Search results for: fully differential bandpass amplifier
3367 Choosing an Optimal Epsilon for Differentially Private Arrhythmia Analysis
Authors: Arin Ghazarian, Cyril Rakovski
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Differential privacy has become the leading technique to protect the privacy of individuals in a database while allowing useful analysis to be done and the results to be shared. It puts a guarantee on the amount of privacy loss in the worst-case scenario. Differential privacy is not a toggle between full privacy and zero privacy. It controls the tradeoff between the accuracy of the results and the privacy loss using a single key parameter calledKeywords: arrhythmia, cardiology, differential privacy, ECG, epsilon, medi-cal data, privacy preserving analytics, statistical databases
Procedia PDF Downloads 1423366 Study and Solving Partial Differential Equation of Danel Equation in the Vibration Shells
Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar
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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane
Procedia PDF Downloads 3143365 Nonlinear Evolution on Graphs
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
Procedia PDF Downloads 1383364 Reduction of Differential Column Shortening in Tall Buildings
Authors: Hansoo Kim, Seunghak Shin
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The differential column shortening in tall buildings can be reduced by improving material and structural characteristics of the structural systems. This paper proposes structural methods to reduce differential column shortening in reinforced concrete tall buildings; connecting columns with rigidly jointed horizontal members, using outriggers, and placing additional reinforcement at the columns. The rigidly connected horizontal members including outriggers reduce the differential shortening between adjacent vertical members. The axial stiffness of columns with greater shortening can be effectively increased by placing additional reinforcement at the columns, thus the differential column shortening can be reduced in the design stage. The optimum distribution of additional reinforcement can be determined by applying a gradient based optimization technique.Keywords: column shortening, long-term behavior, optimization, tall building
Procedia PDF Downloads 2453363 Producing of Amorphous-Nanocrystalline Composite Powders
Authors: K. Tomolya, D. Janovszky, A. Sycheva, M. Sveda, A. Roosz
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CuZrAl amorphous alloys have attracted high interest due to unique physical and mechanical properties, which can be enhanced by adding of Ni and Ti elements. It is known that this properties can be enhanced by crystallization of amorphous alloys creating nanocrystallines in the matrix. The present work intends to produce nanosized crystalline parti-cle reinforced amorphous matrix composite powders by crystallization of amorphous powders. As the first step the amorphous powders were synthe-tized by ball-milling of crystalline powders. (Cu49Zr45Al6) 80Ni10Ti10 and (Cu49Zr44Al7) 80Ni10Ti10 (at%) alloys were ball-milled for 12 hours in order to reach the fully amorphous structure. The impact en-ergy of the balls during milling causes the change of the structure in the powders. Scanning electron microscopical (SEM) images shows that the phases mixed first and then changed into a fully amorphous matrix. Furthermore, nanosized particles in the amorphous matrix were crystallized by heat treatment of the amorphous powders that was confirmed by TEM measurement. It was of importance to define the tem-perature when the amorphous phase starts to crystal-lize. Amorphous alloys have a special heating curve and characteristic temperatures, which can be meas-ured by differential scanning calorimetry (DSC). A typical DSC curve of an amorphous alloy exhibits an endothermic event characteristic of the equilibrium glass transition (Tg) and a distinct undercooled liquid region, followed by one or two exothermic events corresponding to crystallization processes (Tp). After measuring the DSC traces of the amorphous powders, the annealing temperatures should be determined between Tx and Tp. In our experiments several temperatures from the annealing temperature range were selected and de-pendency of crystallized nanoparticles fraction on their hardness was investigated.Keywords: amorphous structure, composite, mechanical milling, powder, scanning electron microscopy (SEM), differential scanning calorimetry (DSC), transmission electronmocroscopy (TEM)
Procedia PDF Downloads 4433362 On Boundary Value Problems of Fractional Differential Equations Involving Stieltjes Derivatives
Authors: Baghdad Said
