Search results for: negative differential conductance

Authors: Renjie Liu, Junshuai Xue, Jiajia Yao, Guanlin Wu, Zumao L, Xueyan Yang, Fang Liu, Zhuang Guo

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Here, we report the study of the performance of AlN/GaN bipolar resonance tunneling diodes (BRTDs) using numerical simulations. The I-V characteristics of BRTDs show double negative differential resistance regions, which exhibit similar peak current density and peak-to-valley current ratio (PVCR). Investigations show that the PVCR can approach 4.6 for the first and 5.75 for the second negative resistance region. The appearance of the two negative differential resistance regions is realized by changing the collector material of conventional GaN RTD to P-doped GaN. As the bias increases, holes in the P-region and electrons in the N-region undergo resonant tunneling, respectively, resulting in two negative resistance regions. The appearance of two negative resistance regions benefits from the high AlN barrier and the precise regulation of the potential well thickness. This result shows the promise of GaN BRTDs in the development of multi-valued logic circuits.

Keywords: GaN bipolar resonant tunneling diode, double negative differential resistance regions, peak to valley current ratio, multi-valued logic

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Authors: Manasa Kalla, Narasimha Raju Chebrolu, Ashok Chatterjee

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We have studied the quantum transport properties of a single molecular transistor in the presence of an external magnetic field using the Keldysh Green function technique. We also used the Anderson-Holstein-Caldeira-Leggett Model to describe the single molecular transistor that consists of a molecular quantum dot (QD) coupled to two metallic leads and placed on a substrate that acts as a heat bath. The phonons are eliminated by the Lang-Firsov transformation and the effective Hamiltonian is used to study the effect of an external magnetic field on the spectral density function, Tunneling Current, Differential Conductance and Spin polarization. A peak in the spectral function corresponds to a possible excitation. In the presence of a magnetic field, the spin-up and spin-down states are degenerate and this degeneracy is lifted by the magnetic field leading to the splitting of the central peak of the spectral function. The tunneling current decreases with increasing magnetic field. We have observed that even the differential conductance peak in the zero magnetic field curve is split in the presence electron-phonon interaction. As the magnetic field is increased, each peak splits into two peaks. And each peak indicates the existence of an energy level. Thus the number of energy levels for transport in the bias window increases with the magnetic field. In the presence of the electron-phonon interaction, Differential Conductance in general gets reduced and decreases faster with the magnetic field. As magnetic field strength increases, the spin polarization of the current is increasing. Our results show that a strongly interacting QD coupled to metallic leads in the presence of external magnetic field parallel to the plane of QD acts as a spin filter at zero temperature.

Keywords: Anderson-Holstein model, Caldeira-Leggett model, spin-polarization, quantum dots

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Authors: Rania M. Abdallah, Ahmed A. S. Dessouki, Moustafa H. Aly

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This paper has presented a new simple small signal model for a resonant tunnelling diode device. The resonant tunnelling diode equivalent circuit elements were calculated and the results led to good agreement between the calculated equivalent circuit elements and the measurement results.

Keywords: resonant tunnelling diode, small signal model, negative differential conductance, electronic engineering

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Authors: Ibtisam Masmali, Edwin Beggs

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In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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Authors: Sarah Abdourraziq, Rachid Elbachtiri

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The use of solar energy as a source for pumping water is one of the promising areas in the photovoltaic (PV) application. The energy of photovoltaic pumping systems (PVPS) can be widely improved by employing an MPPT algorithm. This will lead consequently to maximize the electrical motor speed of the system. This paper presents a modified incremental conductance (IncCond) MPPT algorithm with direct control method applied to a standalone PV pumping system. The influence of the algorithm parameters on system behavior is investigated and compared with the traditional (INC) method. The studied system consists of a PV panel, a DC-DC boost converter, and a PMDC motor-pump. The simulation of the system by MATLAB-SIMULINK is carried out. Simulation results found are satisfactory.

Keywords: photovoltaic pumping system (PVPS), incremental conductance (INC), MPPT algorithm, boost converter

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Lebogang Jane Msiza, Felix Dapare Dakora

