Search results for: Extremal Properties

Authors: Fakhra Aziz, K. Sulaiman, Kh. S. Karimov, M. Hassan Sayyad

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This paper presents a spectroscopic study on doping of Vanadyl pathalocyanine (VOPc) by [6,6]-phenyl C61 butyric acid methyl ester (PCBM). The films are characterized by UV/Vis/NIR spectroscopy. A drastic increase in the absorption coefficient has been observed with increasing dopant concentration. Optical properties of VOPc:PCBM films deposited by spin coating technique were studied in detail. Optical band gap decreased with the PCBM incorporation in the VOPc film. Optical band gap calculated from the absorption spectra decreased from 3.32 eV to 3.26 eV with a variation of 0–75 % of PCBM concentration in the VOPC films.

Keywords: Optical properties, spin-coating, optical properties, optical energy gap

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Authors: Iliana Marinova, Valentin Mateev

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In this paper a computer system for electromagnetic properties measurements is designed. The system employs Agilent 4294A precision impedance analyzer to measure the amplitude and the phase of a signal applied over a tested biological tissue sample. Measured by the developed computer system data could be used for tissue characterization in wide frequency range from 40Hz to 110MHz. The computer system can interface with output devices acquiring flexible testing process.

Keywords: Electromagnetic properties, human tissue, bioimpedance, measurement system.

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Authors: Sh. Hosseini, M. B. Limooei, M. Hossein Zade, E. Askarnia, Z. Asadi

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Manganese steel (Hadfield) is one of the important alloys in industry due to its special properties. High work hardening ability with appropriate toughness and ductility are the properties that caused this alloy to be used in wear resistance parts and in high strength condition. Heat treatment is the main process through which the desired mechanical properties and microstructures are obtained in Hadfield steel. In this study various heat treatment cycles, differing in austenising temperature, time and quenching solution are applied. For this purpose, the same samples of manganese steel was heat treated in 9 different cycles, and then the mechanical properties and microstructures were investigated. Based on the results of the study, the optimum heat treatment cycle was obtained.

Keywords: Manganese steel (Hadfield), heat treatment, austenising temperature, austenising time, quenching solution, mechanical properties.

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Authors: Adil AL-Rammahi

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In this short paper, new properties of transition matrix were introduced. Eigen values for small order transition matrices are calculated in flexible method. For benefit of these properties applications of these properties were studied in the solution of Markov's chain via steady state vector, and information theory via channel entropy. The implemented test examples were promised for usages.

Keywords: Eigen value problem, transition matrix, state vector, information theory.

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Authors: Z. Pavlík, M. Keppert, J. Žumár, M. Pavlíková, A. Trník, R. Černý

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Effect of high temperature exposure on properties of cement mortar containing municipal solid waste incineration (MSWI) bottom ash as partial natural aggregate replacement is analyzed in the paper. The measurements of mechanical properties, bulk density, matrix density, total open porosity, sorption and desorption isotherms are done on samples exposed to the temperatures of 20°C to 1000°C. TGA analysis is performed as well. Finally, the studied samples are analyzed by IR spectroscopy in order to evaluate TGA data.

Keywords: Cement mortar, high temperature exposure, MSWI bottom ash, natural aggregate replacement, mechanical properties

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Authors: Prakash Chand, Anurag Gaur, Ashavani Kumar

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In the present study, we have synthesized Cr and Fe doped zinc oxide (ZnO) nanostructures (Zn1-δCraFebO; where δ = a + b = 20%, a = 5, 6, 8 & 10% and b = 15, 14, 12 & 10%) via sol-gel method at different doping concentrations. The synthesized samples were characterized for structural properties by X-ray diffractrometer and field emission scanning electron microscope and the optical properties were carried out through photoluminescence and UVvisible spectroscopy. The particle size calculated through field emission scanning electron microscope varies from 41 to 96 nm for the samples synthesized at different doping concentrations. The optical band gaps calculated through UV-visible spectroscopy are found to be decreasing from 3.27 to 3.02 eV as the doping concentration of Cr increases and Fe decreases.

Keywords: Nanostructures, Optical Properties, Sol-gel method.

