Search results for: Reich Contraction

Authors: R. Uthayakumar, G. Arockia Prabakar

Abstract:

In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

Keywords: Fractals, Iterated Function System, Compact set, Reich Contraction, Well posedness.

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Authors: M. R. Yadav, A. K. Sharma, B. S. Thakur

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The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

Keywords: Cyclic contraction, rational cyclic contraction, best proximity point and complete metric space.

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Authors: Dehghan Manshadi M., Mirzaei M., Soltani M. R., Ghorbanian K.

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Subsonic wind tunnel experiments were conducted to study the effect of tripped boundary layer on the pressure distribution in the contraction region of the tunnel. Measurements were performed by installing trip strip at two different positions in the concave portion of the contraction. The results show that installation of the trip strips, have significant effects on both turbulence and pressure distribution. The reduction in the free stream turbulence and reduction of the wall static pressure distribution deferred signified with the location of the trip strip.

Keywords: Contraction, pressure distribution, trip strip, turbulence intensity.

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Authors: Malcolm R Davidson, Ram P. Bharti, Petar Liovic, Dalton J.E. Harvie

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The electrokinetic flow resistance (electroviscous effect) is predicted for steady state, pressure-driven liquid flow at low Reynolds number in a microfluidic contraction of rectangular cross-section. Calculations of the three dimensional flow are performed in parallel using a finite volume numerical method. The channel walls are assumed to carry a uniform charge density and the liquid is taken to be a symmetric 1:1 electrolyte. Predictions are presented for a single set of flow and electrokinetic parameters. It is shown that the magnitude of the streaming potential gradient and the charge density of counter-ions in the liquid is greater than that in corresponding two-dimensional slit-like contraction geometry. The apparent viscosity is found to be very close to the value for a rectangular channel of uniform cross-section at the chosen Reynolds number (Re = 0.1). It is speculated that the apparent viscosity for the contraction geometry will increase as the Reynolds number is reduced.

Keywords: Contraction, Electroviscous, Microfluidic, Numerical.

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Authors: Vasilescu M., Rusu L., Nestianu V., Romanescu F., Dragomir M

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The research was designed to examine the relationship between the development of muscle fatigue and the effect it has on sport performance, specifically during maximal voluntary contraction. This kind of this investigation using simultaneous electrophysiological and mechanical recordings, based on advanced mathematical processing, allows us to get parameters, and indexes in a short time, and finally, the mapping to use for the thorough investigation of the muscle contraction force, respectively the phenomenon of local muscle fatigue, both for athletes and other subjects.

Keywords: Electromyography, mechanomyography, musclefatigue

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Authors: Mohamed M. Ragab, Neveen A. Abdel Raoof, Reham H. Diab

Abstract:

Background: Delayed onset muscle soreness (DOMS) is the most common symptom when ordinary individuals and athletes are exposed to unaccustomed physical activity, especially eccentric contraction which impairs athletic performance, ordinary people work ability and physical functioning. Multitudes of methods have been investigated to reduce DOMS. One of the valuable methods to control DOMS is repeated bout effect (RBE) as a prophylactic method. Purpose: To compare the repeated bout effect of submaximal eccentric with maximal isometric contraction on induced DOMS. Methods: Sixty normal male volunteers were assigned randomly into three equal groups: Group A (first study group): 20 subjects received submaximal eccentric contraction on non-dominant elbow flexors as a prophylactic exercise. Group B (second study group): 20 subjects received maximal isometric contraction on nondominant elbow flexors as a prophylactic exercise. Group C (control group): 20 subjects did not receive any prophylactic exercises. Maximal isometric peak torque of elbow flexors and patient related elbow evaluation (PREE) scale were measured for each subject 3 times before, immediately after, and 48 hours after induction of DOMS. Results: Post-hoc test for maximal isometric peak torque and PREE scale immediately and 48 hours after induction of DOMS revealed that group (A) and group (B) resulted in significant decrease in maximal isometric strength loss and elbow pain and disability rather than control group (C), but submaximal eccentric group (A) was more effective than maximal isometric group (B) as it showed more rapid recovery of functional strength and less degrees of elbow pain and disability. Conclusion: Both submaximal eccentric contraction and maximal isometric contraction were effective in prevention of DOMS but submaximal eccentric contraction produced a greater protective effect against muscle damage induced by maximal eccentric exercise performed 2 days later.

Keywords: Delayed onset muscle soreness, maximal isometric peak torque, patient related elbow evaluation scale, repeated bout effect.

