Search results for: delay equations

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

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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: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: mathematical modeling, ordinary differential equations, endocrine system, delay differential equation

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Jin Liang, James H. Liu, Ti-Jun Xiao

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It is known that there exist many physical phenomena where abrupt or impulsive changes occur either in the system dynamics, for example, ad-hoc network, or in the input forces containing impacts, for example, the bombardment of space antenna by micrometeorites. There are many other examples such as ultra high-speed optical signals over communication networks, the collision of particles, inventory control, government decisions, interest changes, changes in stock price, etc. These are impulsive phenomena. Hence, as a combination of the traditional initial value problems and the short-term perturbations whose duration can be negligible in comparison with the duration of the process, the systems with impulsive conditions (i.e., impulsive systems) are more realistic models for describing the impulsive phenomenon. Such a situation is also suitable for the delay systems, which include some of the past states of the system. So far, there have been a lot of research results in the study of impulsive systems with delay both in finite and infinite dimensional spaces. In this paper, we investigate the periodicity of solutions to the nonautonomous impulsive evolution equations with infinite delay in Banach spaces, where the coefficient operators (possibly unbounded) in the linear part depend on the time, which are impulsive systems in infinite dimensional spaces and come from the optimal control theory. It was indicated that the study of periodic solutions for these impulsive evolution equations with infinite delay was challenging because the fixed point theorems requiring some compactness conditions are not applicable to them due to the impulsive condition and the infinite delay. We are happy to report that after detailed analysis, we are able to combine the techniques developed in our previous papers, and some new ideas in this paper, to attack these impulsive evolution equations and derive periodic solutions. More specifically, by virtue of the related transition operator family (evolution family), we present a Poincaré operator given by the nonautonomous impulsive evolution system with infinite delay, and then show that the operator is a condensing operator with respect to Kuratowski's measure of non-compactness in a phase space by using an Amann's lemma. Finally, we derive periodic solutions from bounded solutions in view of the Sadovskii fixed point theorem. We also present a relationship between the boundedness and the periodicity of the solutions of the nonautonomous impulsive evolution system. The new results obtained here extend some earlier results in this area for evolution equations without impulsive conditions or without infinite delay.

Keywords: impulsive, nonautonomous evolution equation, optimal control, periodic solution

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Authors: Ata Khorami, Mohammad Sharifkhani

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In the dynamic comparators, the pre-amplifier amplifies the input differential voltage and when the output Vcm of the pre-amplifier becomes larger than Vth of the latch input transistors, the latch is activated and finalizes the comparison. As a result, the pre-amplification delay is fixed to a value and cannot be set at the minimum required delay, thus, significant power and delay are imposed. In this paper, a novel structure is proposed through which the pre-amplification delay can be set at any low value saving power and time. Simulations show that using the proposed structure, by setting the pre-amplification delay at the minimum required value the power and comparison delay can be reduced by 55% and 100ps respectively.

Keywords: dynamic comparator, low power comparator, analog to digital converter, pre-amplification delay

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Authors: Anandhi Santhosh

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In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Keywords: approximate controllability, impulsive differential system, fixed point theorem, state-dependent delay

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Authors: Y. Gholipour, E. Rezazadeh

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Delay is one of the most serious and common problems of construction project that can affect project delivery unfavorably. This research presents the most important causes of delay in large dam projects based on a survey on some executed dam construction in Iran. In this survey a randomly selected samples of owners, consultants and contractors have been involved. The outcome of this survey revealed that scheduled payments, site management, shop drawing review process, unforeseen ground conditions and contractor experience as the most important factors affecting on delay in dam construction projects.

Keywords: delay, dam construction, project management, Iran

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Authors: Amritpal Singh Nafria, Rohit Sharma, Md. Shami Ansari

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Up to now only five different equations of motion can be derived from velocity time graph without needing to know the normal and frictional forces acting at the point of contact. In this paper we obtained all possible requisite conditions to be considering an equation as an equation of motion. After that we classified equations of motion by considering two equations as fundamental kinematical equations of motion and other three as additional kinematical equations of motion. After deriving these five equations of motion, we examine the easiest way of solving a wide variety of useful numerical problems. At the end of the paper, we discussed the importance and educational benefits of classification of equations of motion.

