Search results for: Matrix modification.

Authors: Kamaldeep Joshi, Rajkumar Yadav, Ashok Kumar Yadav

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Digital Watermarking is a procedure to prevent the unauthorized access and modification of personal data. It assures that the communication between two parties remains secure and their communication should be undetected. This paper investigates the consequence of the watermark strength of the grayscale image using a Discrete Wavelet Transformation (DWT) additive technique. In this method, the gray scale host image is divided into four sub bands: LL (Low-Low), HL (High-Low), LH (Low-High), HH (High-High) and the watermark is inserted in an LL sub band using DWT technique. As the image is divided into four sub bands, a watermark of equal size of the LL sub band has been inserted and the results are discussed. LL represents the average component of the host image which contains the maximum information of the image. Two kinds of experiments are performed. In the first, the same watermark is embedded in different images and in the later on the strength of the watermark varies by a factor of s i.e. (s=10, 20, 30, 40, 50) and it is inserted in the same image.

Keywords: Watermarking, discrete wavelet transform, scaling factor, steganography.

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Authors: Sri Hartati, 1Agus Harjoko, Brad G. Nickerson

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A prototype of an anomaly detection system was developed to automate process of recognizing an anomaly of roentgen image by utilizing fuzzy histogram hyperbolization image enhancement and back propagation artificial neural network. The system consists of image acquisition, pre-processor, feature extractor, response selector and output. Fuzzy Histogram Hyperbolization is chosen to improve the quality of the roentgen image. The fuzzy histogram hyperbolization steps consist of fuzzyfication, modification of values of membership functions and defuzzyfication. Image features are extracted after the the quality of the image is improved. The extracted image features are input to the artificial neural network for detecting anomaly. The number of nodes in the proposed ANN layers was made small. Experimental results indicate that the fuzzy histogram hyperbolization method can be used to improve the quality of the image. The system is capable to detect the anomaly in the roentgen image.

Keywords: Image processing, artificial neural network, anomaly detection.

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Authors: Fituri H Belgassem, Abdulbasit Nigrat, Seddeeq Ghrari

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In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

Keywords: Piece wise linear transforms, Fast transforms, Fast algorithms.

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Authors: Dina K. Badawy, Dina M. Ibrahim, Alsayed A. Sallam

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Distributed database is a collection of logically related databases that cooperate in a transparent manner. Query processing uses a communication network for transmitting data between sites. It refers to one of the challenges in the database world. The development of sophisticated query optimization technology is the reason for the commercial success of database systems, which complexity and cost increase with increasing number of relations in the query. Mariposa, query trading and query trading with processing task-trading strategies developed for autonomous distributed database systems, but they cause high optimization cost because of involvement of all nodes in generating an optimal plan. In this paper, we proposed a modification on the autonomous strategy K-QTPT that make the seller’s nodes with the lowest cost have gradually high priorities to reduce the optimization time. We implement our proposed strategy and present the results and analysis based on those results.

Keywords: Autonomous strategies, distributed database systems, high priority, query optimization.

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Authors: O. P. Vinocha , J. S. Bhullar , Manish Gupta

Abstract:

We considered repeated-root cyclic codes whose block length is divisible by the characteristic of the underlying field. Cyclic self dual codes are also the repeated root cyclic codes. It is known about the one-level squaring construction for binary repeated root cyclic codes. In this correspondence, we introduced of two level squaring construction for binary repeated root cyclic codes of length 2a b , a > 0, b is odd.

Keywords: Squaring Construction, generator matrix, selfdual codes, cyclic codes, coset codes, repeated root cycliccodes.

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Authors: Atman Jbari, Abdellah Adib, Driss Aboutajdine

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This paper addresses the problem of blind source separation (BSS). To recover original signals, from linear instantaneous mixtures, we propose a new contrast function based on the use of a double referenced system. Our approach assumes statistical independence sources. The reference vectors will be incrusted in the cumulant to evaluate the independence. The estimation of the separating matrix will be performed in two steps: whitening observations and joint diagonalization of a set of referenced cumulant matrices. Computer simulations are presented to demonstrate the effectiveness of the suggested approach.

Keywords: Blind source separation, Referenced Cumulant, Contrast, Joint Diagonalization.