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Authors: Alemayehu Geremew Negash

Abstract:

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces.

Keywords: Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.

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Authors: R. Uthayakumar, D. Easwaramoorthy

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This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic fuzzy metrics.

Keywords: Fractal Analysis, Fixed Point, Contraction, Iterated Function System, Intuitionistic Fuzzy Metric Space.

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Authors: R. Uthayakumar, D. Easwaramoorthy

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The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.

Keywords: Contraction, Iterated Function System, Hutchinson- Barnsley Operator, Intuitionistic Fuzzy Metric Space, Hausdorff Intuitionistic Fuzzy Metric.

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Authors: Meng Hu, Lili Wang

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This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form:  Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.

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Authors: Xi Wang, Xiaoming Tao, Raymond C. H. So

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As one of the convenient and noninvasive sensing approaches, the automatic limb girth measurement has been applied to detect intention behind human motion from muscle deformation. The sensing validity has been elaborated by preliminary researches but still need more fundamental studies, especially on kinetic contraction modes. Based on the novel fabric strain sensors, a soft and smart limb girth measurement system was developed by the authors’ group, which can measure the limb girth in-motion. Experiments were carried out on elbow isometric flexion and elbow isokinetic flexion (biceps’ isokinetic contractions) of 90°/s, 60°/s, and 120°/s for 10 subjects (2 canoeists and 8 ordinary people). After removal of natural circumferential increments due to elbow position, the joint torque is found not uniformly sensitive to the limb circumferential strains, but declining as elbow joint angle rises, regardless of the angular speed. Moreover, the maximum joint torque was found as an exponential function of the joint’s angular speed. This research highly contributes to the application of the automatic limb girth measuring during kinetic contractions, and it is useful to predict the contraction level of voluntary skeletal muscles.

Keywords: Fabric strain sensor, muscle deformation, isokinetic contraction, joint torque, limb girth strain.

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Authors: Xiaomei Wang, Shouming Zhong

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In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.

Keywords: Bi-directional associative memory (BAM) neural networks, mixed delays, Lyapunov stability theory, contraction mapping theorem, existence, equilibrium, globally exponential stability.

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Authors: Gong Jie, Yu Qianxu, Liu Min, Shan Weiwei

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The design of methods of the 20 K large dimension cold shield used for infrared radiation demarcating in space environment simulation test were introduced in this paper. The cold shield were cooled by five G-M cryocoolers , and the dimension of the cold shield is the largest in our country.Cold shield installation and distribution and compensator for contraction on cooling were introduced detailedly. The temperature distribution and cool-down time of cold shield surface were also calculated and analysed in this paper. The design of cold shield resolves the difficulty of compensator for contraction on cooling successfully. Test results show that the actual technical performance indicators of cold shield met and exceeded the design requirements.

Keywords: cold shield, G-M cryocooler，infrared radiometer demarcating, satellite, space environment simulation equipments

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Authors: Arun Goel, D. V. S. Verma, Sanjeev Sangwan

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Present study was aimed to develop a discharge measuring device for irrigation and laboratory channels. Experiments were conducted on sharp edged constricted flow meters having four types of width constrictions namely 2:1, 1.5:1, 1:1 and 90o in the direction of flow. These devices were made of MS sheets and installed separately in a rectangular flume. All these four devices were tested under free and submerged flow conditions. Eight different discharges varying from 2 lit/sec to 30 lit/sec were passed through each device. In total around 500 observations of upstream and downstream depths were taken in the present work. For each discharge, free submerged and critical submergence under different flow conditions were noted and plotted. Once the upstream and downstream depths of flow over any of the device are known, the discharge can be easily calculated with the help of the curves developed for free and submerged flow conditions. The device having contraction 2:1 is the most efficient one as it allows maximum critical submergence.

Keywords: Flowrate, flowmeter, open channels, submergence.

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Authors: S. Atabay, T. A. Ali, Md. M. Mortula

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This paper presents the results and findings from a parametric study on the water surface elevation at upstream of bridge constriction for subcritical flow. In this study, the influence of Manning's Roughness Coefficient of main channel (nmc) and floodplain (nfp), and bridge opening (b) flow rate (Q), contraction (kcon) and expansion coefficients (kexp) were investigated on backwater level. The DECK bridge models with different span widths and without any pier were investigated within the two stage channel having various roughness conditions. One of the most commonly used commercial one-dimensional HEC-RAS model was used in this parametric study. This study showed that the effects of main channel roughness (nmc) and flow rate (Q) on the backwater level are much higher than those of the floodplain roughness (nfp). Bridge opening (b) with contraction (kcon) and expansion coefficients (kexp) have very little effect on the backwater level within this range of parameters.

