Search results for: Black Aluminum Oxide

Authors: Hilmi Yazici, Mehmet Akcay, Mustafa Golcu, Mehmet F. Koseoglu, Yakup Sekmen

Abstract:

Energy consumption rate during the cooling process of industrial glass tempering process is considerably high. In this experimental study the effect of dimensionless jet to jet distance (S/D) and jet to plate distance (H/D) on the cooling time have been investigated. In the experiments 4 mm thick glass samples have been used. Cooling unit consists of 16 mutually placed seamless aluminum nozzles of 8 mm in diameter and 80 mm in length. Nozzles were in staggered arrangement. Experiments were conducted with circular jets for H/D values between 1 and 10, and for S/D values between 2 and 10. During the experiments Reynolds number has been kept constant at 30000. Experimental results showed that the longest cooling time with 87 seconds has been observed in the experiments for S/D=10 and H/D=10 values, while the shortest cooling time with 42.5 seconds has been measured in the experiments for S/D=2 and H/D=4 values.

Keywords: Glass tempering, cooling, Reynolds number, nozzle

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Authors: Moataz M. Naguib, Hatem Khater, A. Baith Mohamed

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MARS is a shared-key (symmetric) block cipher algorithm supporting 128-bit block size and a variable key size of between 128 and 448 bits. MARS has a several rounds of cryptographic core that is designed to take advantage of the powerful results for improving security/performance tradeoff over existing ciphers. In this work, a new function added to improve the ciphering process it is called, Meta-Morphic function. This function use XOR, Rotating, Inverting and No-Operation logical operations before and after encryption process. The aim of these operations is to improve MARS cipher process and makes a high confusion criterion for the Ciphertext.

Keywords: AES, MARS, Metamorphic, Cryptography, Block Cipher.

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Authors: S. Ghorbani, N. I. Polushin

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Vibration during machining process is crucial since it affects cutting tool, machine, and workpiece leading to a tool wear, tool breakage, and an unacceptable surface roughness. This paper applies a nonparametric statistical method, single decision tree (SDT), to identify factors affecting on vibration in machining process. Workpiece material (AISI 1045 Steel, AA2024 Aluminum alloy, A48-class30 Gray Cast Iron), cutting tool (conventional, cutting tool with holes in toolholder, cutting tool filled up with epoxy-granite), tool overhang (41-65 mm), spindle speed (630-1000 rpm), feed rate (0.05-0.075 mm/rev) and depth of cut (0.05-0.15 mm) were used as input variables, while vibration was the output parameter. It is concluded that workpiece material is the most important parameters for natural frequency followed by cutting tool and overhang.

Keywords: Cutting condition, vibration, natural frequency, decision tree, CART algorithm.

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Authors: I. Blazkova, A. Moulick, V. Milosavljevic, P. Kopel, M. Vaculovicova, V. Adam, R. Kizek

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Doxorubicin (DOX) is an anthracycline drug used to treat many cancer diseases. Similarly to other cytostatic drugs, DOX has serious side effects; the biggest obstacle is the cardiotoxicity. With the aim of lowering the negative side effects and to target the DOX into the tumor tissue, the different nanoparticles (NPs) are studied. The aim of this work was to synthetized different NPs and conjugated them with DOX and determine the binding capacity of the NPs. For this experiment, carbon nanotubes (CNTs), graphene oxide (GO), fullerene (FUL) and liposomes (LIP) were used. The highest binding capacity was observed in GO (85%). Subsequently the toxicity of NPs and NPs-DOX conjugates was analyzed in in vivo system (chicken embryos). Some NPs (GO) can increase the toxicity of DOX, whereas other NPs (LIP, CNTs) decrease DOX toxicity.

Keywords: Chicken embryos, Doxorubicin, Nanotransporters, Toxicity

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Authors: A. A. Shafie, M. F. Alias, M. H. Ali

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The main objective of this project is to build an autonomous microcontroller-based mobile robot for a local robot soccer competition. The black competition field is equipped with white lines to serve as the guidance path for competing robots. Two prototypes of soccer robot embedded with the Basic Stamp II microcontroller have been developed. Two servo motors are used as the drive train for the first prototype whereas the second prototype uses two DC motors as its drive train. To sense the lines, lightdependent resistors (LDRs) supply the analog inputs for the microcontroller. The performances of both prototypes are evaluated. The DC motor-driven robot has produced better trajectory control over the one using servo motors and has brought the team into the final round.