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Authors: P.Kumar

Abstract:

Fluids are used for heat transfer in many engineering equipments. Water, ethylene glycol and propylene glycol are some of the common heat transfer fluids. Over the years, in an attempt to reduce the size of the equipment and/or efficiency of the process, various techniques have been employed to improve the heat transfer rate of these fluids. Surface modification, use of inserts and increased fluid velocity are some examples of heat transfer enhancement techniques. Addition of milli or micro sized particles to the heat transfer fluid is another way of improving heat transfer rate. Though this looks simple, this method has practical problems such as high pressure loss, clogging and erosion of the material of construction. These problems can be overcome by using nanofluids, which is a dispersion of nanosized particles in a base fluid. Nanoparticles increase the thermal conductivity of the base fluid manifold which in turn increases the heat transfer rate. In this work, the heat transfer enhancement using aluminium oxide nanofluid has been studied by computational fluid dynamic modeling of the nanofluid flow adopting the single phase approach.

Keywords: Heat transfer intensification, nanofluid, CFD, friction factor

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Authors: M. Abdou, M. K. Khalil

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The heat pipe is a thermal device which allows efficient transport of thermal energy. The experimental work of this research was split into two phases; phase 1 is the development of the facilities, material and test rig preparation. Phase 2 is the actual experiments and measurements of the thermal control mockup inside the modified vacuum chamber (MVC). Due to limited funds, the development on the thermal control subsystem was delayed and the experimental facilities such as suitable thermal vacuum chamber with space standard specifications were not available from the beginning of the research and had to be procured over a period of time. In all, these delays extended the project by one and a half year. Thermal control subsystem needs a special facility and equipment to be tested. The available vacuum chamber is not suitable for the thermal tests. Consequently, the modification of the chamber was a must. A vacuum chamber has been modified to be used as a Thermal Vaccum Chamber (TVC). A MVC is a vacuum chamber modified by using a stainless mirror box with perfect reflectability and the infrared lamp connected with the voltage regulator to vary the lamp intensity as it will be illustrated through the paper.

Keywords: Heat pipe, thermal control, thermal vacuum chamber, satellite.

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Authors: P. Meesuk, T. Kulworawanichpong, P. Pao-la-or

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This paper proposes a set of quasi-static mathematical model of magnetic fields caused by high voltage conductors of distribution transformer by using a set of second-order partial differential equation. The modification for complex magnetic field analysis and time-harmonic simulation are also utilized. In this research, transformers were study in both balanced and unbalanced loading conditions. Computer-based simulation utilizing the threedimensional finite element method (3-D FEM) is exploited as a tool for visualizing magnetic fields distribution volume a distribution transformer. Finite Element Method (FEM) is one among popular numerical methods that is able to handle problem complexity in various forms. At present, the FEM has been widely applied in most engineering fields. Even for problems of magnetic field distribution, the FEM is able to estimate solutions of Maxwell-s equations governing the power transmission systems. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Distribution Transformer, Magnetic Field, Load Unbalance, 3-D Finite Element Method (3-D FEM)

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Authors: H. Assaedi, F. U. A. Shaikh, I. M. Low

Abstract:

Geopolymer composites reinforced with flax fabrics and nanoclay are fabricated and studied for physical and mechanical properties using X-Ray Diffraction (XRD), Fourier Transform Infrared Spectroscopy (FTIR), and Scanning Electron Microscope (SEM). Nanoclay platelets at a weight of 1.0%, 2.0%, and 3.0% were added to geopolymer pastes. Nanoclay at 2.0 wt.% was found to improve density and decrease porosity while improving flexural strength and post-peak toughness. A microstructural analysis indicated that nanoclay behaves as filler and as an activator supporting geopolymeric reaction while producing a higher content geopolymer gel improving the microstructure of binders. The process enhances adhesion between the geopolymer matrix and flax fibres.

Keywords: Flax fibres, geopolymer, mechanical properties, nanoclay.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

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In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neutral networks, time-varying delays.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.

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Authors: Nileshkumar Vaishnav, Aditya Tatu

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An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: Graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing.