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Authors: Moez Selmi, Mariem Kacem, Mehrez Jamei, Philippe Dubujet

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Earth pressure balance (EPB) tunnel boring machines are designed for digging in different types of soil, especially clay soils. This operation requires the treatment of soil by lubricants to facilitate the procedure of excavation. A possible use of this soil is limited by the effect of treatment on the hydro-mechanical properties of the soil. This work aims to study the effect of a foaming agent on the hydro-mechanical properties of clay soil. The injection of the foam agent in the soil leads to create a soil matrix in which they are incorporated gas bubbles. The state of the foam in the soil is scalable thanks to the degradation of the gas bubbles in the soil.

Keywords: EPB, clay soils, foam agent, hydro-mechanical properties, degradation.

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Authors: N. H. Ismail, A. A. A. Nassar, K. H. Baz

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Semiconductor crystals smaller than about 10 nm, known as quantum dots, have properties that differ from large samples, including a band gap that becomes larger for smaller particles. These properties create several applications for quantum dots. In this paper new shapes of quantum dot arrays are used to enhance the photo physical properties of gold nano-particles. This paper presents a study of the effect of nano-particles shape, array, and size on their absorption characteristics.

Keywords: Quantum Dots, Nano-Particles, LSPR.

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Authors: J. Davoodi , J. Moradi

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The aim of this research was to calculate the mechanical properties of Pd3Rh and PdRh3 ordered alloys. The molecular dynamics (MD) simulation technique was used to obtain temperature dependence of the energy, the Yong modulus, the shear modulus, the bulk modulus, Poisson-s ratio and the elastic stiffness constants at the isobaric-isothermal (NPT) ensemble in the range of 100-325 K. The interatomic potential energy and force on atoms were calculated by Quantum Sutton-Chen (Q-SC) many body potential. Our MD simulation results show the effect of temperature on the cohesive energy and mechanical properties of Pd3Rh as well as PdRh3 alloys. Our computed results show good agreement with the experimental results where they have been available.

Keywords: Pd-Rh alloy; Mechanical properties; Moleculardynamics simulation

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Authors: Zeinab Jafarian Jeloudar, Hossien Kavianpoor, Abazar Esmali Ouri, Ataollah Kavian

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In this paper spatial variability of some chemical and physical soil properties were investigated in mountain rangelands of Nesho, Mazandaran province, Iran. 110 soil samples from 0-30 cm depth were taken with systematic method on grid 30×30 m2 in regions with different vegetation cover and transported to laboratory. Then soil chemical and physical parameters including Acidity (pH), Electrical conductivity, Caco3, Bulk density, Particle density, total phosphorus, total Nitrogen, available potassium, Organic matter, Saturation moisture, Soil texture (percentage of sand, silt and clay), Sodium, Calcium, magnesium were measured in laboratory. Data normalization was performed then was done statistical analysis for description of soil properties and geostatistical analysis for indication spatial correlation between these properties and were perpetrated maps of spatial distribution of soil properties using Kriging method. Results indicated that in the study area Saturation moisture and percentage of Sand had highest and lowest spatial correlation respectively.

Keywords: Chemical and physical soil properties, Iran, Spatial variability, Nesho Rangeland

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Authors: A. I. Alateyah, H. N. Dhakal, Z. Y. Zhang

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The mechanical properties including flexural and tensile of neat vinyl ester and polymer based on layered silicate nanocomposite materials are discussed. The addition of layered silicate into the polymer matrix increased the tensile and flexural modulus up to 1 wt.% clay loading. The incorporation of more clay resulted in decreasing the mechanical properties which was traced to the existence of aggregation layers. Likewise, up to 1 wt.% clay loading, the thermal behaviour showed significant improvements and at higher clay loading the thermal pattern was reduced. The aggregation layers imparted a negative impact on the overall mechanical and thermal properties. Wide Angle X-ray Diffraction, Scanning Electron Microscopy and Transmission Electron Microscopy were utilised in order to characterise the interlamellar structure of nanocomposites.

Keywords: Vinyl ester, nanocomposites, layered silicate, mechanical properties, thermal analysis.

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Authors: A. Naceri, M. Chikouche Hamina, P. Grosseau

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The effect of artificial pozzolan (waste brick) on the physico-chemical properties of cement manufactured was investigated. The waste brick is generated by the manufacture of bricks. It was used in the proportions of 0%, 5%, 10%, 15% and 20% by mass of cement to study its effect on the physico-chemical properties of cement incorporating artificial pozzolan. The physicochemical properties of cement at anhydrous state and the hydrated state (chemical composition, specific weight, fineness, consistency of the cement paste and setting times) were studied. The experimental results obtained show that the quantity of pozzolanic admixture (waste brick) of cement manufactured is the principal parameter who influences on the variation of the physico-chemical properties of the cement tested.

