Search results for: surface properties.

Authors: Nurcan Tugrul, Nil Baran Acarali, Seyma Kolemen, Emek Moroydor Derun, Sabriye Piskin

Abstract:

Fly ash is a significant waste that is released of thermal power plants and defined as very fine particles that are drifted upward with up taken by the flue gases due to the burning of used coal [1]. The fly-ash is capable of removing organic contaminants in consequence of high carbon content, a large surface area per unit volume and contained heavy metals. Therefore, fly ash is used as an effective coagulant and adsorbent by pelletization [2, 3]. In this study, the possibility of use of fly ash taken from Turkey like low-cost adsorbent for adsorption of zinc ions found in waste water was investigated. The fly ash taken from Turkey was pelletized with bentonite and molass to evaluate the adsorption capaticity. For this purpose; analyses such as sieve analysis, XRD, XRF, FTIR and SEM were performed. As a result, it was seen that pellets prepared from fly ash, bentonite and molass would be used for zinc adsorption.

Keywords: Fly ash, heavy metal, sieve, adsorbent.

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Authors: Chi Man Luk, Ming Kiu Tsang, Chi Fan Chan, Shu Ping Lau

Abstract:

Nitrogen-doped graphene quantum dots (N-GQDs) were fabricated by microwave-assisted hydrothermal technique. The optical properties of the N-GQDs were studied. The luminescence of the N-GQDs can be tuned by varying the excitation wavelength. Furthermore, two-photon luminescence of the N-GQDs excited by near-infrared laser can be obtained. It is shown that N-doping play a key role on two-photon luminescence. The N-GQDs are expected to find application in biological applications including bioimaging and sensing.

Keywords: Graphene quantum dots, nitrogen doping, photoluminescence, two-photon fluorescence.

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Authors: H. Aminfar, M. Mohammadpourfard, K. Khajeh

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This paper has focused on the most important parameters in the LSC uptake; inlet Re number and Sc number in the presence of non-uniform magnetic field. The magnetic field is arising from the thin wire with electric current placed vertically to the arterial blood vessel. According to the results of this study, applying magnetic field can be a treatment for atherosclerosis by reducing LSC along the vessel wall. Homogeneous porous layer as a arterial wall has been regarded. Blood flow has been considered laminar and incompressible containing Ferro fluid (blood and 4 % vol. Fe₃O₄) under steady state conditions. Numerical solution of governing equations was obtained by using the single-phase model and control volume technique for flow field.

Keywords: LDL Surface Concentration (LSC), Magnetic field, Computational fluid dynamics, Porous wall.

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Authors: A. A. Akande, B. P. Dhonge, B. W. Mwakikunga, A. G. J. Machatine

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This article presents gate-voltage controlled humidity sensing performance of vanadium dioxide nanoparticles prepared from NH₄VO₃ precursor using microwave irradiation technique. The X-ray diffraction, transmission electron diffraction, and Raman analyses reveal the formation of VO₂ (B) with V₂O₅ and an amorphous phase. The BET surface area is found to be 67.67 m²/g. The humidity sensing measurements using the patented lateral-gate MOSFET configuration was carried out. The results show the optimum response at 5 V up to 8 V of gate voltages for 10 to 80% of relative humidity. The dose-response equation reveals the enhanced resilience of the gated VO₂ sensor which may saturate above 272% humidity. The response and recovery times are remarkably much faster (about 60 s) than in non-gated VO₂ sensors which normally show response and recovery times of the order of 5 minutes (300 s).

Keywords: VO2, VO2 (B), V2O5, MOSFET, gate voltage, humidity sensor.

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

Abstract:

The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial or non-inertial reference frame.

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Authors: J. P. Dubois

Abstract:

Single side band modulation is a widespread technique in communication with significant impact on communication technologies such as DSL modems and ATSC TV. Its widespread utilization is due to its bandwidth and power saving characteristics. In this paper, we present a new scheme for SSB signal generation which is cost efficient and enjoys superior characteristics in terms of frequency stability, selectivity, and robustness to noise. In the process, we develop novel Hilbert transform properties.

