number. Then the program was run successfully within the MATLAB and presented very good modeling results.

Keywords: water wave, models, Wells turbine, MATLAB program

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Authors: Suad M. Abuzariba, Eman O. Mafaa

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For three level atom interacts with a laser beam, the effect of changing resonance and off-resonance frequencies has been studied. Furthermore, a clear distortion has been seen in both the real and imaginary parts of the electric susceptibility with increasing the frequency of the coupled laser beams so that reaching the off-resonance interaction. With increasing the Rabi frequency of the laser pulse that in resonance with the lower transition the distortion will produce a new peak in the electric susceptibility parts, in both the real and imaginary ones.

Keywords: electric susceptibility, resonance frequency off-resonance frequency, three level atom, laser

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

Procedia PDF Downloads 444