Keywords: velocity-time graph, fundamental equations, additional equations, requisite conditions, importance and educational benefits

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Authors: Mohsen Maadani, Seyed Ahmad Motamedi

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The use of wireless technology in industrial networks has gained vast attraction in recent years. In this paper, we have thoroughly analyzed the effect of contention window (CW) size on the performance of IEEE 802.11-based industrial wireless networks (IWN), from delay and reliability perspective. Results show that the default values of CWmin, CWmax, and retry limit (RL) are far from the optimum performance due to the industrial application characteristics, including short packet and noisy environment. An adaptive CW algorithm (payload-dependent) has been proposed to minimize the average delay. Finally a simple, but effective CW and RL setting has been proposed for industrial applications which outperforms the minimum-average-delay solution from maximum delay and jitter perspective, at the cost of a little higher average delay. Simulation results show an improvement of up to 20%, 25%, and 30% in average delay, maximum delay and jitter respectively.

Keywords: average delay, contention window, distributed coordination function (DCF), jitter, industrial wireless network (IWN), maximum delay, reliability, retry limit

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Authors: Arpita Saha, Satish Chandra, Indrajit Ghosh

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Delay implicates the time loss of a traveler while crossing an intersection. Efficiency of traffic operation at signalized intersections is assessed in terms of delay caused to an individual vehicle. Highway Capacity Manual (HCM) method and Webster’s method are the most widely used in India for delay estimation purpose. However, in India, traffic is highly heterogeneous in nature with extremely poor lane discipline. Therefore, to explore best delay estimation technique for Indian condition, a comparison was made. In this study, seven signalized intersections from three different cities where chosen. Data was collected for both during morning and evening peak hours. Only under saturated cycles were considered for this study. Delay was estimated based on the field data. With the help of Simpson’s 1/3 rd rule, delay of under saturated cycles was estimated by measuring the area under the curve of queue length and cycle time. Moreover, the field observed delay was compared with the delay estimated using HCM, Webster, Probabilistic, Taylor’s expansion and Regression methods. The drawbacks of the existing delay estimation methods to be use in Indian heterogeneous traffic conditions were figured out, and best method was proposed. It was observed that direct estimation of delay using field measured data is more accurate than existing conventional and modified methods.

Keywords: delay estimation technique, field delay, heterogeneous traffic, signalised intersection

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Authors: Sunil Verma

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This report is concerned with study of autoignition delay characterstics of n-pentane. Experiments are done for different equivalents ratio on Rapid compression machine. Dependence of autoignition delay period is clearly explained from lean to rich mixtures. Equivalence ratio is varied from 0.33 to 0.6.

Keywords: combustion, autoignition, ignition delay, rapid compression machine

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Authors: H. Namazi, H. T. N. Kuan

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Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). It is clear that the diffusion of flux cannot be instantaneous and should be some time delay in this propagation. But Fick’s first law doesn’t consider this delay which results in some errors especially when there is a considerable time delay in the process. In this paper, we introduce a time delay to Fick’s first law. By this modification, we consider that the diffusion of flux cannot be instantaneous. In order to verify this claim an application sample in fluid diffusion is discussed and the results of modified Fick’s first law, Fick’s first law and the experimental results are compared. The results of this comparison stand for the accuracy of the modified model. The modified model can be used in any application where the time delay has considerable value and neglecting its effect reflects in undesirable results.

Keywords: Fick's first law, flux, diffusion, time delay, modified Fick’s first law

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

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In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Heisenberg Ferromagnet equations, soliton equations, equivalence, Lax representation

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Authors: Shao-Ku Kao

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This paper presents an active rectifier with time-domain delay compensation to enhance the efficiency. A delay calibration circuit is designed to convert delay time to voltage and adaptive control on/off delay in variable input voltage. This circuit is designed in 0.18 mm CMOS process. The input voltage range is from 2 V to 3.6 V with the output voltage from 1.8 V to 3.4 V. The efficiency can maintain more than 85% when the load from 50 Ω ~ 1500 Ω for 3.6 V input voltage. The maximum efficiency is 92.4 % at output power to be 38.6 mW for 3.6 V input voltage.

Keywords: wireless power transfer, active diode, delay compensation, time to voltage converter, PCE

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Authors: Abdullah Alsehaimi

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Over decades, there have been many studies of delay in construction, and this type of study continues to be popular in construction management research. A synthesis and critical evaluation of delay studies in developing countries reveals that poor project management is cited as one of the main causes of delay. However, despite such consensus, most of the previous studies fall short in providing clear recommendations demonstrating how project management practice could be improved. Moreover, the majority of recommendations are general and not devoted to solving the difficulties associated with particular delay causes. This paper aims to demonstrate that the root cause of this state of affairs is that typical research into delay tends to be descriptive and explanatory, making it inadequate for solving persistent managerial problems in construction. It is contended that many problems in construction could be mitigated via alternative research approaches, i.e. action and constructive research. Such prescriptive research methods can assist in the development and implementation of innovative tools tackling managerial problems of construction, including that of delay. In so doing, those methods will better connect research and practice, and thus strengthen the relevance of academic construction management.