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Photosynthesis is a process by which plants convert light energy to chemical energy for metabolic processes. Plants are known for converting inorganic CO₂ in the atmosphere to organic C by photosynthesis. A decrease in stomatal conductance causes a decrease in the transpiration rate of leaves, thus increasing the water-use efficiency of plants. Water-use efficiency in plants is conditioned by soil moisture availability and is enhanced under conditions of water deficit. This study evaluated leaf photosynthesis and water-use efficiency in 12 legume species inoculated with 26 rhizobial isolates from soybean, 15 from common bean, 10 from cowpea, 15 from Bambara groundnut, 7 from lessertia and 10 from Kersting bean. Gas-exchange studies were used to measure photosynthesis and water-use efficiency. The results revealed a much higher photosynthetic rate (20.95µmol CO₂ m-2s-1) induced by isolated tutpres to a lower rate (7.06 µmol CO₂ m-2s-1) by isolate mgsa 88. Stomatal conductance ranged from to 0.01 mmol m-2.s-1 by mgsa 88 to 0.12 mmol m-2.s-1 by isolate da-pua 128. Transpiration rate also ranged from 0.09 mmol m-2.s-1 induced by da-pua B2 to 3.28 mmol m-2.s-1 by da-pua 3, while water-use efficiency ranged from 91.32 µmol CO₂ m-1 H₂O elicited by mgsa 106 to 4655.50 µmol CO₂ m-1 H₂O by isolate tutswz 13. The results revealed the highest photosynthetic rate in soybean and the lowest in common bean, and also with higher stomatal conductance and transpiration rates in jack bean and Bambara groundnut. Pigeonpea exhibited much higher water-use efficiency than all the tested legumes. The findings showed significant differences between and among the test legume/rhizobia combinations. Leaf photosynthetic rates are reported to be higher in legumes with high stomatal conductance, which suggests that legume productivity can be improved by manipulating leaf stomatal conductance.

Keywords: legumes, photosynthetic rate, stomatal conductance, water-use efficiency

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Authors: Yao Jiajia, Wu Guanlin, LIU Fang, Xue Junshuai, Zhang Jincheng, Hao Yue

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Resonant tunneling diodes (RTDs) based on GaN have been extensively studied. However, no results of multiple logic states achieved by RTDs were reported by the methods of epitaxy in the GaN materials. In this paper, the multiple negative-differential resistance regions by combining two discrete double-barrier RTDs in series have been first demonstrated. Plasma-assisted molecular beam epitaxy (PA-MBE) was used to grow structures consisting of two vertical RTDs. The substrate was a GaN-on-sapphire template. Each resonant tunneling structure was composed of a double barrier of AlN and a single well of GaN with undoped 4-nm space layers of GaN on each side. The AlN barriers were 1.5 nm thick, and the GaN well was 2 nm thick. The resonant tunneling structures were separated from each other by 30-nm thick n+ GaN layers. The bottom and top layers of the structures, grown neighboring to the spacer layers that consist of 200-nm-thick n+ GaN. These devices with two tunneling structures exhibited uniform peaks and valleys current and also had two negative differential resistance NDR regions equally spaced in bias voltage. The current-voltage (I-V) characteristics of resonant tunneling structures with diameters of 1 and 2 μm were analyzed in this study. These structures exhibit three stable operating points, which are investigated in detail. This research demonstrates that using molecular beam epitaxy MBE to vertically grow multiple resonant tunneling structures is a promising method for achieving multiple negative differential resistance regions and stable logic states. These findings have significant implications for the development of digital circuits capable of multi-value logic, which can be achieved with a small number of devices.

Keywords: GaN, AlN, RTDs, MBE, logic state

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Jiajia Yao, Guanlin Wu, Fang Liu, Junshuai Xue, Yue Hao

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This study reports on the epitaxial growth of a GaN-based resonant tunneling diode (RTD) structure with stable and repeatable double negative differential resistance (NDR) characteristics at room temperature on a c-plane GaN-on-sapphire template using plasma-assisted molecular beam epitaxy (PA-MBE) technology. In this structure, two independent AlN/GaN RTDs are epitaxially connected in series in the vertical growth direction through a silicon-doped GaN layer. As the collector electrode bias voltage increases, the two RTDs respectively align the ground state energy level in the quantum well with the 2DEG energy level in the emitter accumulation well to achieve quantum resonant tunneling and then reach the negative differential resistance (NDR) region. The two NDR regions exhibit similar peak current densities and peak-to-valley current ratios, which are 230 kA/cm² and 249 kA/cm², 1.33 and 1.38, respectively, for a device with a collector electrode mesa diameter of 1 µm. The consistency of the NDR is much higher than the results of on-chip discrete RTD device interconnection, resulting from the smaller chip area, fewer interconnect parasitic parameters, and less process complexity. The methods and results presented in this paper show the brilliant prospects of GaN RTDs in the development of multi-value logic digital circuits.