Keywords: Soccer robot, Obstacle detection, Differential drive, Line following.

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Authors: E. Barkanov, E. Skukis, M. Wesolowski, A. Chate

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New nondestructive technique, namely an inverse technique based on vibration tests, to characterize nonlinear mechanical properties of adhesive layers in sandwich composites is developed. An adhesive layer is described as a viscoelastic isotropic material with storage and loss moduli which are both frequency dependent values in wide frequency range. An optimization based on the planning of experiments and response surface technique to minimize the error functional is applied to decrease considerably the computational expenses. The developed identification technique has been tested on aluminum panels and successfully applied to characterize viscoelastic material properties of 3M damping polymer ISD-112 used as a core material in sandwich panels.

Keywords: Adhesive layer, finite element method, inverse technique, sandwich panel, vibration test, viscoelastic material properties.

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Authors: Ali Safdari-Vaighani

Abstract:

Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: Radial basis function, basket option, jump diffusion, RBF-PUM.

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Authors: P. Prema, B. Ramadoss

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Testing is an activity that is required both in the development and maintenance of the software development life cycle in which Integration Testing is an important activity. Integration testing is based on the specification and functionality of the software and thus could be called black-box testing technique. The purpose of integration testing is testing integration between software components. In function or system testing, the concern is with overall behavior and whether the software meets its functional specifications or performance characteristics or how well the software and hardware work together. This explains the importance and necessity of IT for which the emphasis is on interactions between modules and their interfaces. Software errors should be discovered early during IT to reduce the costs of correction. This paper introduces a new type of integration error, presenting an overview of Integration Testing techniques with comparison of each technique and also identifying which technique detects what type of error.

Keywords: Integration Error, Integration Error Types, Integration Testing Techniques, Software Testing

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Authors: Muazzam A. Khan, Ghalib A. Shah, Muhammad Sher

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Wireless sensor network is formed with the combination of sensor nodes and sink nodes. Recently Wireless sensor network has attracted attention of the research community. The main application of wireless sensor network is security from different attacks both for mass public and military. However securing these networks, by itself is a critical issue due to many constraints like limited energy, computational power and lower memory. Researchers working in this area have proposed a number of security techniques for this purpose. Still, more work needs to be done.In this paper we provide a detailed discussion on security in wireless sensor networks. This paper will help to identify different obstacles and requirements for security of wireless sensor networks as well as highlight weaknesses of existing techniques.

Keywords: Wireless senor networks (WSNs), security, denial of service, black hole, cryptography, stenography.

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Authors: A. Badarudin, C. S. Oon, S. N. Kazi, N. Nik-Ghazali, Y. J. Lee, W. T. Chong

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An experimental and simulation flight test has been carried out to evaluate the longitudinal gliding characteristics of a lifting body with blunted half-cone geometry. The novelty here is the lifting body's pitch control mechanism, which consists of a pair of leading-edge rotating cylinders. Flight simulation uses aerodynamic data from computational fluid dynamics supported by wind-tunnel test. Flight test consists of releasing an aluminum lifting body model from a moving vehicle at the appropriate wind speed while measuring the lifting body's variation of altitude against time of flight. Results show that leading-edge rotating cylinder is able to give small amounts of improvement to the longitudinal stability and pitch control to the lifting body.

Keywords: Lifting body, pitch control, aerodynamic, rotating cylinder.

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Authors: Mubina Nazmeen, Iram Rubab

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Formal Specification languages are being widely used for system specification and testing. Highly critical systems such as real time systems, avionics, and medical systems are represented using Formal specification languages. Formal specifications based testing is mostly performed using black box testing approaches thus testing only the set of inputs and outputs of the system. The formal specification language such as VDMµ can be used for white box testing as they provide enough constructs as any other high level programming language. In this work, we perform data and control flow analysis of VDMµ class specifications. The proposed work is discussed with an example of SavingAccount.

Keywords: VDM-SL, VDMµ, data flow graph, control flowgraph, testing, formal specification.

