Search results for: Nonlinear impact response

Authors: Chien-Hua Lee, Cheng-Yi Chen

Abstract:

The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.

Keywords: homogeneous bilinear system, constrained input, time-delay, uncertainty, transient response, decay rate.

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Authors: YasirSalih, AamirSaeed Malik, Wazirahbt.Md-Esa

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In the recent years, high dynamic range imaging has gain popularity with the advancement in digital photography. In this contribution we present a subjective evaluation of various tone production and tone mapping techniques by a number of participants. Firstly, standard HDR images were used and the participants were asked to rate them based on a given rating scheme. After that, the participant was asked to rate HDR image generated using linear and nonlinear combination approach of multiple exposure images. The experimental results showed that linearly generated HDR images have better visualization than the nonlinear combined ones. In addition, Reinhard et al. and the exponential tone mapping operators have shown better results compared to logarithmic and the Garrett et al. tone mapping operators.

Keywords: tone mapping, high dynamic range, low dynamic range, bits per pixel.

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Authors: Atul K. Desai, Hemal J. Shah

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The tall windmill towers are designed as monopole tower or lattice tower. In the present research, a 125-meter high hybrid tower which is a combination of lattice and monopole type is proposed. The response of hybrid tower is compared with conventional monopole tower. The towers were analyzed in finite element method software considering nonlinear seismic time history load. The synthetic seismic time history for different soil is derived using the SeismoARTIF software. From the present research, it is concluded that, in the hybrid tower, we are not getting resonance condition. The base shear is less in hybrid tower compared to monopole tower for different soil conditions.

Keywords: Dynamic analysis, hybrid wind mill tower, resonance condition, synthetic time history.

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Authors: Yifan Fan, Xudong Luo, Pingping Lin

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An essential task in the field of artificial intelligence is to allow computers to interact with people through natural language. Therefore, researches such as virtual assistants and dialogue systems have received widespread attention from industry and academia. The response generation plays a crucial role in dialogue systems, so to push forward the research on this topic, this paper surveys various methods for response generation. We sort out these methods into three categories. First one includes finite state machine methods, framework methods, and instance methods. The second contains full-text indexing methods, ontology methods, vast knowledge base method, and some other methods. The third covers retrieval methods and generative methods. We also discuss some hybrid methods based knowledge and deep learning. We compare their disadvantages and advantages and point out in which ways these studies can be improved further. Our discussion covers some studies published in leading conferences such as IJCAI and AAAI in recent years.

Keywords: Retrieval, generative, deep learning, response generation, knowledge.

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Authors: R. Joseph Raviselvan, K. Ramanathan, P. Perumal, M. R. Thansekhar

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Hard coatings are widely used in cutting and forming tool industries. Titanium Nitride (TiN) possesses good hardness, strength, and corrosion resistance. The coating properties are influenced by many process parameters. The coatings were deposited on steel substrate by changing the process parameters such as substrate temperature, nitrogen flow rate and target power in a D.C planer magnetron sputtering. The structure of coatings were analysed using XRD. The hardness of coatings was found using Micro hardness tester. From the experimental data, a regression model was developed and the optimum response was determined using Response Surface Methodology (RSM).

Keywords: Hardness, RSM, sputtering, TiN XRD.

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Authors: Vijay Janyani, Neetu Joshi, Jigyasa Pagaria, Parul Pathak

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Photonic Crystal (PhC) based devices are being increasingly used in multifunctional, compact devices in integrated optical communication systems. They provide excellent controllability of light, yet maintaining the small size required for miniaturization. In this paper, the band gap properties of PhCs and their typical applications in optical waveguiding are considered. Novel PhC based applications such as nonlinear switching and tapers are considered and simulation results are shown using the accurate time-domain numerical method based on Finite Difference Time Domain (FDTD) scheme. The suitability of these devices for novel applications is discussed and evaluated.

Keywords: Band gap engineering, Nonlinear switching, Photonic crystals, PhC tapers, waveguides.