Keywords: Bridge backwater, parametric study and waterways.

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Authors: N. Thongjub, B. Puangkird, V. Ngamaramvaranggul

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The numerical simulation of the slip effect via vicoelastic fluid for 4:1 contraction problem is investigated with regard to kinematic behaviors of streamlines and stress tensor by models of the Navier-Stokes and Oldroyd-B equations. Twodimensional spatial reference system of incompressible creeping flow with and without slip velocity is determined and the finite element method of a semi-implicit Taylor-Galerkin pressure-correction is applied to compute the problem of this Cartesian coordinate system including the schemes of velocity gradient recovery method and the streamline-Upwind / Petrov-Galerkin procedure. The slip effect at channel wall is added to calculate after each time step in order to intend the alteration of flow path. The result of stress values and the vortices are reduced by the optimum slip coefficient of 0.1 with near the outcome of analytical solution.

Keywords: Slip effect, Oldroyd-B fluid, slip coefficient, time stepping method.

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Authors: Elie H. Karam, Antoine B. Abche

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It is known that the heart interacts with and adapts to its venous and arterial loading conditions. Various experimental studies and modeling approaches have been developed to investigate the underlying mechanisms. This paper presents a model of the left ventricle derived based on nonlinear stress-length myocardial characteristics integrated over truncated ellipsoidal geometry, and second-order dynamic mechanism for the excitation-contraction coupling system. The results of the model presented here describe the effects of the viscoelastic damping element of the electromechanical coupling system on the hemodynamic response. Different heart rates are considered to study the pacing effects on the performance of the left-ventricle against constant preload and afterload conditions under various damping conditions. The results indicate that the pacing process of the left ventricle has to take into account, among other things, the viscoelastic damping conditions of the myofilament excitation-contraction process.

Keywords: Myocardial sarcomere, cardiac pump, excitationcontraction coupling, viscoelasicity

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Authors: Durga C. Dalal, Swapan K. Pandit

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In this paper, a numerical study has been made to analyze the transient 2-D flows of a viscous incompressible fluid through channels with forward or backward constriction. Problems addressed include flow through sudden contraction and sudden expansion channel geometries with rounded and increasingly sharp reentrant corner. In both the cases, numerical results are presented for the separation and reattachment points, streamlines, vorticity and flow patterns. A fourth order accurate compact scheme has been employed to efficiently capture steady state solutions of the governing equations. It appears from our study that sharpness of the throat in the channel is one of the important parameters to control the strength and size of the separation zone without modifying the general flow patterns. The comparison between the two cases shows that the upstream geometry plays a significant role on vortex growth dynamics.

Keywords: Forward and backward constriction, HOC scheme, Incompressible viscous flows, Separation and reattachment points.

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Authors: Elie H. Karam, Antoine B. Abche

Abstract:

It is known that the heart interacts with and adapts to its venous and arterial loading conditions. Various experimental studies and modeling approaches have been developed to investigate the underlying mechanisms. This paper presents a model of the left ventricle derived based on nonlinear stress-length myocardial characteristics integrated over truncated ellipsoidal geometry, and second-order dynamic mechanism for the excitation-contraction coupling system. The results of the model presented here describe the effects of the viscoelastic damping element of the electromechanical coupling system on the hemodynamic response. Different heart rates are considered to study the pacing effects on the performance of the left-ventricle against constant preload and afterload conditions under various damping conditions. The results indicate that the pacing process of the left ventricle has to take into account, among other things, the viscoelastic damping conditions of the myofilament excitation-contraction process. The effects of left ventricular dimensions on the hemdynamic response have been examined. These effects are found to be different at different viscoelastic and pacing conditions.