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Authors: Abd. Rahim Yacob, Mohd Khairul Asyraf Amat Mustajab, Nurshaira Haifa Suhaimi

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This study shows the effect of carbon towards molybdenum carbide alloy when exposed to Microwave. This technique is also known as Microwave Induced Alloying (MIA) for the preparation of molybdenum carbide. In this study ammonium heptamolybdate solution and carbon black powder were heterogeneously mixed and exposed to microwave irradiation for 2 minutes. The effect on amount of carbon towards the produced alloy on morphological and oxidation states changes during microwave is presented. In this experiment, it is expected carbon act as a reducing agent with the ratio 2:7 molybdenum to carbon as the optimum for the production of molybdenum carbide alloy. All the morphological transformations and changes in this experiment were followed and characterized using X-Ray Diffraction and FESEM.

Keywords: Carbon, molybdenum carbide, microwave induced alloying.

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Authors: N. Bahiyah Baba, W. Waugh, A.M. Davidson

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The paper discusses optimising work on a method of processing ceramic / metal composite coatings for various applications and is based on preliminary work on processing anodes for solid oxide fuel cells (SOFCs). The composite coating is manufactured by the electroless co-deposition of nickel and yttria stabilised zirconia (YSZ) simultaneously on to a ceramic substrate. The effect on coating characteristics of substrate surface treatments and electroless nickel bath parameters such as pH and agitation methods are also investigated. Characterisation of the resulting deposit by scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDXA) is also discussed.

Keywords: Electroless deposition, nickel, YSZ, composite

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Authors: E. M. Anawa, A. G. Olabi

Abstract:

The dissimilar joint between aluminum/titanium alloys (Al 6082 and Ti G2) were successfully achieved by CO2 laser welding with a single pass and without filler material using the overlap joint design. Laser welding parameters ranges combinations were experimentally determined using Taguchi approach with the objective of producing welded joint with acceptable welding profile and high quality of mechanical properties. In this study a joining of dissimilar Al 6082 / Ti G2 was resulted in three distinct regions fusion area in the weldment. These regions are studied in terms of its microstructural characteristics and microhardness which are directly affecting the welding quality. The weld metal was mainly composed of martensite alpha prime. In two different metals in the two different sides of joint HAZ, grain growth was detected. The microhardness of the joint distribution also has shown microhardness increasing in the HAZ of two base metals and a varying microhardness in fusion zone.

Keywords: Micro-hardness, Microstructure, laser welding, dissimilar jointed materials.

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Authors: K. L. Verma

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Analysis for the propagation of elastic waves in arbitrary anisotropic plates is investigated, commencing with a formal analysis of waves in a layered plate of an arbitrary anisotropic media, the dispersion relations of elastic waves are obtained by invoking continuity at the interface and boundary of conditions on the surfaces of layered plate. The obtained solutions can be used for material systems of higher symmetry such as monoclinic, orthotropic, transversely isotropic, cubic, and isotropic as it is contained implicitly in the analysis. The cases of free layered plate and layered half space are considered separately. Some special cases have also been deduced and discussed. Finally numerical solution of the frequency equations for an aluminum epoxy is carried out, and the dispersion curves for the few lower modes are presented. The results obtained theoretically have been verified numerically and illustrated graphically.

Keywords: Anisotropic, layered, dispersion, elastic waves, frequency equations.

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Authors: Lei Zhao, Yi Song, Tim Dunne, Jiaxiang (Jason) Ren, Wenhan Yue, Lei Yang, Li Wen, Yu Liu

Abstract:

Fasting dissolving magnesium (DM) alloy technology has contributed significantly to the “Shale Revolution” in oil and gas industry. This application requires DM downhole tools dissolving initially at a slow rate, rapidly accelerating to a high rate after certain period of operation time (typically 8 h to 2 days), a contradicting requirement that can hardly be addressed by traditional Mg alloying or processing itself. Premature disintegration has been broadly reported in downhole DM tool from field trials. To address this issue, “temporary” thin polymers of various formulations are currently coated onto DM surface to delay its initial dissolving. Due to conveying parts, harsh downhole condition, and high dissolving rate of the base material, the current delay coatings relying on pure polymers are found to perform well only at low temperature (typical < 100 ℃) and parts without sharp edges or corners, as severe geometries prevent high quality thin film coatings from forming effectively. In this study, a coating technology combining Plasma Electrolytic Oxide (PEO) coatings with advanced thin film deposition has been developed, which can delay DM complex parts (with sharp corners) in corrosive fluid at 150 ℃ for over 2 days. Synergistic effects between porous hard PEO coating and chemical inert elastic-polymer sealing leads to its delaying dissolution improvement, and strong chemical/physical bonding between these two layers has been found to play essential role. Microstructure of this advanced coating and compatibility between PEO and various polymer selections has been thoroughly investigated and a model is also proposed to explain its delaying performance. This study could not only benefit oil and gas industry to unplug their High Temperature High Pressure (HTHP) unconventional resources inaccessible before, but also potentially provides a technical route for other industries (e.g., bio-medical, automobile, aerospace) where primer anti-corrosive protection on light Mg alloy is highly demanded.

Keywords: Dissolvable magnesium, coating, plasma electrolytic oxide, sealer.

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Authors: Nandy Putra, Atrialdipa Duanovsah, Kristofer Haliansyah

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The aim of this research is to design a LHP with low thermal resistance and low condenser temperature. A Self-designed cascade LHP was tested by using biomaterial, sintered copper powder, and aluminum screen mesh as the wick. Using pure water as the working fluid for the first level of the LHP and 96% alcohol as the working fluid for the second level of LHP, the experiments were run with 10W, 20W, and 30W heat input. Experimental result shows that the usage of biomaterial as wick could reduce more temperature at evaporator than by using sintered copper powder and screen mesh up to 22.63% and 37.41% respectively. The lowest thermal resistance occurred during the usage of biomaterial as wick of heat pipe, which is 2.06 ^oC/W. The usage of cascade system could be applied to LHP to reduce the temperature at condenser and reduced thermal resistance up to 17.6%.

Keywords: Biomaterial, cascade loop heat pipe, screen mesh, sintered Cu.

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Authors: Farhad Kolahan, A. Hamid Khajavi

Abstract:

In this paper, a set of experimental data has been used to assess the influence of abrasive water jet (AWJ) process parameters in cutting 6063-T6 aluminum alloy. The process variables considered here include nozzle diameter, jet traverse rate, jet pressure and abrasive flow rate. The effects of these input parameters are studied on depth of cut (h); one of most important characteristics of AWJ. The Taguchi method and regression modeling are used in order to establish the relationships between input and output parameters. The adequacy of the model is evaluated using analysis of variance (ANOVA) technique. In the next stage, the proposed model is embedded into a Simulated Annealing (SA) algorithm to optimize the AWJ process parameters. The objective is to determine a suitable set of process parameters that can produce a desired depth of cut, considering the ranges of the process parameters. Computational results prove the effectiveness of the proposed model and optimization procedure.

Keywords: AWJ machining, Mathematical modeling, Simulated Annealing, Optimization

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Authors: Shady Sayed, Samer Wagdy, Ahmed Badawy, Moutaz M. Hegaze

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A symmetrical single mass resonant gyroscope is discussed in this paper. The symmetrical design allows matched resonant frequencies for driving and sensing vibration modes, which leads to amplifying the sensitivity of the gyroscope by the mechanical quality factor of the sense mode. It also achieves decoupled vibration modes for getting a low zero-rate output shift and more stable operation environment. A new suspension beams design is developed to get a symmetrical gyroscope with matched and decoupled modes at the same time. Finite element simulations are performed using ANSYS software package to verify the theoretical calculations. The gyroscope is fabricated from aluminum alloy 2024 substrate, the measured drive and sense resonant frequencies of the fabricated model are matched and equal 81.4 Hz with 5.7% error from the simulation results.

Keywords: Decoupled mode shapes, resonant sensor, symmetrical gyroscope, finite element simulation.