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Authors: Qiaozhen Song

Abstract:

Based on the feature of model disturbances and uncertainty being compensated dynamically in auto – disturbances-rejection-controller (ADRC), a new method using ADRC is proposed for the decoupling control of dispenser longitudinal movement in big flight envelope. Developed from nonlinear model directly, ADRC is especially suitable for dynamic model that has big disturbances. Furthermore, without changing the structure and parameters of the controller in big flight envelope, this scheme can simplify the design of flight control system. The simulation results in big flight envelope show that the system achieves high dynamic performance, steady state performance and the controller has strong robustness.

Keywords: ADRC, ESO, nonlinear system

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Authors: Zsolt Szilvágyi, Jakub Panuska, Orsolya Kegyes-Brassai, Ákos Wolf, Péter Tildy, Richard P. Ray

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Near-surface loose sediments and local ground conditions in general have a major influence on seismic response of structures. It is a difficult task to model ground behavior in seismic soil-structure-foundation interaction problems, fully account for them in seismic design of structures, or even properly consider them in seismic hazard assessment. In this study, we focused on applying seismic soil investigation methods, used for determining soil stiffness and damping properties, to response analysis used in seismic design. A site in Budapest, Hungary was investigated using Multichannel Analysis of Surface Waves, Seismic Cone Penetration Tests, Bender Elements, Resonant Column and Torsional Shear tests. Our aim was to compare the results of the different test methods and use the resulting soil properties for 1D ground response analysis. Often in practice, there are little-to no data available on dynamic soil properties and estimated parameters are used for design. Therefore, a comparison is made between results based on estimated parameters and those based on detailed investigations. Ground response results are also compared to Eurocode 8 design spectra.

Keywords: Bender element, ground response analysis, MASW, resonant column test, SCPT, torsional shear test.

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Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor

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One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.

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Authors: Rajlaxmi Chouhan, Pritee Khanna

Abstract:

In this manuscript, a wavelet-based blind watermarking scheme has been proposed as a means to provide security to authenticity of a fingerprint. The information used for identification or verification of a fingerprint mainly lies in its minutiae. By robust watermarking of the minutiae in the fingerprint image itself, the useful information can be extracted accurately even if the fingerprint is severely degraded. The minutiae are converted in a binary watermark and embedding these watermarks in the detail regions increases the robustness of watermarking, at little to no additional impact on image quality. It has been experimentally shown that when the minutiae is embedded into wavelet detail coefficients of a fingerprint image in spread spectrum fashion using a pseudorandom sequence, the robustness is observed to have a proportional response while perceptual invisibility has an inversely proportional response to amplification factor “K". The DWT-based technique has been found to be very robust against noises, geometrical distortions filtering and JPEG compression attacks and is also found to give remarkably better performance than DCT-based technique in terms of correlation coefficient and number of erroneous minutiae.

Keywords: Fingerprint watermarking, minutiae, discrete wavelet transform, PN sequence

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Authors: Mixed Frequency Excitation of an Electrostatically Actuated Resonator

Abstract:

We investigate experimentally and theoretically the dynamics of a capacitive resonator under mixed frequency excitation of two AC harmonic signals. The resonator is composed of a proof mass suspended by two cantilever beams. Experimental measurements are conducted using a laser Doppler Vibrometer to reveal the interesting dynamics of the system when subjected to twosource excitation. A nonlinear single-degree-of-freedom model is used for the theoretical investigation. The results reveal combination resonances of additive and subtractive type, which are shown to be promising to increase the bandwidth of the resonator near primary resonance frequency. Our results also demonstrate the ability to shift the combination resonances to much lower or much higher frequency ranges. We also demonstrate the dynamic pull-in instability under mixed frequency excitation.

Keywords: Nonlinear electrostatically actuated resonator.