Keywords: construction delay, action research, constructive research, industrial engineering

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Authors: Tzu-Yang Lin, Chuan-Ching Sue

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Sleep mechanisms are commonly used to ensure the energy efficiency of each optical network unit (ONU) that concerns a single class delay constraint in the Ethernet Passive Optical Network (EPON). How long the ONUs can sleep without violating the delay constraint has become a research problem. Particularly, we can derive an analytical model to determine the optimal sleep time of ONUs in every cycle without violating the maximum class delay constraint. The bandwidth allocation considering such optimal sleep time is called Green Bandwidth Allocation (GBA). Although the GBA mechanism guarantees that the different class delay constraints do not violate the maximum class delay constraint, packets with a more relaxed delay constraint will be treated as those with the most stringent delay constraint and may be sent early. This means that the ONU will waste energy in active mode to send packets in advance which did not need to be sent at the current time. Accordingly, we proposed a QoS-aware GBA using a novel intra-ONU scheduling to control the packets to be sent according to their respective delay constraints, thereby enhancing energy efficiency without deteriorating delay performance. If packets are not explicitly classified but with different packet delay constraints, we can modify the intra-ONU scheduling to classify packets according to their packet delay constraints rather than their classes. Moreover, we propose the switchable ONU architecture in which the ONU can switch the architecture according to the sleep time length, thus improving energy efficiency in the QoS-aware GBA. The simulation results show that the QoS-aware GBA ensures that packets in different classes or with different delay constraints do not violate their respective delay constraints and consume less power than the original GBA.

Keywords: Passive Optical Networks, PONs, Optical Network Unit, ONU, energy efficiency, delay constraint

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Authors: Iyai Davies, Olivier L. C. Haas

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In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability

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Authors: Sulaiman Yunus

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The need for modeling response to urban fire disaster cannot be over emphasized, as recurrent fire outbreaks have gutted most cities of the world. This necessitated the need for a prompt and efficient response system in order to mitigate the impact of the disaster. Promptness, as a function of time, is seen to be the fundamental determinant for efficiency of a response system and magnitude of a fire disaster. Delay, as a result of several factors, is one of the major determinants of promptgness of a response system and also the magnitude of a fire disaster. Response Delay Model (RDM) intends to bridge the gap in urban fire disaster response system through incorporating and synchronizing the delay moments in measuring the overall efficiency of a response system and determining the magnitude of a fire disaster. The model identified two delay moments (pre-notification and Intra-reflex sequence delay) that can be elastic and collectively plays a significant role in influencing the efficiency of a response system. Due to variation in the elasticity of the delay moments, the model provides for measuring the length of delays in order to arrive at a standard average delay moment for different parts of the world, putting into consideration geographic location, level of preparedness and awareness, technological advancement, socio-economic and environmental factors. It is recommended that participatory researches should be embarked on locally and globally to determine standard average delay moments within each phase of the system so as to enable determining the efficiency of response systems and predicting fire disaster magnitudes.

Keywords: delay moment, fire disaster, reflex sequence, response, response delay moment

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Authors: Sangeeta Singh, Pankaj Kumar, P. N. Kondekar

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In this paper, the transient device performance analysis of n-type Gate Inside Junctionless Transistor (GIJLT)has been evaluated. 3-D Bohm Quantum Potential (BQP)transport device simulation has been used to evaluate the delay and power dissipation performance. GI-JLT has a number of desirable device parameters such as reduced propagation delay, dynamic power dissipation, power and delay product, intrinsic gate delay and energy delay product as compared to Gate-all-around transistors GAA-JLT. In addition to this, various other device performance parameters namely, on/off current ratio, short channel effects (SCE), transconductance Generation Factor(TGF) and unity gain cut-off frequency (fT) and subthreshold slope (SS) of the GI-JLT and Gate-all-around junctionless transistor(GAA-JLT) have been analyzed and compared. GI-JLT shows better device performance characteristics than GAA-JLT for low power and high frequency applications, because of its larger gate electrostatic control on the device operation.