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Authors: Othman S. Alsheraida, Sherif El-Gamal

Abstract:

Fiber Reinforced Polymer (FRP) is a composite material with exceptional properties that are capable to replace conventional steel reinforcement in reinforced and pre-stressed concrete structures. However, the main obstacle for their wide use in pre-stressed concrete application is the anchorage system. Due to the weakness of FRP in the transverse direction, the pre-stressing capacity of FRP bars are limited. This paper investigates the modification of the conventional wedge anchorage system to be used for stressing of FRP bars in pre-stressed applications. Epoxy adhesive material with glass FRP (GFRP) bars and conventional steel wedge were used in this paper. The GFRP bars are encased with epoxy at the anchor zone and the wedge system was used in pull-out test. The results showed a loading capacity of 47.6 kN which is 69% of the bar ultimate capacity. Additionally, nylon wedge was made with the same dimensions of the steel wedge and tested for GFRP bars without epoxy layer. The nylon wedge showed a loading capacity of 19.7 kN which is only 28.5% of the ultimate bar capacity.

Keywords: Anchorage, concrete, epoxy, FRP, pre-stressed.

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Authors: Tayeb Lardjane, Rabah Messaci

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We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.

Keywords: Steady state solution, matrix formulation, convex set, shortest queue, linear programming.

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Authors: Samra Isadounene, Amar Boukerrou, Dalila Hammiche

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In this work, the composites were prepared with poly(lactic acid) (PLA) and olive husk flour (OHF) with different percentages (10, 20 and 30%) using extrusion method followed by injection molding. The morphological, mechanical properties and thermal behavior of composites were investigated. Tensile strength and elongation at break of composites showed a decreasing trend with increasing fiber content. On the other hand, Young modulus and storage modulus were increased. The addition of OHF resulted in a decrease in thermal stability of composites. The presence of OHF led to an increase in percentage of crystallinity (Xc) of PLA matrix.

Keywords: Biopolymers, composites, mechanical properties, poly(lactic acid).

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Authors: Aman Patidar, Dipankar Sarkar, Manish Pal

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Due to rapid development, increase in the traffic load, higher traffic volume and seasonal variation in temperature, asphalt pavement shows distresses like rutting, fatigue and thermal cracking etc. because of this pavement fails during service life so that bitumen needs to be modified with some additive. In this study VG30 grade bitumen modify with addition of nanosilica with 1% to 5% (increment of 1%) by weight of bitumen. Hot mix asphalt (HMA) have higher mixing, laying and rolling temperatures which leads to higher consumption of fuel. To address this issue, a nano material named ZycoTherm which is chemical warm mix asphalt (WMA) additive is added to bitumen. Nanosilica modification (NSMB) results in the increase in stability compared to unmodified bitumen (UMB). WMA modified mix shows slightly higher stability than UMB and NSMB in a lower bitumen content. The Retained stability and tensile strength ratio (TSR) is more than 75% and 80% respectively for both mixes. Nanosilica with WMA has more resistant to temperature susceptibility, moisture susceptibility and short term aging than NSMB.

Keywords: HMA, nanosilica, NSMB, temperature, TSR, UMB, WMA.

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Authors: P.-W. Tsai, J.-W. Chen, C.-W. Chen, C.-Y. Chen

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In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: Half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method.

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Authors: I. Ioannou, I. M. Gitman

Abstract:

This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.

Keywords: Effective properties, representative volume element, short fiber reinforced composites.

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Authors: Abeer A. M., Allawi A. A., Chai H. K.

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A new analytical method to predict the torsional capacity and behavior of R.C multi-cell box girders strengthened with carbon fiber reinforced polymer (CFRP) sheets is presented. Modification was done on the Softened Truss Model (STM) in the proposed method; the concrete torsional problem is solved by combining the equilibrium conditions, compatibility conditions and constitutive laws of materials by taking into account the confinement of concrete with CFRP sheets. A specific algorithm is developed to predict the torsional behavior of reinforced concrete multi-cell box girders with or without strengthening by CFRP sheets. Applications of the developed method as an assessment tool to strengthened multicell box girders with CFRP and first analytical example that demonstrate the contribution of the CFRP materials on the torsional response is also included.

Keywords: Carbon fiber reinforced polymer, Concrete torsion, Modified Softened Truss Model, Multi-Cell box girder.