Keywords: Myocardial sarcomere, cardiac pump, excitationcontractioncoupling, viscoelasicity

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Authors: Daniel Olmos-Liceaga

Abstract:

Ventricular fibrillation is a very important health problem as is the cause of most of the sudden deaths in the world. Waves of electrical activity are sent by the SA node, propagate through the cardiac tissue and activate the mechanisms of cell contraction, and therefore are responsible to pump blood to the body harmonically. A spiral wave is an abnormal auto sustainable wave that is responsible of certain types of arrhythmias. When these waves break up, give rise to the fibrillation regime, in which there is a complete loss in the coordination of the contraction of the heart muscle. Interaction of spiral waves and obstacles is also of great importance as it is believed that the attachment of a spiral wave to an obstacle can provide with a transition of two different arrhythmias. An obstacle can be partially excitable or non excitable. In this talk, we present a numerical study of the interaction of meandering spiral waves with partially and non excitable obstacles and focus on the problem where the obstacle plays a fundamental role in the switch between different spiral regimes, which represent different arrhythmic regimes. Particularly, we study the phenomenon of destabilization of spiral waves due to the presence of obstacles, a phenomenon not completely understood (This work will appear as a Chapter in a Book named Cardiac Arrhytmias by INTECH under the name "Spiral Waves, Obstacles and Cardiac Arrhythmias", ISBN 979-953-307-050-5.).

Keywords: Arrhythmias, Cardiac tissue, Obstacles, Spiral waves

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Authors: V. Ngamaramvaranggul, S. Thenissara

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The simulation of extrusion process is studied widely in order to both increase products and improve quality, with broad application in wire coating. The annular tube-tooling extrusion was set up by a model that is termed as Navier-Stokes equation in addition to a rheological model of differential form based on singlemode exponential Phan-Thien/Tanner constitutive equation in a twodimensional cylindrical coordinate system for predicting the contraction point of the polymer melt beyond the die. Numerical solutions are sought through semi-implicit Taylor-Galerkin pressurecorrection finite element scheme. The investigation was focused on incompressible creeping flow with long relaxation time in terms of Weissenberg numbers up to 200. The isothermal case was considered with surface tension effect on free surface in extrudate flow and no slip at die wall. The Stream Line Upwind Petrov-Galerkin has been proposed to stabilize solution. The structure of mesh after die exit was adjusted following prediction of both top and bottom free surfaces so as to keep the location of contraction point around one unit length which is close to experimental results. The simulation of extrusion process is studied widely in order to both increase products and improve quality, with broad application in wire coating. The annular tube-tooling extrusion was set up by a model that is termed as Navier-Stokes equation in addition to a rheological model of differential form based on single-mode exponential Phan- Thien/Tanner constitutive equation in a two-dimensional cylindrical coordinate system for predicting the contraction point of the polymer melt beyond the die. Numerical solutions are sought through semiimplicit Taylor-Galerkin pressure-correction finite element scheme. The investigation was focused on incompressible creeping flow with long relaxation time in terms of Weissenberg numbers up to 200. The isothermal case was considered with surface tension effect on free surface in extrudate flow and no slip at die wall. The Stream Line Upwind Petrov-Galerkin has been proposed to stabilize solution. The structure of mesh after die exit was adjusted following prediction of both top and bottom free surfaces so as to keep the location of contraction point around one unit length which is close to experimental results.

Keywords: wire coating, free surface, tube-tooling, extrudate swell, surface tension, finite element method.

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Authors: Anthony Bawa, Konstantinos Banitsas

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Rheumatism is a muscular disorder that affects the muscles of the upper and lower limbs. This condition could potentially progress to impair the movement of patients. This study aims to investigate the hip muscular imbalance in patients with chronic rheumatism. A clinical trial involving a total of 15 participants, made up of 10 patients and five control subjects, took place in KATH Hospital between August and September. Participants recruited for the study were of age 54 ± 8 years, weight 65 ± 8 kg, and height 176 ± 8 cm. Muscle signals were recorded from the rectus femoris, and vastus lateralis on the right and left hip of participants. The parameters used in determining the hip muscular imbalances were the maximum voluntary contraction (MVC%), the mean difference, and hip muscle fatigue levels. The mean signals were compared using a t-test, and the metrics for muscle fatigue assessment were based on the root mean square (RMS), mean absolute value (MAV) and mean frequency (MEF), which were computed between the hip muscles of participants. The results indicated that there were significant imbalances in the muscle coactivity between the right and left hip muscles of patients. The patients’ MVC values were observed to be above 10% when compared with control subjects. Furthermore, the mean difference was seen to be higher with p > 0.002 among patients, which indicated clear differences in the hip muscle contraction activities. The findings indicate significant hip muscular imbalances for patients with rheumatism compared with control subjects. Information about the imbalances among patients will be useful for clinicians in designing therapeutic muscle-strengthening exercises.

Keywords: Muscular, imbalances, rheumatism, hip.