Keywords: gate-inside junctionless transistor GI-JLT, gate-all-around junctionless transistor GAA-JLT, propagation delay, power delay product

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Authors: Jong-Jy Shyu, Soo-Chang Pei, Yun-Da Huang

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In this paper, design of wide-range variable fractional-delay (WR-VFD) finite impulse response (FIR) digital filters is proposed. With respect to the conventional VFD filter which is designed such that its delay is adjustable within one unit, the proposed VFD FIR filter is designed such that its delay can be tunable within a wider range. By the traces of coefficients of the fractional-delay FIR filter, it is found that the conventional method of polynomial substitution for filter coefficients no longer satisfies the design demand, and the circuits perform the sinc function (sinc converter) are added to overcome this problem. In this paper, least-squares method is adopted to design WR-VFD FIR filter. Throughout this paper, several examples will be proposed to demonstrate the effectiveness of the presented methods.

Keywords: digital filter, FIR filter, variable fractional-delay (VFD) filter, least-squares approximation

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Authors: Purva Joshi, Rohit Thanki, Omar Hanif

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Unmanned aerial vehicles (UAVs) are becoming increasingly important in various industrial applications and sectors. Nowadays, a multi UAV network is used for specific types of communication (e.g., military) and monitoring purposes. Therefore, it is critical to reducing propagation delay during communication between UAVs, which is essential in a multi UAV network. This paper presents how the propagation delay between the base station (BS) and the UAVs is reduced using a searching algorithm. Furthermore, the iterative-based K-nearest neighbor (k-NN) algorithm and Travelling Salesmen Problem (TSP) algorthm were utilized to optimize the distance between BS and individual UAV to overcome the problem of propagation delay in multi UAV networks. The simulation results show that this proposed method reduced complexity, improved reliability, and reduced propagation delay in multi UAV networks.

Keywords: multi UAV network, optimal distance, propagation delay, K - nearest neighbor, traveling salesmen problem

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Authors: Ibrahim Mahamid, A. Al-Ghonamy, M. Aichouni

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This study aims at identifying the risk matrix for delay causes in construction projects in Saudi Arabia from consultants’ viewpoint. A questionnaire survey was undertaken of 51 consultants working on construction projects in the Northern Province of Saudi Arabia. 35 delay causes were identified through a literature review. The study concluded that the top delay causes in construction projects in Saudi Arabia from consultants’ perspective are: bid award for lowest price, changes in material types and specifications during construction, contract management, duration of contract period, fluctuation of prices of materials, frequent changes in design, improper planning, inflationary pressure, lack of adequate manpower, long period of design and time of implementation, payments delay, poor labor productivity, and rework.

Keywords: delays, construction, consultants, contributors, risk map

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Authors: K.T Alade, A.F Lawal, A.A Omonori

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Construction is an everlasting activity across the globe. Likewise, the problem of delay in the construction industry is a global phenomenon. Although there are several reasons that may be responsible for delay during construction, this may vary from place to place and can be reduced to the minimum when identified. This study considered the major causes and effects of delay in the execution of construction projects in Akure, Ondo State, Nigeria. Using literatures, a total number of 30 causes of construction delays were identified. The convenient sampling technique was used to select sixty respondents for a survey. The respondents comprise twenty-two (22) clients, eighteen consultants (18) and twenty (20) contractors. The analyses of the primary data revealed that the three most important causes of delay in construction projects in Akure, Ondo State Nigeria are poor site management and supervision, inadequate contractors experience and client’s financial difficulties. Based on the findings of this study, recommendations were given on how the causes and effects of delay in construction can be mitigated.

Keywords: Akure, causes, construction projects, delay, effects

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: K. R. Guna, Aldin Justin Sundararaj, B. C. Pillai, A. N. Subash

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A systematic study has been made for ignition delay times measurement behind a reflected shock wave for the low molecular weight hydrocarbon fuel in argon simulated gas mixtures. The low molecular hydrocarbon fuel–oxygen was diluted with argon for desired concentration is taken for the study. The suitability of the shock tube for measuring the ignition delay time is demonstrated by measuring the ignition delay for the liquefied petroleum gas for equivalence ratios (ф=0.5 & 1) in the temperature range 1150-1650 K. The pressure range was fixed from 5-15 bar. The ignition delay was measured by recording the ignition-induced pressure jump and emission from CH radical simultaneously. From conducting experiments, it was found that the ignition delay time for liquefied petroleum gas reduces with increase in temperature. The shock tube was calibrated for ethane-oxygen gas mixture and the results obtained from this study is compared with the earlier reported values and found to be comparably well suited for the measurement of ignition delay times. The above work was carried out using the shock tube facility at propulsion and high enthalpy laboratory, Karunya University.

Keywords: ignition delay, LPG, reflected shock, shock wave

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