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Differential equations of fractional order have proved to be important tools to describe many physical phenomena and have been used in diverse fields such as engineering, mathematics as well as other applied sciences. On the other hand, the theory of differential equations involving the Stieltjes derivative (SD) with respect to a non-decreasing function is a new class of differential equations and has many applications as a unified framework for dynamic equations on time scales and differential equations with impulses at fixed times. The aim of this paper is to investigate the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability (UHRS) of solutions for a boundary value problem of sequential fractional differential equations (SFDE) containing (SD). This study is based on the technique of noncompactness measures (MNCs) combined with Monch-Krasnoselski fixed point theorems (FPT), and the results are proven in an appropriate Banach space under sufficient hypotheses. We also give an illustrative example. In this work, we introduced a class of (SFDE) and the results are obtained under a few hypotheses. Future directions connected to this work could focus on another problem with different types of fractional integrals and derivatives, and the (SD) will be assumed under a more general hypothesis in more general functional spaces.Keywords: SFDE, SD, UHRS, MNCs, FPT
Procedia PDF Downloads 313361 Low Cost Surface Electromyographic Signal Amplifier Based on Arduino Microcontroller
Authors: Igor Luiz Bernardes de Moura, Luan Carlos de Sena Monteiro Ozelim, Fabiano Araujo Soares
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The development of a low cost acquisition system of S-EMG signals which are reliable, comfortable for the user and with high mobility shows to be a relevant proposition in modern biomedical engineering scenario. In the study, the sampling capacity of the Arduino microcontroller Atmel Atmega328 with an A/D converter with 10-bit resolution and its reconstructing capability of a signal of surface electromyography are analyzed. An electronic circuit to capture the signal through two differential channels was designed, signals from Biceps Brachialis of a healthy man of 21 years was acquired to test the system prototype. ARV, MDF, MNF and RMS estimators were used to compare de acquired signals with physiological values. The Arduino was configured with a sampling frequency of 1.5 kHz for each channel, and the tests with the circuit designed offered a SNR of 20.57dB.Keywords: electromyography, Arduino, low-cost, atmel atmega328 microcontroller
Procedia PDF Downloads 3593360 A Study of Flow near the Leading Edge of a Flat Plate by New Idea in Analytical Methods
Authors: M. R. Akbari, S. Akbari, L. Abdollahpour
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The present paper is concerned with calculating the 2-dimensional velocity profile of a viscous flow for an incompressible fluid along the leading edge of a flat plate by using the continuity and motion equations with a simple and innovative approach. A Comparison between Numerical method and AGM has been made and the results have been revealed that AGM is very accurate and easy and can be applied for a wide variety of nonlinear problems. It is notable that most of the differential equations can be solved in this approach which in the other approaches they do not have this capability. Moreover, there are some valuable benefits in this method of solving differential equations, for instance: Without any dimensionless procedure, we can solve many differential equation(s), that is, differential equations are directly solvable by this method. In addition, it is not necessary to convert variables into new ones. According to the afore-mentioned expressions which will be proved in this literature, the process of solving nonlinear differential equation(s) will be very simple and convenient in contrast to the other approaches.Keywords: leading edge, new idea, flat plate, incompressible fluid
Procedia PDF Downloads 2773359 Free Vibration of Axially Functionally Graded Simply Supported Beams Using Differential Transformation Method
Authors: A. Selmi
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Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.Keywords: differential transformation method, functionally graded material, mode shape, natural frequency
Procedia PDF Downloads 3003358 Study of Three Channel Electrode Position to Detect Optimum Myoelectric Signal on Five Type Grasp Movement
Authors: Ilham Priadythama, Pringgo Widyo Laksono, Agung Pamungkas
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Myoelectric is prosthetic, flexible, and offered industrial application has been highly developed and widely used. Myoelectric hand use myoelectric signal from muscle to activate and control the membrane part of hand. Commonly myoelectric signal is detected on human arm from skin surface. So that it only small magnitude signal captured. Detecting myoelectric signal on the skin surface takes proper and consistent procedure. This paper provides preliminary study of electrodes position which gives best signal strength for five basic grasping. Two-position scenario used to place three channel electrodes set. A bi-potential amplifier based on AD620 used to amplify the signal. Finally, the signal was analyzed using DSSF3 software. From this study, we found that grasp type was stronger using first scenario electrode placement while the rest type better with another scenario.Keywords: myoelectric signal, basic grasp, DSSF3, electrode, bi-potential amplifier