Keywords: MBE, AlN/GaN, RTDs, double NDR

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Authors: D. S. Palimkar

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The FRIGDI (functional random integrodifferential inclusion) seems to be new and includes several known random differential inclusions already studied in the literature as special cases have been discussed in the literature for various aspects of the solutions. In this paper, we prove the existence result for FIGDI under the non-convex case of multi-valued function involved in it.Using random fixed point theorem of B. C. Dhage and caratheodory condition. This result is new to the theory of differential inclusion.

Keywords: caratheodory condition, random differential inclusion, random solution, integro-differential inclusion

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

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We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

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Authors: Muhaned Zaidi, Ian Grout, Abu Khari bin A’ain

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In this paper, a two-stage op-amp design is considered using both Miller and negative Miller compensation techniques. The first op-amp design uses Miller compensation around the second amplification stage, whilst the second op-amp design uses negative Miller compensation around the first stage and Miller compensation around the second amplification stage. The aims of this work were to compare the gain and phase margins obtained using the different compensation techniques and identify the ability to choose either compensation technique based on a particular set of design requirements. The two op-amp designs created are based on the same two-stage rail-to-rail output CMOS op-amp architecture where the first stage of the op-amp consists of differential input and cascode circuits, and the second stage is a class AB amplifier. The op-amps have been designed using a 0.35mm CMOS fabrication process.

Keywords: op-amp, rail-to-rail output, Miller compensation, Negative Miller capacitance

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Fang Liu, JunShuai Xue, JiaJia Yao, XueYan Yang, ZuMao Li, GuanLin Wu, HePeng Zhang, ZhiPeng Sun

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III-Nitride resonant tunneling diode (RTD) is one of the most promising candidates for multiple-valued logic (MVL) elements. Here, we report a monolithic integration of GaN resonant tunneling diodes to realize multiple negative differential resistance (NDR) regions for MVL application. GaN RTDs, composed of a 2 nm quantum well embedded in two 1 nm quantum barriers, are grown by plasma-assisted molecular beam epitaxy on free-standing c-plane GaN substrates. Negative differential resistance characteristic with a peak current density of 178 kA/cm² in conjunction with a peak-to-valley current ratio (PVCR) of 2.07 is observed. Statistical properties exhibit high consistency showing a peak current density standard deviation of almost 1%, laying the foundation for the monolithic integration. After complete electrical isolation, two diodes of the designed same area are connected in series. By solving the Poisson equation and Schrodinger equation in one dimension, the energy band structure is calculated to explain the transport mechanism of the differential negative resistance phenomenon. Resonant tunneling events in a sequence of the series-connected RTD pair (SCRTD) form multiple NDR regions with nearly equal peak current, obtaining three stable operating states corresponding to ternary logic. A frequency multiplier circuit achieved using this integration is demonstrated, attesting to the robustness of this multiple peaks feature. This article presents a monolithic integration of SCRTD with multiple NDR regions driven by the resonant tunneling mechanism, which can be applied to a multiple-valued logic field, promising a fast operation speed and a great reduction of circuit complexity and demonstrating a new solution for nitride devices to break through the limitations of binary logic.

Keywords: GaN resonant tunneling diode, multiple-valued logic system, frequency multiplier, negative differential resistance, peak-to-valley current ratio

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Saurabh Basu, Sudin Ganguly

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Conductance in graphene nanoribbons (GNR) in presence of magnetic (for example, Iron) and non-magnetic (for example, Gold) adatoms are explored theoretically within a Kane-Mele model for their possible spintronic applications and topologically non-trivial properties. In our work, we have considered the magnetic adatoms to induce a Rashba spin-orbit coupling (RSOC) and an exchange bias field, while the non-magnetic ones induce an RSOC and an intrinsic spin-orbit (SO) coupling. Even though RSOC is present in both, they, however, represent very different physical situations, where the magnetic adatoms do not preserve the time reversal symmetry, while the non-magnetic case does. This has important implications on the topological properties. For example, the non-magnetic adatoms, for moderately strong values of SO, the GNR denotes a quantum spin Hall insulator as evident from a 2e²/h plateau in the longitudinal conductance and presence of distinct conducting edge states with an insulating bulk. Since the edge states are protected by time reversal symmetry, the magnetic adatoms in GNR yield trivial insulators and do not possess any non-trivial topological property. However, they have greater utility than the non-magnetic adatoms from the point of view of spintronic applications. Owing to the broken spatial symmetry induced by the presence of adatoms of either type, all the x, y and z components of the spin-polarized conductance become non-zero (only the y-component survives in pristine Graphene owing to a mirror symmetry present there) and hence become suitable for spintronic applications. However, the values of the spin polarized conductances are at least two orders of magnitude larger in the case of magnetic adatoms than their non-magnetic counterpart, thereby ensuring more efficient spintronic applications. Further the applications are tunable by altering the adatom densities.