Keywords: Artificial pozzolan, waste brick, cement, physicochemicalcharacteristics.

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Authors: Maruf Yinka Kolawole, Jacob Olayiwola Aweda, Farasat Iqbal, Asif Ali, Sulaiman Abdulkareem

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Zinc is a non-ferrous metal with potential application in orthopaedic implant materials. However, its poor mechanical properties were major challenge to its application. Therefore, this paper studies the mechanical properties of biodegradable Zn-based alloy for biomedical application. Pure zinc powder with varying (0, 1, 2, 3 & 6) wt% of magnesium powders were ball milled using ball-to-powder ratio (B:P) of 10:1 at 350 rpm for 4 hours. The resulting milled powders were compacted and sintered at 300 MPa and 350 °C respectively. Microstructural, phase and mechanical properties analyses were performed following American standard of testing and measurement. The results show that magnesium has influence on the mechanical properties of zinc. The compressive strength, hardness and elastic modulus of 210 ± 8.878 MPa, 76 ± 5.707 HV and 45 ± 11.616 GPa respectively as obtained in Zn-2Mg alloy were optimum and meet the minimum requirement of biodegradable metal for orthopaedics application. These results indicate an increase of 111, 93 and 93% in compressive strength, hardness and elastic modulus respectively as compared to pure zinc. The increase in mechanical properties was adduced to effectiveness of compaction pressure and intermetallic phase formation within the matrix resulting in high dislocation density for improving strength. The study concluded that, Zn-2Mg alloy with optimum mechanical properties can therefore be considered a potential candidate for orthopaedic application.

Keywords: Biodegradable metal, biomedical application mechanical properties, powder metallurgy, zinc.

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Authors: M. Li, V. D. Thi, M. Khelifa, M. El Ganaoui

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This study presents an overview of the work carried out by the use of wood waste as coarse aggregate in mortar. The paper describes experimental and numerical investigations carried on pervious concrete made of wood chips and also sheds lights on the mechanical properties of this new product. The properties of pervious wood-concrete such as strength, elastic modulus, and failure modes are compared and evaluated. The characterization procedure of the mechanical properties of wood waste ash are presented and discussed. The numerical and tested load–deflection response results are compared. It was observed that the numerical results are in good agreement with the experimental results.

Keywords: Wood waste ash, characterization, mechanical properties, finite element analysis, flexural behavior, bending tests.

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Authors: Olesia Mikhailova, Pavel Rovnaník

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In the present work, metakaolin-based geopolymer including different polymer admixtures was studied. Different types of commercial polymer admixtures VINNAPAS^® and polyethylene glycol of different relative molecular weight were used as polymer admixtures. The main objective of this work is to investigate the influence of different types of admixtures on the properties of metakaolin-based geopolymer mortars considering their different dosage. Mechanical properties, such as flexural and compressive strength were experimentally determined. Also, study of the microstructure of selected specimens by using a scanning electron microscope was performed. The results showed that the specimen with addition of 1.5% of VINNAPAS^® 7016 F and 10% of polyethylene glycol 400 achieved maximum mechanical properties.

Keywords: Metakaolin, geopolymer, polymer admixtures, mechanical properties, microstructure.

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Authors: K. Kalaiselvan, A. Elango, N.M. Nagarajan, N. Mathiazhagan

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Dissimilar joining of Titanium and Aluminum thin sheets has potential applications in aerospace and automobile industry which can reduce weight and cost and improve strength, corrosion resistance and high temperature properties. However successful welding of Titanium/Aluminium sheets is of challenge due to differences in physical, chemical and metallurgical properties between the two. This paper describes research results of Laser Beam Welding (LBW) of Ti/Al thin sheets in which many researchers have recently performed and critically reviewed from different perspectives. Also some of notable works in the field of laser welding with changes in mechanical properties, crack propagation, diffusion behavior, chemical potential, interfacial reaction and the microstructure are reported.

Keywords: Laser Beam Welding (LBW), Mechanical properties, Titanium and Aluminium thin sheets.

