We construct some generalized difference Hahn sequence spaces by mean of sequence of modulus functions. The topological properties and some inclusion relations of spaces h p ((F, u, Δ(r)) are investigated. Also we compute the dual of these spaces, and some matrix transformations are characterized.
By making use of basic hypergeometric functions, a class of complex harmonic meromorphic functions with positive coefficients is introduced. We obtain some properties such as coefficient inequality, growth theorems, and extreme points.
In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.
We extend the concept of relaxed α-monotonicity to mixed relaxed α-β-monotonicity. The concept of mixed relaxed α-β-monotonicity is more general than many existing concepts of monotonicities. Finally, we apply this concept and well known KKM-theory to obtain the solution of generalized equilibrium problem.
A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design.
High-speed current controller for vector controlled permanent magnet synchronous motor (PMSM) is presented. The controller is developed based on modular design for faster calculation and uses fixed-point proportional-integral (PI) method for improved accuracy. Current dq controller is usually implemented in digital signal processor (DSP) based computer. However, DSP based solutions are reaching their physical limits, which are few microseconds. Besides, digital solutions suffer from high implementation cost. In this research, the overall controller is realizing in field programmable gate array (FPGA). FPGA implementation of the overall controlling algorithm will certainly trim down the execution time significantly to guarantee the steadiness of the motor. Agilent 16821A Logic Analyzer is employed to validate the result of the implemented design in FPGA. Experimental results indicate that the proposed current dq PI controller needs only 50 ns of execution time in 40 MHz clock, which is the lowest computational cycle for the era.
This paper deals with a deterministic mathematical model of dengue based on a system of fractional-order differential equations (FODEs). In this study, we consider dengue control strategies that are relevant to the current situation in Malaysia. They are the use of adulticides, larvicides, destruction of the breeding sites, and individual protection. The global stability of the disease-free equilibrium and the endemic equilibrium is constructed using the Lyapunov function theory. The relations between the order of the operator and control parameters are briefly analysed. Numerical simulations are performed to verify theoretical results and examine the significance of each intervention strategy in controlling the spread of dengue in the community. The model shows that vector control tools are the most efficient method to combat the spread of the dengue virus, and when combined with individual protection, make it more effective. In fact, the massive use of personal protection alone can significantly reduce the number of dengue cases. Inversely, mechanical control alone cannot suppress the excessive number of infections in the population, although it can reduce the Aedes mosquito population. The result of the real-data fitting revealed that the FODE model slightly outperformed the integer-order model. Thus, we suggest that the FODE approach is worth to be considered in modelling an infectious disease like dengue.
Knowing the place-value of digits in multi-digit numbers allows us to identify, understand and distinguish between numbers with the same digits (e.g., 1492 vs. 1942). Research using the size congruency task has shown that the place-value in a string of three zeros and a non-zero digit (e.g., 0090) is processed automatically. In the present study, we explored whether place-value is also automatically activated when more complex numbers (e.g., 2795) are presented. Twenty-five participants were exposed to pairs of four-digit numbers that differed regarding the position of some digits and their physical size. Participants had to decide which of the two numbers was presented in a larger font size. In the congruent condition, the number shown in a bigger font size was numerically larger. In the incongruent condition, the number shown in a smaller font size was numerically larger. Two types of numbers were employed: numbers composed of three zeros and one non-zero digit (e.g., 0040-0400) and numbers composed of four non-zero digits (e.g., 2795-2759). Results showed larger congruency effects in more distant pairs in both type of numbers. Interestingly, this effect was considerably stronger in the strings composed of zeros. These results indicate that place-value coding is partially automatic, as it depends on the perceptual and numerical properties of the numbers to be processed.
The application of compressed sensing (CS) to biomedical imaging is sensational since it permits a rationally accurate reconstruction of images by exploiting the image sparsity. The quality of CS reconstruction methods largely depends on the use of various sparsifying transforms, such as wavelets, curvelets or total variation (TV), to recover MR images. As per recently developed mathematical concepts of CS, the biomedical images with sparse representation can be recovered from randomly undersampled data, provided that an appropriate nonlinear recovery method is used. Due to high under-sampling, the reconstructed images have noise like artifacts because of aliasing. Reconstruction of images from CS involves two steps, one for dictionary learning and the other for sparse coding. In this novel framework, we choose Simultaneous code word optimization (SimCO) patch-based dictionary learning that updates the atoms simultaneously, whereas Focal underdetermined system solver (FOCUSS) is used for sparse representation because of a soft constraint on sparsity of an image. Combining SimCO and FOCUSS, we propose a new scheme called SiFo. Our proposed alternating reconstruction scheme learns the dictionary, uses it to eliminate aliasing and noise in one stage, and afterwards restores and fills in the k-space data in the second stage. Experiments were performed using different sampling schemes with noisy and noiseless cases of both phantom and real brain images. Based on various performance parameters, it has been shown that our designed technique outperforms the conventional techniques, like K-SVD with OMP, used in dictionary learning based MRI (DLMRI) reconstruction.