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Authors: Hamidullah Binol, Abdullah Bal

Abstract:

Nowadays, food safety is a great public concern; therefore, robust and effective techniques are required for detecting the safety situation of goods. Hyperspectral Imaging (HSI) is an attractive material for researchers to inspect food quality and safety estimation such as meat quality assessment, automated poultry carcass inspection, quality evaluation of fish, bruise detection of apples, quality analysis and grading of citrus fruits, bruise detection of strawberry, visualization of sugar distribution of melons, measuring ripening of tomatoes, defect detection of pickling cucumber, and classification of wheat kernels. HSI can be used to concurrently collect large amounts of spatial and spectral data on the objects being observed. This technique yields with exceptional detection skills, which otherwise cannot be achieved with either imaging or spectroscopy alone. This paper presents a nonlinear technique based on kernel Fukunaga-Koontz transform (KFKT) for detection of fat content in ground meat using HSI. The KFKT which is the nonlinear version of FKT is one of the most effective techniques for solving problems involving two-pattern nature. The conventional FKT method has been improved with kernel machines for increasing the nonlinear discrimination ability and capturing higher order of statistics of data. The proposed approach in this paper aims to segment the fat content of the ground meat by regarding the fat as target class which is tried to be separated from the remaining classes (as clutter). We have applied the KFKT on visible and nearinfrared (VNIR) hyperspectral images of ground meat to determine fat percentage. The experimental studies indicate that the proposed technique produces high detection performance for fat ratio in ground meat.

Keywords: Food (Ground meat) inspection, Fukunaga-Koontz transform, hyperspectral imaging, kernel methods.

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Authors: Hong Dongchen, Chen Qiuxiao, Wu Shuang

Abstract:

Systematic Science reveals the complex nonlinear mechanisms of behavior in urban system. However, when confronted with such system, most city planners in China are still utilizing simple linear thinking to learn and understand this open complex giant system. In this paper, the hypercycle theory was introduced, which is one of the basis theories of systematic science. Based on the analysis of the reasons for the failure of current urban planning in China, and in consideration of the nonlinear characteristics of the urban system as well, optimization ideas for urban planning formulation were presented such as the shift from blueprint planning to progressive planning and from the rigid urban planning management control to its dynamically monitor and in time feedback.

Keywords: Systematic science, hypercycle theory, urban planning.

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Authors: Mohammadreza Vafaei, Amirali Moradi, Sophia C. Alih

Abstract:

The method selected for the design of structures not only can affect their seismic vulnerability but also can affect their construction cost. For the design of steel structures, two distinct methods have been introduced by existing codes, namely allowable stress design (ASD) and load resistant factor design (LRFD). This study investigates the effect of using the aforementioned design methods on the seismic vulnerability and construction cost of steel structures. Specifically, a 20-story building equipped with special moment resisting frame and an eccentrically braced system was selected for this study. The building was designed for three different intensities of peak ground acceleration including 0.2 g, 0.25 g, and 0.3 g using the ASD and LRFD methods. The required sizes of beams, columns, and braces were obtained using response spectrum analysis. Then, the designed frames were subjected to nine natural earthquake records which were scaled to the designed response spectrum. For each frame, the base shear, story shears, and inter-story drifts were calculated and then were compared. Results indicated that the LRFD method led to a more economical design for the frames. In addition, the LRFD method resulted in lower base shears and larger inter-story drifts when compared with the ASD method. It was concluded that the application of the LRFD method not only reduced the weights of structural elements but also provided a higher safety margin against seismic actions when compared with the ASD method.

Keywords: Allowable stress design, load resistant factor design, nonlinear time history analysis, seismic vulnerability, steel structures.

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Authors: E. Barkanov, E. Skukis, M. Wesolowski, A. Chate

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New nondestructive technique, namely an inverse technique based on vibration tests, to characterize nonlinear mechanical properties of adhesive layers in sandwich composites is developed. An adhesive layer is described as a viscoelastic isotropic material with storage and loss moduli which are both frequency dependent values in wide frequency range. An optimization based on the planning of experiments and response surface technique to minimize the error functional is applied to decrease considerably the computational expenses. The developed identification technique has been tested on aluminum panels and successfully applied to characterize viscoelastic material properties of 3M damping polymer ISD-112 used as a core material in sandwich panels.