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Authors: Serafettin Ekinci, Kursat Zuhtuogullari

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This paper proposes a Fuzzy Expert System design to determine the wearing properties of nitrided and non nitrided steel. The proposed Fuzzy Expert System approach helps the user and the manufacturer to forecast the wearing properties of nitrided and non nitrided steel under specified laboratory conditions. Surfaces of the engineering components are often nitrided for improving wear, corosion, fatigue specifications. A major property of nitriding process is reducing distortion and wearing of the metalic alloys. A Fuzzy Expert System was developed for determining the wearing and durability properties of nitrided and non nitrided steels that were tested under different loads and different sliding speeds in the laboratory conditions.

Keywords: Fuzzy Expert System Design, Rule Based Systems, Fatigue, Corrosion

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Authors: Yeong-Hwa Chang, Chang-Hung Hsu, Huei-Lung Chu, Chia-Wen Chang, Wei-Shou Chan, Chun-Yao Lee; Chia-Shiang Yao, Yan-Lou He

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This study reports the preparation of soft magnetic ribbons of Fe-based amorphous alloys using the single-roller melt-spinning technique. Ribbon width varied from 142 mm to 213 mm and, with a thickness of approximately 22 μm 2 μm. The microstructure and magnetic properties of the ribbons were characterized by differential scanning calorimeter (DSC), X-ray diffraction (XRD), vibrating sample magnetometer (VSM), and electrical resistivity measurements (ERM). The amorphous material properties dependence of the cooling rate and nozzle pressure have uneven surface in ribbon thicknesses are investigated. Magnetic measurement results indicate that some region of the ribbon exhibits good magnetic properties, higher saturation induction and lower coercivity. However, due to the uneven surface of 213 mm wide ribbon, the magnetic responses are not uniformly distributed. To understand the transformer magnetic performances, this study analyzes the measurements of a three-phase 2 MVA amorphous-cored transformer. Experimental results confirm that the transformer with a ribbon width of 142 mm has better magnetic properties in terms of lower core loss, exciting power, and audible noise. 

Keywords: Amorphous ribbon, uneven surface, magnetic properties, and rapid solidification

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Authors: Risdiana, D. Suhendar, S. Pratiwi, W. A. Somantri, T. Saragi

Abstract:

The effect of partially substitution of magnetic impurity Fe for Cu to the magnetic and transport properties in electron-doped superconducting cuprates of Eu1.85+yCe0.15-yCu1-yFeyO4+α-δ (ECCFO) with y = 0, 0.010, 0.020, and 0.050 has been studied, in order to investigate the mechanism of magnetic and transport properties of ECCFO in normal-state. Magnetic properties are investigated by DC magnetic-susceptibility measurements that carried out at low temperatures down to 2 K using a standard SQUID magnetometer in a magnetic field of 5 Oe on field cooling. Transport properties addressed to electron mobility, are extracted from radius of electron localization calculated from temperature dependence of resistivity. For y = 0, temperature dependence of dc magnetic-susceptibility (χ) indicated the change of magnetic behavior from paramagnetic to diamagnetic below 15 K. Above 15 K, all samples show paramagnetic behavior with the values of magnetic moment in every volume unit increased with increasing y. Electron mobility decreased with increasing y.

Keywords: DC magnetic-susceptibility, electron mobility, Eu1.85+yCe0.15-yCu1-yFeyO4+α-δ, normal state.

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Authors: Chang-Hung Hsu, Yeong-Hwa Chang, Chun-Yao Lee, Chia-Shiang Yao, Yan-Lou He, Huei-Lung Chu, Chia-Wen Chang, Wei-Shou Chan

Abstract:

This study reports the preparation of soft magnetic ribbons of Fe-based amorphous alloys using the single-roller melt-spinning technique. Ribbon width varied from 142 mm to 213 mm and, with a thickness of approximately 22 μm ± 2 μm. The microstructure and magnetic properties of the ribbons were characterized by differential scanning calorimeter (DSC), X-ray diffraction (XRD), vibrating sample magnetometer (VSM), and electrical resistivity measurements (ERM). The amorphous material properties dependence of the cooling rate and nozzle pressure have uneven surface in ribbon thicknesses are investigated. Magnetic measurement results indicate that some region of the ribbon exhibits good magnetic properties, higher saturation induction and lower coercivity. However, due to the uneven surface of 213 mm wide ribbon, the magnetic responses are not uniformly distributed. To understand the transformer magnetic performances, this study analyzes the measurements of a three-phase 2 MVA amorphous-cored transformer. Experimental results confirm that the transformer with a ribbon width of 142 mm has better magnetic properties in terms of lower core loss, exciting power, and audible noise.