Keywords: Crystal filter, frequency drift, frequency mixing, Hilbert transform, phasing, selectivity, single side band AM.

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Authors: M. Sundararaman, K. Chandrasekhara Rao

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The aim of this paper is to continue the study of (T1, T2)-semi star generalized closed sets by introducing the concepts of (T1, T2)-semi star generalized locally closed sets and study their basic properties in bitopological spaces.

Keywords: (T1, T2)*-semi star generalized locally closed sets, T1T2-semi star generalized closed sets.

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Authors: Muthana Saleh Alalaki, Michael Opoku Agyeman

Abstract:

The growth in the number of Intellectual Properties (IPs) or the number of cores on the same chip becomes a critical issue in System-on-Chip (SoC) due to the intra-communication problem between the chip elements. As a result, Network-on-Chip (NoC) has emerged as a system architecture to overcome intra-communication issues. This paper presents a study of recent contributions on simulation tools for NoC. Furthermore, an overview of NoC is covered as well as a comparison between some NoC simulators to help facilitate research in on-chip communication.

Keywords: Network-on-Chip, System-on-Chip, embedded systems, computer architecture.

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Authors: Samit Kumar Majumder

Abstract:

In this paper the concept of Q-fuzzification of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semigroups.

Keywords: Q-Fuzzy set, Γ-semigroup, Regular Γ-semigroup, Q-Fuzzy left(right) ideal, Operator semigroups.

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Authors: Hideki Igawa, Yoshinori Kitsutaka, Takashi Yokomuro, Hideo Eguchi

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In this study, the crack self-healing performance of the heavyweight concrete used in the walls of containers and structures designed to shield radioactive materials was investigated. A steam curing temperature that preserves self-healing properties and demolding strength was identified. The presented simultaneously mixing method using the expanding material and the fly ash in the process of admixture can maximize the self-curing performance. Also adding synthetic fibers in the heavyweight concrete improved the self-healing performance.

Keywords: Expanding material, heavyweight concrete, self-healing performance, synthetic fiber.

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Authors: A. A Velásquez, J.Baena

Abstract:

This article presents the simulation, parameterization and optimization of an electromagnet with the C–shaped configuration, intended for the study of magnetic properties of materials. The electromagnet studied consists of a C-shaped yoke, which provides self–shielding for minimizing losses of magnetic flux density, two poles of high magnetic permeability and power coils wound on the poles. The main physical variable studied was the static magnetic flux density in a column within the gap between the poles, with 4cm2 of square cross section and a length of 5cm, seeking a suitable set of parameters that allow us to achieve a uniform magnetic flux density of 1x104 Gaussor values above this in the column, when the system operates at room temperature and with a current consumption not exceeding 5A. By means of a magnetostatic analysis by the finite element method, the magnetic flux density and the distribution of the magnetic field lines were visualized and quantified. From the results obtained by simulating an initial configuration of electromagnet, a structural optimization of the geometry of the adjustable caps for the ends of the poles was performed. The magnetic permeability effect of the soft magnetic materials used in the poles system, such as low– carbon steel (0.08% C), Permalloy (45% Ni, 54.7% Fe) and Mumetal (21.2% Fe, 78.5% Ni), was also evaluated. The intensity and uniformity of the magnetic field in the gap showed a high dependence with the factors described above. The magnetic field achieved in the column was uniform and its magnitude ranged between 1.5x104 Gauss and 1.9x104 Gauss according to the material of the pole used, with the possibility of increasing the magnetic field by choosing a suitable geometry of the cap, introducing a cooling system for the coils and adjusting the spacing between the poles. This makes the device a versatile and scalable tool to generate the magnetic field necessary to perform magnetic characterization of materials by techniques such as vibrating sample magnetometry (VSM), Hall-effect, Kerr-effect magnetometry, among others. Additionally, a CAD design of the modules of the electromagnet is presented in order to facilitate the construction and scaling of the physical device.