This paper studies the heat transfer analysis caused due to free convection in a vertically oscillating cylinder. Exact solutions are determined by applying the Laplace and finite Hankel transforms. Expressions for temperature distribution and velocity field corresponding to cosine and sine oscillations are obtained. The solutions that have been obtained for velocity are presented in the forms of transient and post-transient solutions. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. Numerical computations and graphical illustrations are used in order to study the effects of Prandtl and Grashof numbers on velocity and temperature for various times. The transient solutions for both cosine and sine oscillations are also computed in tables. It is found that, the transient solutions are of considerable interest up to the times t = 15 for cosine oscillations and t = 1.75 for sine oscillations. After these moments, the transient solutions can be neglected and, the fluid moves according with the post-transient solutions.
The increase in the number of fatalities caused by road accidents involving heavy vehicles every year has raised the level of concern and awareness on road safety in developing countries like Malaysia. Changes in the vehicle dynamic characteristics such as gross vehicle weight, travel speed, and vehicle classification will affect a heavy vehicle's braking performance and its ability to stop safely in emergency situations. As such, the aim of this study is to establish a more realistic new distance-based safety indicator called the minimum safe distance gap (MSDG), which incorporates vehicle classification (VC), speed, and gross vehicle weight (GVW).
The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.
In settings with limited resources, sentinel lymph node biopsy (SNB) is only offered to breast cancer patients with small tumors and a low a priori risk of axillary metastases.
Many of the similarity-based virtual screening approaches assume that molecular fragments that are not related to the biological activity carry the same weight as the important ones. This was the reason that led to the use of Bayesian networks as an alternative to existing tools for similarity-based virtual screening. In our recent work, the retrieval performance of the Bayesian inference network (BIN) was observed to improve significantly when molecular fragments were reweighted using the relevance feedback information. In this paper, a set of active reference structures were used to reweight the fragments in the reference structure. In this approach, higher weights were assigned to those fragments that occur more frequently in the set of active reference structures while others were penalized. Simulated virtual screening experiments with MDL Drug Data Report datasets showed that the proposed approach significantly improved the retrieval effectiveness of ligand-based virtual screening, especially when the active molecules being sought had a high degree of structural heterogeneity.
Load shedding is some of the essential requirement for maintaining security of modern power systems, particularly in competitive energy markets. This paper proposes an intelligent scheme for fast and accurate load shedding using neural networks for predicting the possible loss of load at the early stage and neuro-fuzzy for determining the amount of load shed in order to avoid a cascading outage. A large scale electrical power system has been considered to validate the performance of the proposed technique in determining the amount of load shed. The proposed techniques can provide tools for improving the reliability and continuity of power supply. This was confirmed by the results obtained in this research of which sample results are given in this paper.
Researchers used a hybrid model (a combination of health resource demand model and disease transmission model), Bayesian model, and susceptible-exposed-infectious-removed (SEIR) model to predict health service utilization and deaths and mixed-effect nonlinear regression. Further, they used the mixture model to predict the number of confirmed cases and deaths or to predict when the curve would flatten. In this article, we show, through scenarios developed using system dynamics methodology, besides close to real-world results, the detrimental effects of ignoring social distancing guidelines (in terms of the number of people infected, which decreased as the percentage of noncompliance decreased).
The present paper studies a predator-prey fishery model which incorporates the independent harvesting strategies and nonlinear impact of an anthropogenic toxicant. Both fish populations are harvested with different harvesting efforts, and the cases for the presence and non-presence of harvesting effort are discussed. The prey fish population is assumed to be infected by the toxicant directly which causes indirect infection to predator fish population through the feeding process. Each equilibrium of the proposed system is examined by analyzing the respective local stability properties. Dynamical behavior and bifurcations are studied with the assistance of threshold conditions influencing the persistence and extinction of both predator and prey. Bionomic equilibrium solutions for three possible cases are investigated with certain restrictions. Optimal harvesting policy is explored by utilizing the Pontryagin's Maximum Principle to optimize the profit while maintaining the sustainability of the marine ecosystem. Bifurcation analysis showed that the harvesting parameters are the key elements causing fishery extinction. Numerical simulations of bionomic and optimal equilibrium solutions showed that the presence of toxicant has a detrimental effect on the fish populations.
This study aimed to develop demi-span equations for predicting height in the Malaysian elderly and to explore the applicability of previous published demi-span equations derived from adult populations to the elderly.