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Authors: S. Ghorbani, N. I. Polushin

Abstract:

The machinability of workpieces (AISI 1045 Steel, AA2024 aluminum alloy, A48-class30 gray cast iron) in turning operation has been carried out using different types of cutting tool (conventional, cutting tool with holes in toolholder and cutting tool filled up with composite material) under dry conditions on a turning machine at different stages of spindle speed (630-1000 rpm), feed rate (0.05-0.075 mm/rev), depth of cut (0.05-0.15 mm) and tool overhang (41-65 mm). Experimentation was performed as per Taguchi’s orthogonal array. To evaluate the relative importance of factors affecting surface roughness the single decision tree (SDT), Decision tree forest (DTF) and Group method of data handling (GMDH) were applied.

Keywords: Decision Tree Forest, GMDH, surface roughness, taguchi method, turning process.

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Authors: Mandana Amiri, Sima Nouhi, Yashar Azizan-Kalandaragh

Abstract:

Silver nanostructures have been successfully fabricated by using electrodeposition method onto indium-tin-oxide (ITO) substrate. Scanning electron microscopy (SEM), electrochemical impedance spectroscopy (EIS) and ultraviolet-visible spectroscopy (UV-Vis) techniques were employed for characterization of silver nanostructures. The results show nanostructures with different morphology and electrochemical properties can be obtained by various the deposition potentials and times. Electrochemical behavior of the nanostructures has been studied by using cyclic voltammetry. Silver nanostructures exhibits good electrocatalytic activity towards the reduction of H₂O₂. The presented electrode can be employed as sensing element for hydrogen peroxide.

Keywords: Electrochemical sensor, electrodeposition, hydrogen peroxide, silver nanostructures.

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Authors: J. H. Lv, W. Z. Wang, S.W. Liu

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The major concern in the aviation industry is the flight safety. Although great effort has been put onto the development of material and system reliability, the failure cases of fatal accidents still occur nowadays. Due to the complexity of the aviation system, and the interaction among the failure components, the failure analysis of the related equipment is a little difficult. This study focuses on surveying the failure cases in aviation, which are extracted from failure analysis journals, including Engineering Failure Analysis and Case studies in Engineering Failure Analysis, in order to obtain the failure sensitive factors or failure sensitive parts. The analytical results show that, among the failure cases, fatigue failure is the largest in number of occurrence. The most failed components are the disk, blade, landing gear, bearing, and fastener. The frequently failed materials consist of steel, aluminum alloy, superalloy, and titanium alloy. Therefore, in order to assure the safety in aviation, more attention should be paid to the fatigue failures.

Keywords: Aviation industry, failure analysis, failure component, fatigue.

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Authors: Abo-El-Nour N. Abd-Alla, Fatimah A. Alsheikh

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This study deals with the phenomena of reflection and transmission (refraction) of qSV-waves, for an incident of quasi transverse vertically waves, at a plane interface of two semi-infinite piezoelectric elastic media under the influence of the initial stresses. The relations governing the reflection and transmission coefficients of these reflected waves for various suitable boundary conditions are derived. We have shown analytically that reflection and transmission coefficients of (qP) and (qSV) waves depend upon the angle of incidence, the parameters of electric potential, the material constants of the medium as will as the initial stresses presented in the media. The numerical calculations of the reflection and transmission amplitude ratios for different values of initial stresses have been carried out by computer for different materials as examples and the results are given in the form of graphs. Finally, some of particular cases are considered.

Keywords: Quasi plane vertical transverse waves, reflection and transmission coefficients, initial stresses, PZT-5H Ceramic, Aluminum Nitride (AlN), Piezoelectricity

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Authors: Ali Eltayeb Muhsin, Mohamed Elhadi Elsari

Abstract:

The substrate heater designed for this investigation is a front side substrate heating system. It consists of 10 conventional tungsten halogen lamps and an aluminum reflector, total input electrical power of 5 kW. The substrate is heated by means of a radiation from conventional tungsten halogen lamps directed to the substrate through a glass window. This design allows easy replacement of the lamps and maintenance of the system. Within 2 to 6 minutes the substrate temperature reaches 500 to 830 C by varying the vertical distance between the glass window and the substrate holder. Moreover, the substrate temperature can be easily controlled by controlling the input power to the system. This design gives excellent opportunity to deposit many deferent films at deferent temperatures in the same deposition time. This substrate heater was successfully used for Chemical Vapor Deposition (CVD) of many thin films, such as Silicon, iron, etc.