Procedia PDF Downloads 3183357 Critical Buckling Load of Carbon Nanotube with Non-Local Timoshenko Beam Using the Differential Transform Method
Authors: Tayeb Bensattalah, Mohamed Zidour, Mohamed Ait Amar Meziane, Tahar Hassaine Daouadji, Abdelouahed Tounsi
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In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. Influence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated.Keywords: boundary conditions, buckling, non-local, differential transform method
Procedia PDF Downloads 2933356 Stability Analysis of Two-delay Differential Equation for Parkinson's Disease Models with Positive Feedback
Authors: M. A. Sohaly, M. A. Elfouly
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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.Keywords: Parkinson's disease, stability, simulation, two delay differential equation
Procedia PDF Downloads 1233355 Analytical Solving of Nonlinear Differential Equations in the Nonlinear Phenomena for Viscos Fluids
Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin
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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena
Procedia PDF Downloads 2773354 Existence Theory for First Order Functional Random Differential Equations
Authors: Rajkumar N. Ingle
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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon
Procedia PDF Downloads 4923353 Design of CMOS CFOA Based on Pseudo Operational Transconductance Amplifier
Authors: Hassan Jassim Motlak
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A novel design technique employing CMOS Current Feedback Operational Amplifier (CFOA) is presented. The feature of consumption whivh has a very low power in designing pseudo-OTA is used to decreasing the total power consumption of the proposed CFOA. This design approach applies pseudo-OTA as input stage cascaded with buffer stage. Moreover, the DC input offset voltage and harmonic distortion (HD) of the proposed CFOA are very low values compared with the conventional CMOS CFOA due to symmetrical input stage. P-Spice simulation results using 0.18µm MIETEC CMOS process parameters using supply voltage of ±1.2V and 50μA biasing current. The P-Spice simulation shows excellent improvement of the proposed CFOA over existing CMOS CFOA. Some of these performance parameters, for example, are DC gain of 62. dB, open-loop gain-bandwidth product of 108 MHz, slew rate (SR+) of +71.2V/µS, THD of -63dB and DC consumption power (PC) of 2mW.Keywords: pseudo-OTA used CMOS CFOA, low power CFOA, high-performance CFOA, novel CFOA
Procedia PDF Downloads 3073352 Comprehensive Investigation of Solving Analytical of Nonlinear Differential Equations at Chemical Reactions to Design of Reactors by New Method “AGM”
Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji
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In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed
Procedia PDF Downloads 3733351 Micro-Oscillator: Passive Production and Manipulation of Microdrops
Authors: Khelfaoui Rachid, Chekifi Tawfiq, Dennai Brahim, Maazouzi A. Hak
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A numerical and experimental studies of passive micro drops production have been presented. This paper focuses on the modeling of micro-oscillators systems which are composed by passive amplifier without moving part. The micro-system modeling is based on geometrical oscillators form. An asymmetric micro-oscillator design that is based on a bistable fluidic amplifier is proposed. The characteristic size of the channels is generally about 35 microns of depth. The numerical results indicate that the production and manipulation of microdrops are possible with passive device within a typical oscillators chamber of 2.25 mm diameter and 0.20 mm length when the Reynolds number is Re = 490. The novel micro drops method that is presented in this study provides a simple solution about the production of microdrops problems in micro system. We undertake an experimental step. The first part is based on the realisation of sample oscillator; the second part is consisted of visualization, production and manipulation of microdrops.Keywords: modelling, miscible, micro drops, production, oscillator sample, capillary
Procedia PDF Downloads 3703350 Effects of the Slope Embankment Variation on Influence Areas That Causes the Differential Settlement around of Embankment
Authors: Safitri W. Nur, Prathisto Panuntun L. Unggul, M. Ivan Adi Perdana, R. Dary Wira Mahadika