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Authors: Udaya Kumar Reddy K. R, K. Viswanathan Iyer

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Given a simple connected unweighted undirected graph G = (V (G), E(G)) with |V (G)| = n and |E(G)| = m, we present a new algorithm for the all-pairs shortest-path (APSP) problem. The running time of our algorithm is in O(n2 log n). This bound is an improvement over previous best known O(n2.376) time bound of Raimund Seidel (1995) for general graphs. The algorithm presented does not rely on fast matrix multiplication. Our algorithm with slight modifications, enables us to compute the APSP problem for unweighted directed graph in time O(n2 log n), improving a previous best known O(n2.575) time bound of Uri Zwick (2002).

Keywords: Distance in graphs, Dynamic programming, Graphalgorithms, Shortest paths.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

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In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

Keywords: Stability, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.

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Authors: Kavita Khairnar, Shikha Nema

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DS-CDMA system is well known wireless technology. This system suffers from MAI (Multiple Access Interference) caused by Direct Sequence users. Multi-User Detection schemes were introduced to detect the users- data in presence of MAI. This paper focuses on linear multi-user detection schemes used for data demodulation. Simulation results depict the performance of three detectors viz-conventional detector, Decorrelating detector and Subspace MMSE (Minimum Mean Square Error) detector. It is seen that the performance of these detectors depends on the number of paths and the length of Gold code used.

Keywords: Cross Correlation Matrix, MAI, Multi-UserDetection, Multipath Effect.

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Authors: Uma Thanganathan

Abstract:

The hybrid membranes containing inorganic materials in polymer matrix are identified as a remarkable family of proton conducting hybrid electrolytes. In this work, the proton conducting inorganic/organic hybrid membranes for proton exchange membrane fuel cells (PEMFCs) were prepared using polyvinyl alcohol (PVA), tetraethoxyorthosilane (TEOS) and heteropolyacid (HPA). The synthesized hybrid membranes were characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction spectroscopy (XRD), Scanning electron microscopy (SEM) and Thermogravimetry analysis (TGA). The effects of heteropolyacid incorporation on membrane properties, including morphology and thermal stability were extensively investigated.

Keywords: PEMFC, Hybrid membrane, FTIR, TGA, Phosphomolybdic acid

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Authors: Priyankar Pratim Deka, Sutanu Samanta

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This paper describes the development of new class of epoxy based rice husk filled jute reinforced composites. Rice husk flour is added in 0%, 1%, 3%, 5% by weight. Epoxy resin and triethylenetetramine (T.E.T.A) is used as matrix and hardener respectively. It investigates the mechanical properties of the composites and a comparison is done for monolithic jute composite and the filled ones. The specimens are prepared according to the ASTM standards and experimentation is carried out using INSTRON 8801. The result shows that with the increase of filler percentage the tensile properties increases but compressive and flexural properties decreases.

Keywords: Jute, mechanical characterization, natural fiber, rice husk.

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Authors: Ko-Shao Chen, Yun Tsao, Chia-Hsuan Tsen, Chien-Chung Chen, Shu-Chuan Liao

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Electrospun microtube array membranes (MTAMs) made of PLLA (poly-L-lactic acid) have wide potential applications in tissue engineering. However, their surface hydrophobicity and poor biocompatability have limited their further usage. In this study, the surface of PLLA MTAMs were made hydrophilic by introducing extra functional groups, such as peroxide, via an acetic acid plasma (AAP). UV-graft polymerization of acrylic acid (G-AAc) was then used to produce carboxyl group on MTAMs surface, which bonded covalently with chitosan through EDC / NHS crosslinking agents. To evaluate the effects of the surface modification on PLLA MTAMs, water contact angle (WCA) measurement and cell compatibility tests were carried out. We found that AAP treated electrospun PLLA MTAMs grafted with AAc and, finally, with chitosan immobilized via crosslinking agent, exhibited improved hydrophilic and cell compatibility.

Keywords: Plasma, EDC/NHS, UV grafting, chitosan, microtube array membrane.