Keywords: Electromagnet, Finite Elements Method, Magnetostatic, Magnetometry, Modeling.

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Authors: Hou Youfu, Wang Daoming, Meng Qingrui

Abstract:

To reveal the temperature field distribution of disc brake in downward belt conveyor, mathematical models of heat transfer for disc brake were established combined with heat transfer theory. Then, the simulation process was stated in detail and the temperature field of disc brake under conditions of dynamic speed and dynamic braking torque was numerically simulated by using ANSYS software. Finally the distribution and variation laws of temperature field in the braking process were analyzed. Results indicate that the maximum surface temperature occurs at a time before the brake end and there exist large temperature gradients in both radial and axial directions, while it is relatively small in the circumferential direction.

Keywords: Downward belt conveyor, Disc brake, Temperature field, Numerical simulation.

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Authors: Md. Fazlul Karim, Esa Al-Islam

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This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. We develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.

Keywords: Boundary-fitted nested grid model, finite difference method, Indonesian tsunami of 2004, Southern Thailand.

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Authors: Peter Andráš, Adam Lichý, Jana Rusková, Lenka Matúšková

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The heavy metal contamination of the technogenous sediments and soils at the investigated dump-field show irregular planar distribution. Also the heavy metal content in the surface water, drainage water and in the groundwater was studied both in the dry as well as during the rainy periods. The cementation process causes substitution of iron by copper. Natural installation and development of plant species was observed at the old mine waste dumps, specific to the local chemical conditions such as low content of essential nutrients and high content of heavy metals. The individual parts of the plant tissues (roots, branches/stems, leaves/needles, flowers/ fruits) are contaminated by heavy metals and tissues are damaged differently, respectively.

Keywords: Contamination, dump-field, heavy metals, plants, sediment, water.

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Authors: M. H. M. Rashid

Abstract:

A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl’s theorem, Weyl spectrum, polaroid operators, property (gm), property (m).

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Authors: Tsubasa Seto, Kentaro Nagata, Kazushige Magatani

Abstract:

SEMG (Surface Electromyogram) is one of the bio-signals and is generated from the muscle. And there are many research results that use forearm EMG to detect hand motions. In this paper, we will talk about our developed the robot hand system that can control grasping power by SEMG. In our system, we suppose that muscle power is proportional to the amplitude of SEMG. The power is estimated and the grip power of a robot hand is able to be controlled using estimated muscle power in our system. In addition, to perform a more precise control can be considered to build a closed loop feedback system as an object to a subject to pressure from the edge of hand. Our objectives of this study are the development of a method that makes perfect detection of the hand grip force possible using SEMG patterns, and applying this method to the man-machine interface.

Keywords: SEMG, multi electrode, robot hand, power control

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Authors: G. Toker, V. Bulatov, T. Kovalchuk, I. Schechter

Abstract:

Dynamics of laser radiation – metal target interaction in water at 1064 nm by applying Mach-Zehnder interference technique was studied. The mechanism of generating the well developed regime of evaporation of a metal surface and a spherical shock wave in water is proposed. Critical intensities of the NIR for the well developed evaporation of silver and gold targets were determined. Dynamics of shock waves was investigated for earlier (dozens) and later (hundreds) nanoseconds of time. Transparent expanding plasma-vapor-compressed water object was visualized and measured. The thickness of compressed layer of water and pressures behind the front of a shock wave for later time delays were obtained from the optical treatment of interferograms.