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On soft soil areas, high embankment as a preloading needed to improve the bearing capacity of the soil. For sustainable development, the construction of embankment must not disturb the area around of them. So, the influence area must be known before the contractor applied their embankment design. For several cases in Indonesia, the area around of embankment construction is housing resident and other building. So that, the influence area must be identified to avoid the differential settlement occurs on the buildings around of them. Differential settlement causes the building crack. Each building has a limited tolerance for the differential settlement. For concrete buildings, the tolerance is 0,002 – 0,003 m and for steel buildings, the tolerance is 0,006 – 0,008 m. If the differential settlement stands on the range of that value, building crack can be avoided. In fact, the settlement around of embankment is assumed as zero. Because of that, so many problems happen when high embankment applied on soft soil area. This research used the superposition method combined with plaxis analysis to know the influences area around of embankment in some location with the differential characteristic of the soft soil. The undisturbed soil samples take on 55 locations with undisturbed soil samples at some soft soils location in Indonesia. Based on this research, it was concluded that the effects of embankment variation are if more gentle the slope, the influence area will be greater and vice versa. The largest of the influence area with h initial embankment equal to 2 - 6 m with slopes 1:1, 1:2, 1:3, 1:4, 1:5, 1:6, 1:7, 1:8 is 32 m from the edge of the embankment.Keywords: differential settlement, embankment, influence area, slope, soft soil
Procedia PDF Downloads 4043349 Modelling and Technical Assessment of Multi-Motor for Electric Vehicle Drivetrains by Using Electric Differential
Authors: Mohamed Abdel-Monem, Gamal Sowilam, Omar Hegazy
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This paper presents a technical assessment of an electric vehicle with two independent rear-wheel motor and an improved traction control system. The electric differential and the control strategy have been implemented to assure that in a straight trajectory, the two rear-wheels run exactly at the same speed, considering the same/different road conditions under the left and right side of the wheels. In case of turning to right/left, the difference between the two rear-wheels speeds assures a vehicle trajectory without sliding, thanks to a harmony between the electric differential and the control strategy. The present article demonstrates a complete model and analysis of a traction control system, considering four different traction scenarios, for two independent rear-wheels motors for electric vehicles. Furthermore, the vehicle model, including wheel dynamics, load forces, electric differential, and control strategy, is designed and verified by using MATLAB/Simulink environment.Keywords: electric vehicle, energy saving, multi-motor, electric differential, simulation and control
Procedia PDF Downloads 3483348 The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model
Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma
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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations
Procedia PDF Downloads 1383347 Low-Noise Amplifier Design for Improvement of Communication Range for Wake-Up Receiver Based Wireless Sensor Network Application
Authors: Ilef Ketata, Mohamed Khalil Baazaoui, Robert Fromm, Ahmad Fakhfakh, Faouzi Derbel
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The integration of wireless communication, e. g. in real-or quasi-real-time applications, is related to many challenges such as energy consumption, communication range, latency, quality of service, and reliability. To minimize the latency without increasing energy consumption, wake-up receiver (WuRx) nodes have been introduced in recent works. Low-noise amplifiers (LNAs) are introduced to improve the WuRx sensitivity but increase the supply current severely. Different WuRx approaches exist with always-on, power-gated, or duty-cycled receiver designs. This paper presents a comparative study for improving communication range and decreasing the energy consumption of wireless sensor nodes.Keywords: wireless sensor network, wake-up receiver, duty-cycled, low-noise amplifier, envelope detector, range study
Procedia PDF Downloads 1033346 Improved Impossible Differential Cryptanalysis of Midori64
Authors: Zhan Chen, Wenquan Bi, Xiaoyun Wang