Keywords: Adhesive layer, finite element method, inverse technique, sandwich panel, vibration test, viscoelastic material properties.

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Authors: Christopher Spiewak, M. R. Islam, Mohammad Arifur Rahaman, Mohammad H. Rahman, Roger Smith, Maarouf Saad

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For those who have lost the ability to move their hand, going through repetitious motions with the assistance of a therapist is the main method of recovery. We have been developed a robotic assistive device to rehabilitate the hand motions in place of the traditional therapy. The developed assistive device (RAD-HR) is comprised of four degrees of freedom enabling basic movements, hand function, and assists in supporting the hand during rehabilitation. We used a nonlinear computed torque control technique to control the RAD-HR. The accuracy of the controller was evaluated in simulations (MATLAB/Simulink environment). To see the robustness of the controller external disturbance as modelling uncertainty (±10% of joint torques) were added in each joints.

Keywords: Biorobotics, rehabilitation, nonlinear control, robotic assistive device, exoskeleton.

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Authors: Peyman Shadman Heidari, Mohammad Khorasani

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The principal purpose of this article is to present a new method based on Adaptive Neural Network Fuzzy Inference System (ANFIS) to generate additional artificial earthquake accelerograms from presented data, which are compatible with specified response spectra. The proposed method uses the learning abilities of ANFIS to develop the knowledge of the inverse mapping from response spectrum to earthquake records. In addition, wavelet packet transform is used to decompose specified earthquake records and then ANFISs are trained to relate the response spectrum of records to their wavelet packet coefficients. Finally, an interpretive example is presented which uses an ensemble of recorded accelerograms to demonstrate the effectiveness of the proposed method.

Keywords: Adaptive Neural Network Fuzzy Inference System, Wavelet Packet Transform, Response Spectrum.

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Authors: Osama A. Marzouk

Abstract:

We propose a reduced-ordermodel for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its perpendicular or parallel projection (the lift and drag), and captures the complete force rather than the oscillatory part only. We study and provide descriptions of the relationship between the model parameters, evaluated utilizing results from numerical simulations, and the Reynolds number so that the model can be used at any arbitrary value within the considered range of 100 to 500 to provide accurate representation of the force without the need to perform timeconsuming simulations and solving the partial differential equations (PDEs) governing the flow field.

Keywords: reduced-order model, wake oscillator, nonlinear, ODEsystem

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Authors: P. Saravanan, A. Vasumathi

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The authors conducted a study for the sample size of 75 HR managers from an Indian IT company through systematic sampling method. This study identifies that the female employees are facing lesser conflict than the male employees against their managers within the organization. There is a positive correlation between gender and conflict management with the superior towards the work. There is a significant variance between age and response towards appraisal system, succession planning and employee engagement. The education qualification plays a major role in determining the compensation factor for the employees working in the organization. The study determines the impact of demographic profile on strategic HRM practices and its challenges faced by HR managers in IT firm, India.

Keywords: Strategic Human resource management, Change agent, Employee engagement, Performance management, Succession planning and Conflict management.

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Authors: H. Rong, X. C. Yin, J. Yang, Y. N. Shen

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Based on Rayleigh beam theory, the sub-impacts of a free-free beam struck horizontally by a round-nosed rigid mass is simulated by the finite difference method and the impact-separation conditions. In order to obtain the sub-impact force, a uniaxial compression elastic-plastic contact model is employed to analyze the local deformation field on contact zone. It is found that the horizontal impact is a complicated process including the elastic plastic sub-impacts in sequence. There are two sub-zones of sub-impact. In addition, it found that the elastic energy of the free-free beam is more suitable for the Poisson collision hypothesis to explain compression and recovery processes.

Keywords: beam, sub-impact, elastic-plastic deformation, finite difference method.