Keywords: magnetic and non-magnetic adatoms, quantum spin hall phase, spintronic applications, spin polarized conductance, time reversal symmetry

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Authors: John K. Mensah, Mary A. Sword Sayer, Ryan L. Nadel, George Matusick, Zhaofei Fan, Lori G. Eckhardt

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Leptographium terebrantis is an opportunistic root pathogen commonly associated with loblolly pine (Pinus taeda L.) stands that are undergoing a loss of vigor in the southeastern US. In order to understand the relationship between L. terebrantis inoculum density and host physiology, an artificial inoculation study was conducted in a five-year-old naturally regenerated loblolly pine stand over a 24 week period in a completely randomized design. L. terebrantis caused sapwood occlusions that increased in severity as inoculum density increased. The occlusions significantly reduced water transport through the stem but did not interfere with fascicle-level stomatal conductance or induce moisture stress in the saplings. The resilience of stomatal conductance among pathogen-infested saplings is attributed to the growth and hydraulic function of new sapwood that developed after artificial inoculation. Results demonstrate that faster-growing families of loblolly pine may be capable of tolerating the vascular root disease when the formation of new sapwood is supported by sustained crown health.

Keywords: hydraulic conductance, inoculum density, Leptographium terebrantis, Pinus taeda, sapwood occlusion

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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: Mustafa Engin Başoğlu, Bekir Çakır

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The most important component affecting the efficiency of photovoltaic power systems are solar panels. Efficiency of these systems are significantly affected because of being low efficiency of solar panel. Therefore, solar panels should be operated under maximum power point conditions through a power converter. In this study, design boost converter with maximum power point tracking (MPPT) operation has been designed and performed with Incremental Conductance (Inc-Cond) algorithm by using direct duty control. Furthermore, it is shown that performance of boost converter with MPPT operation fails under low load resistance connection.

Keywords: boost converter, incremental conductance (Inc-Cond), MPPT, solar panel

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Mehdi Ameur, Ahmed Essadki, Tamou Nasser

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The purpose of this paper is the evaluation of photovoltaic system with MPPT techniques. This system is developed by combining the models of established solar module and DC-DC converter with the algorithms of perturbing and observing (P&O), incremental conductance (INC) and fuzzy logic controller (FLC). The system is simulated under different climate conditions and MPPT algorithms to determine the influence of these conditions on characteristic power-voltage of PV system. According to the comparisons of the simulation results, the photovoltaic system can extract the maximum power with precision and rapidity using the MPPT algorithms discussed in this paper.

Keywords: fuzzy logic controller, FLC, hill climbing, HC, incremental conductance (INC), perturb and observe (P&O), maximum power point, MPP, maximum power point tracking, MPPT

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: Fang Liu, JiaJia Yao, GuanLin Wu, ZuMaoLi, XueYan Yang, HePeng Zhang, ZhiPeng Sun, JunShuai Xue

Abstract:

The explosive increasing needs of data processing and information storage strongly drive the advancement of the binary logic system to multiple-valued logic system. Inherent negative differential resistance characteristic, ultra-high-speed switching time, and robust anti-irradiation capability make III-nitride resonant tunneling diode one of the most promising candidates for multi-valued logic devices. Here we report the monolithic integration of GaN resonant tunneling diodes in series to realize multiple negative differential resistance regions, obtaining at least three stable operating states. A multiply-by-three circuit is achieved by this combination, increasing the frequency of the input triangular wave from f0 to 3f0. The resonant tunneling diodes are grown by plasma-assistedmolecular beam epitaxy on free-standing c-plane GaN substrates, comprising double barriers and a single quantum well both at the atomic level. Device with a peak current density of 183kA/cm² in conjunction with a peak-to-valley current ratio (PVCR) of 2.07 is observed, which is the best result reported in nitride-based resonant tunneling diodes. Microwave oscillation event at room temperature was discovered with a fundamental frequency of 0.31GHz and an output power of 5.37μW, verifying the high repeatability and robustness of our device. The switching behavior measurement was successfully carried out, featuring rise and fall times in the order of picoseconds, which can be used in high-speed digital circuits. Limited by the measuring equipment and the layer structure, the switching time can be further improved. In general, this article presents a novel nitride device with multiple negative differential regions driven by the resonant tunneling mechanism, which can be used in high-speed multiple value logic field with reduced circuit complexity, demonstrating a new solution of nitride devices to break through the limitations of binary logic.

Keywords: GaN resonant tunneling diode, negative differential resistance, multiple-valued logic system, switching time, peak-to-valley current ratio

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

Procedia PDF Downloads 477