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Authors: Jan Stodt, Christoph Reich

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The usage of machine learning models for prediction is growing rapidly and proof that the intended requirements are met is essential. Audits are a proven method to determine whether requirements or guidelines are met. However, machine learning models have intrinsic characteristics, such as the quality of training data, that make it difficult to demonstrate the required behavior and make audits more challenging. This paper describes an ML audit framework that evaluates and reviews the risks of machine learning applications, the quality of the training data, and the machine learning model. We evaluate and demonstrate the functionality of the proposed framework by auditing an steel plate fault prediction model.

Keywords: Audit, machine learning, assessment, metrics.

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Authors: Atena Sajedin, Shokoufeh Zakernejad, Soheil Faridi, Mehrdad Javadi, Reza Ebrahimpour

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This paper illustrates the use of a combined neural network model for classification of electrocardiogram (ECG) beats. We present a trainable neural network ensemble approach to develop customized electrocardiogram beat classifier in an effort to further improve the performance of ECG processing and to offer individualized health care. We process a three stage technique for detection of premature ventricular contraction (PVC) from normal beats and other heart diseases. This method includes a denoising, a feature extraction and a classification. At first we investigate the application of stationary wavelet transform (SWT) for noise reduction of the electrocardiogram (ECG) signals. Then feature extraction module extracts 10 ECG morphological features and one timing interval feature. Then a number of multilayer perceptrons (MLPs) neural networks with different topologies are designed. The performance of the different combination methods as well as the efficiency of the whole system is presented. Among them, Stacked Generalization as a proposed trainable combined neural network model possesses the highest recognition rate of around 95%. Therefore, this network proves to be a suitable candidate in ECG signal diagnosis systems. ECG samples attributing to the different ECG beat types were extracted from the MIT-BIH arrhythmia database for the study.

Keywords: ECG beat Classification; Combining Classifiers;Premature Ventricular Contraction (PVC); Multi Layer Perceptrons;Wavelet Transform

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Authors: D. Reich, R. Stark

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To provide reliable and valid findings when evaluating innovative in-car devices in the automotive context highly realistic driving environments are recommended. Nowadays, in-car devices are mostly evaluated due to driving simulator studies followed by real car driving experiments. Driving simulators are characterized by high internal validity, but weak regarding ecological validity. Real car driving experiments are ecologically valid, but difficult to standardize, more time-robbing and costly. One economizing suggestion is to implement more immersive driving environments when applying driving simulator studies. This paper presents research comparing non-immersive standard PC conditions with mobile and highly immersive Oculus Rift conditions while performing the Lane Change Task (LCT). Subjective data with twenty participants show advantages regarding presence and immersion experience when performing the LCT with the Oculus Rift, but affect adversely cognitive workload and simulator sickness, compared to non-immersive PC condition.

Keywords: LCT, immersion, oculus rift, presence, situation awareness.

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Authors: Nawin Raj, Zhenquan Li

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Streamtube is used to visualize expansion, contraction and various properties of the fluid flow. These are useful in fluid mechanics, engineering and geophysics. The streamtube constructed in this paper only reveals the flow expansion rate along streamline. Based on the mass conservative streamline, we will show how to construct the streamtube.

Keywords: Flow visualization, mass conservative, streamline, streamtube.

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Authors: R. Uthayakumar, D. Easwaramoorthy

Abstract:

The purpose of this paper is to present the fuzzy contraction properties of the Hutchinson-Barnsley operator on the fuzzy hyperspace with respect to the Hausdorff fuzzy metrics. Also we discuss about the relationships between the Hausdorff fuzzy metrics on the fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces.

Keywords: Fractals, Iterated Function System, Hutchinson- Barnsley Operator, Fuzzy Metric Space, Hausdorff Fuzzy Metric.

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Authors: Ling Liu, Yuan Ye

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In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results.

Keywords: Discrete-time SIR epidemic model, time delay, nonlinear incidence rate, impulse.

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Authors: N. Namviriyachote, N. Bang, P. Aramwit

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Silk sericin (SS) is a glue-like protein from silkworm cocoon. With its outstanding moisturization and activation collagen synthesis properties, silk protein is applied for wound healing. Since wound dressing in film preparation can facilitate patients- convenience and reduce risk of wound contraction, SS and polyvinyl alcohol (PVA) films were prepared with various concentrations of SS. Their physical properties such as surface density, light transmission, protein dissolution and tensile modulus were investigated. The results presented that 3% SS with 2% PVA is the best ingredient for SS film forming.

Keywords: Sericin, silk protein, film, wound healing.

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Authors: Chun Wen, Tingzhu Huang

Abstract:

We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.

Keywords: Markov chains, tandem queueing networks, convergence, effectiveness.

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