Keywords: CVD, Halogen Lamp, Substrate Heater, Thin Films.

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Authors: S. Ghorbani, N. I. Polushin

Abstract:

In this study, an approach to identify factors affecting on surface roughness in a machining process is presented. This study is based on 81 data about surface roughness over a wide range of cutting tools (conventional, cutting tool with holes, cutting tool with composite material), workpiece materials (AISI 1045 Steel, AA2024 aluminum alloy, A48-class30 gray cast iron), spindle speed (630-1000 rpm), feed rate (0.05-0.075 mm/rev), depth of cut (0.05-0.15 mm) and tool overhang (41-65 mm). A single decision tree (SDT) analysis was done to identify factors for predicting a model of surface roughness, and the CART algorithm was employed for building and evaluating regression tree. Results show that a single decision tree is better than traditional regression models with higher rate and forecast accuracy and strong value.

Keywords: Cutting condition, surface roughness, decision tree, CART algorithm.

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Authors: Bharti Negi, Gargi Dey

Abstract:

This is the first report from India on a beverage resulting from alcoholic fermentation of the juice of sea buckthorn (Hippophae rhamnoides L) using lab isolated yeast strain. The health promoting potential of the product was evaluated based on its total phenolic content. The most important finding was that under the present fermentation condition, the total phenolic content of the wine product was 689 mg GAE/L. Investigation of influence of bottle ageing on the sea buckthorn wine showed a slight decrease in the phenolic content (534 m mg GAE/L). This study also includes the comparative analysis of the phenolic content of wines from other selected fruit juices like grape, apple and black currant. KeywordsAlcoholic fermentation, Hippophae, Total phenolic content, Wine

Keywords: Alcoholic fermentation, Hippophae, Total phenolic content, Wine

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Authors: Qing Fang, Lianxi Jia, Junfeng Song, Chao Li, Xianshu Luo, Mingbin Yu, Guoqiang Lo

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In this paper, we demonstrated a 1 × 4 silicon photonic cascaded arrayed waveguide grating, which is fabricated on a SOI wafer with a 220 nm top Si layer and a 2µm buried oxide layer. The measured on-chip transmission loss of this cascaded arrayed waveguide grating is ~ 5.6 dB, including the fiber-to-waveguide coupling loss. The adjacent crosstalk is 33.2 dB. Compared to the normal single silicon photonic arrayed waveguide grating with a crosstalk of ~ 12.5 dB, the crosstalk of this device has been dramatically increased.

Keywords: Silicon photonic, arrayed waveguide grating, high-crosstalk, cascaded structure.

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Authors: Porag Jyoti Ligira, Gargi Khanna

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The paper presents a simulation study of the electrical characteristic of Bulk Planar Junctionless Transistor (BPJLT) using spacer. The BPJLT is a transistor without any PN junctions in the vertical direction. It is a gate controlled variable resistor. The characteristics of BPJLT are analyzed by varying the oxide material under the gate. It can be shown from the simulation that an ideal subthreshold slope of ~60 mV/decade can be achieved by using highk dielectric. The effects of variation of spacer length and material on the electrical characteristic of BPJLT are also investigated in the paper. The ION / IOFF ratio improvement is of the order of 107 and the OFF current reduction of 10-4 is obtained by using gate dielectric of HfO2 instead of SiO2.

Keywords: BPJLT, double gate, high-k, spacer.

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Authors: Ünal Kızıl, Levent Genç, Sefa Aksu, Ahmet Tapınç

Abstract:

The Figaro AM-1 sensor module which employs TGS 2600 model gas sensor in air quality assessment was used. The system was coupled with a microprocessor that enables sensor module to create warning message via telephone. This low cot sensor system’s performance was compared with a DiagNose II commercial electronic nose system. Both air quality sensor and electronic nose system employ metal oxide chemical gas sensors. In the study experimental setup, data acquisition methods for electronic nose system, and performance of the low cost air quality system were evaluated and explained.

Keywords: Air quality, electronic nose, environmental quality, gas sensor.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

Abstract:

An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Option price valuation, Partial Differential Equations, Black-Scholes PDEs, Ito process.

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