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The Midori family of light weight block cipher is proposed in ASIACRYPT2015. It has attracted the attention of numerous cryptanalysts. There are two versions of Midori: Midori64 which takes a 64-bit block size and Midori128 the size of which is 128-bit. In this paper an improved 10-round impossible differential attack on Midori64 is proposed. Pre-whitening keys are considered in this attack. A better impossible differential path is used to reduce time complexity by decreasing the number of key bits guessed. A hash table is built in the pre-computation phase to reduce computational complexity. Partial abort technique is used in the key seiving phase. The attack requires 259 chosen plaintexts, 214.58 blocks of memory and 268.83 10-round Midori64 encryptions.Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori
Procedia PDF Downloads 3433345 Solution of Hybrid Fuzzy Differential Equations
Authors: Mahmood Otadi, Maryam Mosleh
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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.Keywords: fuzzy number, fuzzy ODE, HAM, approximate method
Procedia PDF Downloads 5063344 Investigate and Solving Analytic of Nonlinear Differential at Vibrations (Earthquake)and Beam-Column, by New Approach “AGM”
Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Sara Akbari
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In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations.Keywords: new method AGM, vibrations, beam-column, angular frequency, energy dissipated, critical load
Procedia PDF Downloads 3813343 On a Continuous Formulation of Block Method for Solving First Order Ordinary Differential Equations (ODEs)
Authors: A. M. Sagir
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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.Keywords: block method, first order ordinary differential equations, linear multistep, self-starting
Procedia PDF Downloads 3013342 Comparing Numerical Accuracy of Solutions of Ordinary Differential Equations (ODE) Using Taylor's Series Method, Euler's Method and Runge-Kutta (RK) Method
Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh
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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method
Procedia PDF Downloads 3513341 A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society
Authors: Weihua Ruan, Kuan-Chou Chen
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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models
Procedia PDF Downloads 3693340 Empirical Evaluation of Gradient-Based Training Algorithms for Ordinary Differential Equation Networks
Authors: Martin K. Steiger, Lukas Heisler, Hans-Georg Brachtendorf
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Deep neural networks and their variants form the backbone of many AI applications. Based on the so-called residual networks, a continuous formulation of such models as ordinary differential equations (ODEs) has proven advantageous since different techniques may be applied that significantly increase the learning speed and enable controlled trade-offs with the resulting error at the same time. For the evaluation of such models, high-performance numerical differential equation solvers are used, which also provide the gradients required for training. However, whether classical gradient-based methods are even applicable or which one yields the best results has not been discussed yet. This paper aims to redeem this situation by providing empirical results for different applications.Keywords: deep neural networks, gradient-based learning, image processing, ordinary differential equation networks
Procedia PDF Downloads 1543339 The Application of Variable Coefficient Jacobian elliptic Function Method to Differential-Difference Equations
Authors: Chao-Qing Dai
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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation
Procedia PDF Downloads 6623338 A 1.8 GHz to 43 GHz Low Noise Amplifier with 4 dB Noise Figure in 0.1 µm Galium Arsenide Technology
Authors: Mantas Sakalas, Paulius Sakalas
Abstract:
This paper presents an analysis and design of a ultrawideband 1.8GHz to 43GHz Low Noise Amplifier (LNA) in 0.1 μm Galium Arsenide (GaAs) pseudomorphic High Electron Mobility Transistor (pHEMT) technology. The feedback based bandwidth extension techniques is analyzed and based on the outcome, a two stage LNA is designed. The impedance fine tuning is implemented by using Transmission Line (TL) structures. The measured performance shows a good agreement with simulation results and an outstanding wideband noise matching. The measured small signal gain was 12 dB, whereas a 3 dB gain flatness in range from 1.8 - 43 GHz was reached. The noise figure was below 4 dB almost all over the entire frequency band of 1.8GHz to 43GHz, the output power at 1 dB compression point was 6 dBm and the DC power consumption was 95 mW. To the best knowledge of the authors the designed LNA outperforms the State of the Art (SotA) reported LNA designs in terms of combined parameters of noise figure within the addressed ultra-wide 3 dB bandwidth, linearity and DC power consumption.Keywords: feedback amplifiers, GaAs pHEMT, monolithic microwave integrated circuit, LNA, noise matching
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