Keywords: Amorphous ribbon, uneven surface, magnetic properties, and rapid solidification

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Authors: Chun-Wei Tung, Chyn Liaw, Shinn-Jang Ho, Shinn-Ying Ho

Abstract:

Protein subchloroplast locations are correlated with its functions. In contrast to the large amount of available protein sequences, the information of their locations and functions is less known. The experiment works for identification of protein locations and functions are costly and time consuming. The accurate prediction of protein subchloroplast locations can accelerate the study of functions of proteins in chloroplast. This study proposes a Random Forest based method, ChloroRF, to predict protein subchloroplast locations using interpretable physicochemical properties. In addition to high prediction accuracy, the ChloroRF is able to select important physicochemical properties. The important physicochemical properties are also analyzed to provide insights into the underlying mechanism.

Keywords: Chloroplast, Physicochemical properties, Proteinlocations, Random Forests.

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Authors: Z. Pavlík, J. Fořt, J. Žumár, M. Pavlíková, R. Černý

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The cup method is applied for the measurement of water vapor transport properties of porous materials worldwide. However, in practical applications the experimental results are often used without taking into account some secondary effects which can play an important role under specific conditions. In this paper, the effect of temperature on water vapor transport properties of cellular concrete is studied, together with the influence of sample thickness. At first, the bulk density, matrix density, total open porosity and sorption and desorption isotherms are measured for material characterization purposes. Then, the steady state cup method is used for determination of water vapor transport properties, whereas the measurements are performed at several temperatures and for three different sample thicknesses.

Keywords: Water vapor transport, cellular concrete, cup method, temperature, sample thickness.

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Authors: Alan Vaško, Juraj Belan, Lenka Hurtalová, Eva Tillová

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The aim of this study is to evaluate the influence of raw material composition on the microstructure, mechanical and fatigue properties and micromechanisms of failure of nodular cast iron. In order to evaluate the influence of charge composition, the structural analysis, mechanical and fatigue tests and microfractographic analysis were carried out on specimens of ten melts with different charge compositions. The basic charge of individual melts was formed by different ratio of pig iron and steel scrap and by different additive for regulation of chemical composition (silicon carbide or ferrosilicon). The results show differences in mechanical and fatigue properties, which are connected with the microstructure. SiC additive positively influences microstructure. Consequently, mechanical and fatigue properties of nodular cast iron are improved, especially in the melts with higher ratio of steel scrap in the charge.

Keywords: Nodular cast iron, silicon carbide, microstructure, mechanical properties.

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Authors: Nidal H. Abu-Zahra, Parisa Khoshnoud, Murtatha Jamel, Subhashini Gunashekar

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PVC foam-fly ash composites (PVC-FA) are characterized for their structural, morphological, mechanical and thermal properties. The tensile strength of the composites increased modestly with higher fly ash loading, while there was a significant increase in the elastic modulus for the same composites. On the other hand, a decrease in elongation at UTS was observed upon increasing fly ash content due to increased rigidity of the composites. Similarly, the flexural modulus increased as the fly ash loading increased, where the composites containing 25 phr fly ash showed the highest flexural strength. Thermal properties of PVC-fly ash composites were determined by Thermo Gravimetric Analysis (TGA). The microstructural properties were studied by Scanning Electron Microscopy (SEM). SEM results confirm that fly ash particles were mechanically interlocked in PVC matrix with good interfacial interaction with the matrix. Particle agglomeration and debonding was observed in samples containing higher amounts of fly ash.

Keywords: PVC Foam, Polyvinyl Chloride, Rigid PVC, Fly Ash Composites.

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Authors: Kai-Ti Hsu, Hui-Ling Huang, Chun-Wei Tung, Yi-Hsiung Chen, Shinn-Ying Ho

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Bioinformatics methods for predicting the T cell coreceptor usage from the array of membrane protein of HIV-1 are investigated. In this study, we aim to propose an effective prediction method for dealing with the three-class classification problem of CXCR4 (X4), CCR5 (R5) and CCR5/CXCR4 (R5X4). We made efforts in investigating the coreceptor prediction problem as follows: 1) proposing a feature set of informative physicochemical properties which is cooperated with SVM to achieve high prediction test accuracy of 81.48%, compared with the existing method with accuracy of 70.00%; 2) establishing a large up-to-date data set by increasing the size from 159 to 1225 sequences to verify the proposed prediction method where the mean test accuracy is 88.59%, and 3) analyzing the set of 14 informative physicochemical properties to further understand the characteristics of HIV-1coreceptors.