Keywords: laser, shock wave, metal target, underwater

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Authors: S. Distantina, Rochmadi, M. Fahrurrozi, Wiratni

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Preparation of hydrogel based on carrageenan extracted from Kappaphycus alvarezii was conducted with film immersion in glutaraldehyde solution (GA 4%w/w) for 2min and then followed by thermal curing at 110°C for 25min. The method of carrageenan recovery strongly determines the properties of crosslinked carrageenan. Hydrogel obtained from alkali treated carrageenan showed higher swelling ability compared to hydrogel from nonalkali treated carrageenan. Hydrogel from alkali treated showed the ability of sensitive to pH media.

Keywords: Hydrogel, carrageenan, swelling, alkali treated.

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Authors: Shazia Javed, Noor Atinah Ahmad

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In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.

Keywords: Autocorrelation matrix, Cholesky's factor, eigenvalue spread, Markov input.

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Authors: Shagufta Tabassum

Abstract:

The study of dielectric properties in a binary mixture of liquids is very useful to understand the liquid structure, molecular interaction, dynamics, and kinematics of the mixture. Time-domain reflectometry (TDR) is a powerful tool for studying the cooperation and molecular dynamics of the H-bonded system. Here we discuss the basic calibration and normalization procedure for TDR measurements. Our aim is to explain different types of error occur during TDR measurements and how to minimize it.

Keywords: time domain reflectometry measurement technique, cable and connector loss, oscilloscope loss, normalization technique

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Authors: Fengshuo Zhang, Zhouhong Li

Abstract:

In this paper, we obtain sufficient conditions for the existence of at least four positive almost periodic solutions to an impulsive delayed periodic plankton allelopathy system with multiple exploited (or harvesting) terms. This result is obtained through the use of Mawhins continuation theorem of coincidence degree theory along with some properties relating to inequalities.

Keywords: Almost periodic solutions, plankton allelopathy system, coincidence degree, impulse.

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Authors: F. Javier Benitez, Carolina Garcia, Juan Luis Acero, Francisco J. Real

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Four phenylurea herbicides (isoproturon, chlortoluron, diuron and linuron) were dissolved in different water matrices in order to study their chemical degradation by using UV radiation, ozone and some advanced oxidation processes (UV/H2O2, O3/H2O2, Fenton reagent and the photo- Fenton system). The waters used were: ultra-pure water, a commercial mineral water, a groundwater and a surface water taken from a reservoir. Elimination levels were established for each herbicide and for several global quality parameters, and a kinetic study was performed in order to determine basic kinetic parameters of each reaction between the target phenylureas and these oxidizing systems.

Keywords: Phenylurea herbicides, UV radiation; Ozone, Fenton reagent, Hydroxyl radicals, Rate constants, Quantum yields

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Authors: Yan Wang, Yasushi Asami, Yukio Sadahiro

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In urban context, urban nodes such as amenity or hazard will certainly affect house price, while classic hedonic analysis will employ distance variables measured from each urban nodes. However, effects from distances to facilities on house prices generally do not represent the true price of the property. Distance variables measured on the same surface are suffering a problem called multicollinearity, which is usually presented as magnitude variance and mean value in regression, errors caused by instability. In this paper, we provided a theoretical framework to identify and gather the data with less bias, and also provided specific sampling method on locating the sample region to avoid the spatial multicollinerity problem in three distance variable’s case.

Keywords: Hedonic regression, urban node, distance variables, multicollinerity, collinearity.

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Authors: Flora Elvistia Firdaus

Abstract:

The epoxidation of soybean oil at temperature of 600C was provided the best result in terms of attaching the –OH functionality. Temperatures below and above 600C it is likely the attaching reaction did not proceed sufficiently fast. The considerable yield below 40%, implies the oil is not completely converted, it is not possible by conventional methods, because the epoxide decomposes at the temperature required. The objective of this work was the development of catalyst toward the conversion of epoxide and polyol with reaction temperature at 50,60, and 700C. The effect of different type of catalyst were studied, the effect of alcohols with different molecular configuration was determined which leads to selective addition of alcohols to the epoxide oils.