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Authors: R. Samsudin, Yogendra, Hairil Satar, Y.Zaidey

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Power transformer consists of components which are under consistent thermal and electrical stresses. The major component which degrades under these stresses is the paper insulation of the power transformer. At site, lightning impulses and cable faults may cause the winding deformation. In addition, the winding may deform due to impact during transportation. A deformed winding will excite more stress to its insulating paper thus will degrade it. Insulation degradation will shorten the life-span of the transformer. Currently there are two methods of detecting the winding deformation which are Sweep Frequency Response Analysis (SFRA) and Low Voltage Impulse Test (LVI). The latter injects current pulses to the winding and capture the admittance plot. In this paper, a transformer which experienced overheating and arcing was identified, and both SFRA and LVI were performed. Next, the transformer was brought to the factory for untanking. The untanking results revealed that the LVI is more accurate than the SFRA method for this case study.

Keywords: Winding Deformation, Arcing, Dissolved GasAnalysis, Sweep Frequency Response Analysis, Low VoltageImpulse Method

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Authors: Mohammed Farag, Mina Attari, S. Andrew Gadsden, Saeid R. Habibi

Abstract:

Battery state of charge (SOC) estimation is an important parameter as it measures the total amount of electrical energy stored at a current time. The SOC percentage acts as a fuel gauge if it is compared with a conventional vehicle. Estimating the SOC is, therefore, essential for monitoring the amount of useful life remaining in the battery system. This paper looks at the implementation of three nonlinear estimation strategies for Li-Ion battery SOC estimation. One of the most common behavioral battery models is the one state hysteresis (OSH) model. The extended Kalman filter (EKF), the smooth variable structure filter (SVSF), and the time-varying smoothing boundary layer SVSF are applied on this model, and the results are compared.

Keywords: State of charge estimation, battery modeling, one-state hysteresis, filtering and estimation.

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Authors: Ya-Fen Lee, Yun-Yao Chi

Abstract:

This paper aims to quantify the impact of natural disaster on tourism by the change of annual visitors to scenic spots. The data of visitors to Alishan, Sun Moon Lake, Sitou and Palace Museum in Taiwan during 1986 to 2012 year is collected, and the trend analysis is used to predict the annual visitors to these scenic spots. The findings show that 1999 Taiwan earthquake had significant effect on the visitors to Alishan, Sun Moon Lake and Sitou with an average impact of 55.75% during 1999 to 2000 year except for Palace Museum. The impact was greater as closer epicenter of 1999 earthquake. And the discovery period of visitors is about 2 to 9 years. Further, the impact of heavy rainfall on Alishan, Taiwan is estimated. As the accumulative rainfall reaches to 500 mm, the impact on visitors can be predicted. 

Keywords: Impact, Natural disaster, tourism, visitors.

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Authors: E. Hlavacova, J. Chrenova, Z. Rausova, M. Vlcek, A. Penesova, L. Dedik

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En bloc assumes modeling all phases of the orthostatic test with the only one mathematical model, which allows the complex parametric view of orthostatic response. The work presents the implementation of a mathematical model for processing of the measurements of systolic, diastolic blood pressure and heart rate performed on volunteers during orthostatic test. The original assumption of model hypothesis that every postural change means only one Stressor, did not complying with the measurements of physiological circulation factor-time profiles. Results of the identification support the hypothesis that second postural change of orthostatic test causes induced Stressors, with the observation of a physiological regulation mechanism. Maximal demonstrations are on the heart rate and diastolic blood pressure-time profile, minimal are for the measurements of the systolic blood pressure. Presented study gives a new view on orthostatic test with impact on clinical practice.

Keywords: En bloc modeling, physiological circulatory factor, postural change, stressor

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Authors: Seong-Ho Song, Ki-Seob Kim, Seop-Hyeong Park, Seon-Woo Lee

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In this paper, the data correction algorithm is suggested when the environmental air temperature varies. To correct the infrared data in this paper, the initial temperature or the initial infrared image data is used so that a target source system may not be necessary. The temperature data obtained from infrared detector show nonlinear property depending on the surface temperature. In order to handle this nonlinear property, Taylor series approach is adopted. It is shown that the proposed algorithm can reduce the influence of environmental temperature on the components in the board. The main advantage of this algorithm is to use only the initial temperature of the components on the board rather than using other reference device such as black body sources in order to get reference temperatures.