Keywords: Coreceptor, genetic algorithm, HIV-1, SVM, physicochemical properties, prediction.

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Authors: Onur Ayaz, Nuray Ucar, Elif Bahar, Oguzhan Ucar, Mustafa Oksuz, Aysen Onen, Mehmet Ucar, Ezgi İşmar, Ali Demir

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In this study, single nozzle method used for electrospinning technique which composite polymer solution with cellulose nanowiskers (CNW) was treated by ultrasonic sonificator have been compared with coaxial (double) nozzle method, in terms of mechanical, thermal and morphological properties of composite nanofiber. The effect of water content in composite polymer solution on properties of nanofiber has also been examined. It has been seen that single nozzle method which polymer solution does not contain water has better results than that of coaxial method, in terms of mechanical, thermal and morphological properties of nanofiber. However, it is necessary to make an optimization study on setting condition of ultrasonic treatment to get better dispersion of CNW in composite nanofiber and to get better mechanical and thermal properties

Keywords: cellulose nanowhiskers, coaxial nozzle, composite nanofiber, electrospinning

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

Abstract:

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: Muhammad Nouman Haral, Abdulaziz I. Al-Negheimesh, Galal Fares, Mohammad Iqbal Khan, Abdulrahman M. Alhozaimy

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Natural pozzolan (NP) is one of the potential prehistoric alternative binders in the construction industry. It has been investigated as cement replacement in ordinary concrete by several researchers for many purposes. Various supplementary cementitious materials (SCMs) such as fly ash, limestone dust and silica fume are widely used in the production of SCC; however, limited studies to address the effect of NP on the properties of SCC are documented. The current research is composed of different SCC paste and concrete mixtures containing different replacement levels of local NP as an alternative SCM. The effect of volume of paste containing different amounts of local NP related to W/B ratio and cement content on SCC fresh properties was assessed. The variations in the fresh properties of SCC paste and concrete represented by slump flow (flowability) and the flow rate were determined and discussed. The results indicated that the flow properties of SCC paste and concrete mixtures, at their optimized superplasticizer dosages, were affected by the binder content of local NP and the total volume fraction of SCC paste.

Keywords: Binder, fresh properties, natural pozzolan, paste, SCC.

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Authors: Baha Vural Kök, Mehmet Yilmaz, Mustafa Akpolat, Cihat Sav

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Various types of additives are used frequently in order to improve the rheological and mechanical properties of bituminous mixtures. Small devices instead of full scale machines are used for bitumen modification in the laboratory. These laboratory scale devices vary in terms of their properties such as mixing rate, mixing blade and the amount of binder. In this study, the effect of mixing rate and time during the bitumen modification processes on conventional and rheological properties of pure and crumb rubber modified binder were investigated. Penetration, softening point, rotational viscosity (RV) and dynamic shear rheometer (DSR) tests were applied to pure and CR modified bitumen. It was concluded that the penetration and softening point test did not show the efficiency of CR obtained by different mixing conditions. Besides, oxidation that occurred during the preparation processes plays a great part in the improvement effects of the modified binder.

Keywords: Bitumen, crumb rubber, modification, rheological properties.

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Authors: G.K.Panda, S.S.Rout

Abstract:

The balancing numbers are natural numbers n satisfying the Diophantine equation 1 + 2 + 3 + · · · + (n - 1) = (n + 1) + (n + 2) + · · · + (n + r); r is the balancer corresponding to the balancing number n.The nth balancing number is denoted by Bn and the sequence {Bn}1 n=1 satisfies the recurrence relation Bn+1 = 6Bn-Bn-1. The balancing numbers posses some curious properties, some like Fibonacci numbers and some others are more interesting. This paper is a study of recurrent sequence {xn}1 n=1 satisfying the recurrence relation xn+1 = Axn - Bxn-1 and possessing some curious properties like the balancing numbers.

Keywords: Recurrent sequences, Balancing numbers, Lucas balancing numbers, Binet form.

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