Keywords: optimization, epoxide, soybean, catalyst

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Authors: Maksudur Rahman Khan, Kar Min Chan, Huei Ruey Ong, Chin Kui Cheng, Wasikur Rahman

Abstract:

Microbial fuel cells (MFCs) represent a promising technology for simultaneous bioelectricity generation and wastewater treatment. Catalysts are significant portions of the cost of microbial fuel cell cathodes. Many materials have been tested as aqueous cathodes, but air-cathodes are needed to avoid energy demands for water aeration. The sluggish oxygen reduction reaction (ORR) rate at air cathode necessitates efficient electrocatalyst such as carbon supported platinum catalyst (Pt/C) which is very costly. Manganese oxide (MnO2) was a representative metal oxide which has been studied as a promising alternative electrocatalyst for ORR and has been tested in air-cathode MFCs. However the single MnO2 has poor electric conductivity and low stability. In the present work, the MnO2 catalyst has been modified by doping Pt nanoparticle. The goal of the work was to improve the performance of the MFC with minimum Pt loading. MnO2 and Pt nanoparticles were prepared by hydrothermal and sol gel methods, respectively. Wet impregnation method was used to synthesize Pt/MnO2 catalyst. The catalysts were further used as cathode catalysts in air-cathode cubic MFCs, in which anaerobic sludge was inoculated as biocatalysts and palm oil mill effluent (POME) was used as the substrate in the anode chamber. The asprepared Pt/MnO2 was characterized comprehensively through field emission scanning electron microscope (FESEM), X-Ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and cyclic voltammetry (CV) where its surface morphology, crystallinity, oxidation state and electrochemical activity were examined, respectively. XPS revealed Mn (IV) oxidation state and Pt (0) nanoparticle metal, indicating the presence of MnO2 and Pt. Morphology of Pt/MnO2 observed from FESEM shows that the doping of Pt did not cause change in needle-like shape of MnO2 which provides large contacting surface area. The electrochemical active area of the Pt/MnO2 catalysts has been increased from 276 to 617 m2/g with the increase in Pt loading from 0.2 to 0.8 wt%. The CV results in O2 saturated neutral Na2SO4 solution showed that MnO2 and Pt/MnO2 catalysts could catalyze ORR with different catalytic activities. MFC with Pt/MnO2 (0.4 wt% Pt) as air cathode catalyst generates a maximum power density of 165 mW/m3, which is higher than that of MFC with MnO2 catalyst (95 mW/m3). The open circuit voltage (OCV) of the MFC operated with MnO2 cathode gradually decreased during 14 days of operation, whereas the MFC with Pt/MnO2 cathode remained almost constant throughout the operation suggesting the higher stability of the Pt/MnO2 catalyst. Therefore, Pt/MnO2 with 0.4 wt% Pt successfully demonstrated as an efficient and low cost electrocatalyst for ORR in air cathode MFC with higher electrochemical activity, stability and hence enhanced performance.

Keywords: Microbial fuel cell, oxygen reduction reaction, Pt/MnO2, palm oil mill effluent, polarization curve.

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Authors: Rajan Rajabalaya, Li-Qun Tor, Sheba David

Abstract:

Transdermal delivery of ondansetron hydrochloride (OdHCl) can prevent the problems encountered with oral ondansetron. In previously conducted studies, effect of amount of polyvinyl pyrrolidone, permeation enhancer and casting solvent on the physicochemical properties on OdHCl were investigated. It is feasible to develop ondansetron transdermal patch by using ethyl cellulose and polyvinyl pyrrolidone with dibutyl pthalate as plasticizer, however, the desired flux is not achieved. The primary aim of this study is to use dimethyl succinate (DMS) and propylene glycol that are not incorporated in previous studies to determine their effect on the physicochemical properties of an OdHCl transdermal patch using ethyl cellulose and polyvinyl pyrrolidone. This study also investigates the effect of permeation enhancer (eugenol and phosphatidylcholine) on the release of OdHCl. The results showed that propylene glycol is a more suitable plasticizer compared to DMS in the fabrication of OdHCl transdermal patch using ethyl cellulose and polyvinyl pyrrolidone as polymers. Propylene glycol containing patch has optimum drug content, thickness, moisture content and water absorption, tensile strength, and a better release profile than DMS. Eugenol and phosphatidylcholine can increase release of OdHCl from the patches. From the physicochemical result and permeation profile, a combination of 350mg of ethyl cellulose, 150mg polyvinyl pyrrolidone, 3% of total polymer weight of eugenol, and 40% of total polymer weight of propylene glycol is the most suitable formulation to develop an OdHCl patch. OdHCl release did not increase with increasing the percentage of plasticiser. DMS 4, PG 4, DMS 9, PG 9, DMS 14, and PG 14 gave better release profiles where using 300mg: 0mg, 300mg: 100mg, and 350mg: 150mg of EC: PVP. Thus, 40% of PG or DMS appeared to be the optimum amount of plasticiser when the above combination where EC: PVP was used. It was concluded from the study that a patch formulation containing 350mg EC, 150mg PVP, 40% PG and 3% eugenol is the best transdermal matrix patch compositions for the uniform and continuous release/permeation of OdHCl over an extended period. This patch design can be used for further pharmacokinetic and pharmacodynamic studies in suitable animal models.

Keywords: Ondansetron hydrochloride, dimethyl succinate, eugenol.

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Authors: Hong Son Hoang, Remy Baraille

Abstract:

The (sub)-optimal soolution of linear filtering problem with correlated noises is considered. The special recursive form of the class of filters and criteria for selecting the best estimator are the essential elements of the design method. The properties of the proposed filter are studied. In particular, for Markovian observation noise, the approximate filter becomes an optimal Gevers-Kailath filter subject to a special choice of the parameter in the class of given linear recursive filters.

Keywords: Linear dynamical system, filtering, minimum meansquare filter, correlated noise

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Authors: Onder Yakut, Serdar Solak, Emine Dogru Bolat

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Measuring the Electrocardiogram (ECG) signal is an essential process for the diagnosis of the heart diseases. The ECG signal has the information of the degree of how much the heart performs its functions. In medical diagnosis and treatment systems, Decision Support Systems processing the ECG signal are being developed for the use of clinicians while medical examination. In this study, a modular wireless ECG (WECG) measuring and recording system using a single board computer and e-Health sensor platform is developed. In this designed modular system, after the ECG signal is taken from the body surface by the electrodes first, it is filtered and converted to digital form. Then, it is recorded to the health database using Wi-Fi communication technology. The real time access of the ECG data is provided through the internet utilizing the developed web interface.

Keywords: ECG, e-health sensor shield, raspberry Pi, wifi technology.

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Authors: Preeyaphorn Kosa, Thanutch Sukwimolseree

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The climate change is a main parameter which affects the element of hydrological cycle especially runoff. Then, the purpose of this study is to determine the impact of the climate change on surface runoff using land use map on 2008 and daily weather data during January 1, 1979 to September 30, 2010 for SWAT model. SWAT continuously simulate time model and operates on a daily time step at basin scale. The results present that the effect of temperature change cannot be clearly presented on the change of runoff while the rainfall, relative humidity and evaporation are the parameters for the considering of runoff change. If there are the increasing of rainfall and relative humidity, there is also the increasing of runoff. On the other hand, if there is the increasing of evaporation, there is the decreasing of runoff.

Keywords: Climate, Runoff, SWAT, Upper Mun River Basin

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Authors: Mohsen Zahraei

Abstract:

In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for Є > 0, the notion of Birkhoff-James approximate orthogonality sets for Є−higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: Rank−k numerical range, isometry, numerical range, rectangular matrix polynomials.

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