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Authors: Sajjad H. Kasanagh, Perviz Ahmedzade, Alexander Fainleib, Taylan Gunay

Abstract:

Modification of asphalt is a fundamental method around the world mainly on the purpose of providing more durable pavements which lead to diminish repairing cost during the lifetime of highways. Various polymers such as styrene-butadiene-styrene (SBS) and ethylene vinyl acetate (EVA) make up the greater parts of the all-over asphalt modifiers generally providing better physical properties of asphalt by decreasing temperature dependency which eventually diminishes permanent deformation on highways such as rutting. However, some waste and low-cost materials such as recycled plastics and ground rubber tire have been attempted to utilize in asphalt as modifier instead of manufactured polymer modifiers due to decreasing the eventual highway cost. On the other hand, the usage of recycled plastics has become a worldwide requirement and awareness in order to decrease the pollution made by waste plastics. Hence, finding an area in which recycling plastics could be utilized has been targeted by many research teams so as to reduce polymer manufacturing and plastic pollution. To this end, in this paper, thermoplastic dynamic vulcanizate (TDV) obtained from recycled post-consumer polyethylene and ground tire rubber (GTR) were used to provide an efficient modifier for asphalt which decreases the production cost as well and finally might provide an ecological solution by decreasing polymer disposal problems. TDV was synthesized by the chemists in the research group by means of the abovementioned components that are considered as compatible physical characteristic of asphalt materials. TDV modified asphalt samples having different rate of proportions of 3, 4, 5, 6, 7 wt.% TDV modifier were prepared. Conventional tests, such as penetration, softening point and roll thin film oven (RTFO) tests were performed to obtain fundamental physical and aging properties of the base and modified binders. The high temperature performance grade (PG) of binders was determined by Superpave tests conducted on original and aged binders. The multiple stress creep and recovery (MSCR) test which is relatively up-to-date method for classifying asphalts taking account of their elasticity abilities was carried out to evaluate PG plus grades of binders. The results obtained from performance grading, and MSCR tests were also evaluated together so as to make a comparison between the methods both aiming to determine rheological parameters of asphalt. The test results revealed that TDV modification leads to a decrease in penetration, an increase in softening point, which proves an increasing stiffness of asphalt. DSR results indicate an improvement in PG for modified binders compared to base asphalt. On the other hand, MSCR results that are compatible with DSR results also indicate an enhancement on rheological properties of asphalt. However, according to the results, the improvement is not as distinct as observed in DSR results since elastic properties are fundamental in MSCR. At the end of the testing program, it can be concluded that TDV can be used as modifier which provides better rheological properties for asphalt and might diminish plastic waste pollution since the material is 100% recycled.

Keywords: Asphalt, ground tire rubber, recycled polymer, thermoplastic dynamic vulcanized.

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Authors: Abdelmalek Fermas, Adel Belouchrani, Otmane Ait Mohamed

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In Blind Source Separation (BSS) processing, taking advantage of scaling factor indetermination and based on the floatingpoint representation, we propose a scaling technique applied to the separation matrix, to avoid the saturation or the weakness in the recovered source signals. This technique performs an Automatic Gain Control (AGC) in an on-line BSS environment. We demonstrate the effectiveness of this technique by using the implementation of a division free BSS algorithm with two input, two output. This technique is computationally cheaper and efficient for a hardware implementation.

Keywords: Automatic Gain Control, Blind Source Separation, Floating-Point Representation, FPGA Implementation.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

In this paper, delay-dependent stability analysis for neutral type neural networks with uncertain paramters and time-varying delay is studied. By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments, a novel sufficient condition is established to guarantee the globally asymptotically stability of the considered system. Finally, a numerical example is provided to illustrate the usefulness of the proposed main results.

Keywords: Neutral type neural networks, Time-varying delay, Stability, Linear matrix inequality(LMI).

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Authors: Mikhail Gritskevich, Sebastian Hohenstein

Abstract:

The paper presents the results of a detailed assessment of several modern Reynolds Averaged Navier-Stokes (RANS) turbulence models for prediction of C3X vane film cooling at various injection regimes. Three models are considered, namely the Shear Stress Transport (SST) model, the modification of the SST model accounting for the streamlines curvature (SST-CC), and the Explicit Algebraic Reynolds Stress Model (EARSM). It is shown that all the considered models face with a problem in prediction of the adiabatic effectiveness in the vicinity of the cooling holes; however, accounting for the Reynolds stress anisotropy within the EARSM model noticeably increases the solution accuracy. On the other hand, further downstream all the models provide a reasonable agreement with the experimental data for the adiabatic effectiveness and among the considered models the most accurate results are obtained with the use EARMS.

Keywords: Discrete holes film cooling, Reynolds Averaged Navier-Stokes, Reynolds stress tensor anisotropy, turbulent heat transfer.

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