Keywords: Infrared camera, Temperature Data compensation, Environmental Ambient Temperature, Electric Component

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Authors: Minh Tuan, Nguyen, Chung-Ruey Yen

Abstract:

The experiment was performed to evaluate the effect of GA3, 2,4-D on fruit growth and fruit quality of wax apple. The experiment consisted of Red A, Monulla, Atu, Red B cultivars. GA3 and 2,4-D were applied at the small bud and petal fall stage. Physiological, biochemical characters of fruit were recoded. The result showed application of GA3, 2,4-D greatly response in increasing fruit set for all treatment as compared to control. Fruit weight, fruit size were increased at 10 ppm 2,4-D in ‘Red A’, ‘Red B’, however it was also enhancing at 10 ppm GA3 in ‘Monulla’, ‘Atu’. For ‘Monulla’, ‘Atu’ fruit crack reduced by 10 ppm 2,4-D application, but ‘Red B’, ‘Red A’ gave least fruit crack at 10 and 30 ppm GA3, respectively. ‘Monulla’, ‘Atu’ and ‘Red B’ resulted in response well to 10 ppm GA3 on improving TSS, whereas application of 30 ppm GA3 greatly enhancing TSS in ‘Red A’. For ‘Atu’ titratable acidity markedly reduced by 10 ppm GA3 application, but spraying with 30 ppm GA3 greatly response in reducing titratable acidity in ‘Red A’, ‘Red B’ and ‘Monulla’. It was concluded that GA3, 2,4-D can be an effective tool to enhancing fruit set, fruit growth as well as improving fruit quality of wax apple.

Keywords: Wax apple, GA3, 2, 4-D, fruit growth, fruit quality. Abbreviations: GA3, gibberellic acid; 2, 4-D, 2, 4- dichlorophenoxyacetic acid.

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Authors: Keigo Matsuura, Isao Tomita

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We have studied a method to widen the spectrum of optical pulses that pass through an InGaAsP waveguide for application to broadband optical communication. In particular, we have investigated the competitive effect between spectral broadening arising from nonlinear refraction (optical Kerr effect) and shrinking due to two photon absorption in the InGaAsP waveguide with χ(3) nonlinearity. The shrunk spectrum recovers broadening by the enhancement effect of the nonlinear refractive index near the bandgap of InGaAsP with a bandgap wavelength of 1490 nm. The broadened spectral width at around 1525 nm (196.7 THz) becomes 10.7 times wider than that at around 1560 nm (192.3 THz) without the enhancement effect, where amplified optical pulses with a pulse width of ∼ 2 ps and a peak power of 10 W propagate through a 1-cm-long InGaAsP waveguide with a cross-section of 4 (μm)2.

Keywords: InGaAsP Waveguide, χ(3) Nonlinearity, Spectral Broadening.

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Authors: Ejaz Khan, Conor Heneghan

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In this paper we propose a new criterion for solving the problem of channel shortening in multi-carrier systems. In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Minimum mean square error (MMSE) method for TEQ does not give satisfactory results. In [1] a new criterion for partially equalizing severe ISI channels to reduce the cyclic prefix overhead of the discrete multitone transceiver (DMT), assuming a fixed transmission bandwidth, is introduced. Due to specific constrained (unit morm constraint on the target impulse response (TIR)) in their method, the freedom to choose optimum vector (TIR) is reduced. Better results can be obtained by avoiding the unit norm constraint on the target impulse response (TIR). In this paper we change the cost function proposed in [1] to the cost function of determining the maximum of a determinant subject to linear matrix inequality (LMI) and quadratic constraint and solve the resulting optimization problem. Usefulness of the proposed method is shown with the help of simulations.

Keywords: Equalizer, target impulse response, convex optimization, matrix inequality.

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Authors: Ramandeep Behl, S. S. Motsa

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The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: Reza Abazari, Rasool Abazari

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In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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