Search results for: Nadia Masood Khan

Authors: Md. Sharif Imam Ibne Amir, Mohammad Masud Kamal khan, Mohammad Golam Rasul, Raj H Sharma, Fatema Akram

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Future flood can be predicted using the probable maximum flood (PMF). PMF is calculated using the historical discharge or rainfall data considering the other climatic parameters remaining stationary. However climate is changing globally and the key climatic variables are temperature, evaporation, rainfall and sea level rise are likely to change. To develop scenarios to a basin or catchment scale these important climatic variables should be considered. Nowadays scenario based on climatic variables is more suitable than PMF. Six scenarios were developed for a large Fitzroy basin and presented in this paper.

Keywords: Climate change, rainfall, potential evaporation, scenario, sea level rise (SLR), sub-catchment.

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Authors: Attiya Mahmood, Syed Ali Abbas, Shoab A. Khan

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Streaming Applications usually run in parallel or in series that incrementally transform a stream of input data. It poses a design challenge to break such an application into distinguishable blocks and then to map them into independent hardware processing elements. For this, there is required a generic controller that automatically maps such a stream of data into independent processing elements without any dependencies and manual considerations. In this paper, Kahn Process Networks (KPN) for such streaming applications is designed and developed that will be mapped on MPSoC. This is designed in such a way that there is a generic Cbased compiler that will take the mapping specifications as an input from the user and then it will automate these design constraints and automatically generate the synthesized RTL optimized code for specified application.

Keywords: KPN, DFG, FPGA

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Authors: Khaled M. Khan, Armstrong Nhlabatsi

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This article attempts to analyse behavioural traits of lone-wolves who struck and killed innocents in six different attacks in Europe in last nine months. The main objective of this study is to develop a profiling template in order to capture commonality of characteristics of these attackers. This study tries to understand the homogeneity of lone-wolves in terms of their social background and state of mind. The commonality among them can possibly be used to build a profiling template that could help detecting vulnerable persons who are prone to be self-radicalised or radicalised by someone else. The result of this study provides us an understanding of their commonality in terms of their state of mind and social characteristics.

Keywords: Behavioral pattern, terrorism, profiling, commonality.

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Authors: Muhammad Salam, Nasir Rashid, Shah Khalid, Muhammad Raees Khan

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In this paper a modified version NXM of traditional 5X5 playfair cipher is introduced which enable the user to encrypt message of any Natural language by taking appropriate size of the matrix depending upon the size of the natural language. 5X5 matrix has the capability of storing only 26 characters of English language and unable to store characters of any language having more than 26 characters. To overcome this limitation NXM matrix is introduced which solve this limitation. In this paper a special case of Urdu language is discussed. Where # is used for completing odd pair and * is used for repeating letters.

Keywords: cryptography, decryption, encryption, playfair cipher, traditional cipher.

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Authors: Rana Khalid Naeem, Asif Mansoor, Waseem Ahmed Khan, Aurangzaib

Abstract:

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating  that the flow equations possess an infinite set of solutions. 

Keywords: Exact solutions, Fluid of variable viscosity, Navier-Stokes equations, Steady plane flows

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Authors: H. Ali, K. Hameed, N. Khan

Abstract:

In DMVC, we have more than one options of sources available for construction of side information. The newer techniques make use of both the techniques simultaneously by constructing a bitmask that determines the source of every block or pixel of the side information. A lot of computation is done to determine each bit in the bitmask. In this paper, we have tried to define areas that can only be well predicted by temporal interpolation and not by multiview interpolation or synthesis. We predict that all such areas that are not covered by two cameras cannot be appropriately predicted by multiview synthesis and if we can identify such areas in the first place, we don-t need to go through the script of computations for all the pixels that lie in those areas. Moreover, this paper also defines a technique based on KLT to mark the above mentioned areas before any other processing is done on the side view.

Keywords: Side Information, Distributed Multiview Video Coding, Fusion, Early Decision.

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Authors: Imran Usman, Asifullah Khan, Rafiullah Chamlawi, Abdul Majid

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Information hiding for authenticating and verifying the content integrity of the multimedia has been exploited extensively in the last decade. We propose the idea of using genetic algorithm and non-deterministic dependence by involving the un-watermarkable coefficients for digital image authentication. Genetic algorithm is used to intelligently select coefficients for watermarking in a DCT based image authentication scheme, which implicitly watermark all the un-watermarkable coefficients also, in order to thwart different attacks. Experimental results show that such intelligent selection results in improvement of imperceptibility of the watermarked image, and implicit watermarking of all the coefficients improves security against attacks such as cover-up, vector quantization and transplantation.

Keywords: Digital watermarking, fragile watermarking, geneticalgorithm, Image authentication.

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Authors: Nisar Ahmed Memon, Anwar Majid Mirza, S.A.M. Gilani

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Segmentation is an important step in medical image analysis and classification for radiological evaluation or computer aided diagnosis. This paper presents the problem of inaccurate lung segmentation as observed in algorithms presented by researchers working in the area of medical image analysis. The different lung segmentation techniques have been tested using the dataset of 19 patients consisting of a total of 917 images. We obtained datasets of 11 patients from Ackron University, USA and of 8 patients from AGA Khan Medical University, Pakistan. After testing the algorithms against datasets, the deficiencies of each algorithm have been highlighted.

Keywords: Computer Aided Diagnosis (CAD), MathematicalMorphology, Medical Image Analysis, Region Growing, Segmentation, Thresholding,

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Authors: Shehzad Ashraf Ch., Aftab Ahmed Khan, Zahid Mehmood, Muhammad Ahsan Habib, Qasim Mehmood

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Energy efficiency is the key requirement in wireless sensor network as sensors are small, cheap and are deployed in very large number in a large geographical area, so there is no question of replacing the batteries of the sensors once deployed. Different ways can be used for efficient energy transmission including Multi-Hop algorithms, collaborative communication, cooperativecommunication, Beam- forming, routing algorithm, phase, frequency and time synchronization. The paper reviews the need for time synchronization and proposed a BFS based synchronization algorithm to achieve energy efficiency. The efficiency of our protocol has been tested and verified by simulation

Keywords: time synchronization, sensor networks, energy efficiency, breadth first search

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Authors: Eklas Hossain, Sheroz Khan, Ahad Ali

Abstract:

Power line communications may be used as a data communication channel in public and indoor distribution networks so that it does not require the installing of new cables. Industrial low voltage distribution network may be utilized for data transfer required by the on-line condition monitoring of electric motors. This paper presents a pilot distribution network for modeling low voltage power line as data transfer channel. The signal attenuation in communication channels in the pilot environment is presented and the analysis is done by varying the corresponding parameters for the signal attenuation.

Keywords: Data communication, indoor distribution networks, low voltage, power line.

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Authors: D.K. Rao, M.G.M. Khan, K.G. Reddy

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The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries(OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy isskewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB isformulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: Stratified sampling, Optimum strata boundaries, Optimum sample size, Pareto distribution, Mathematical programming problem, Dynamic programming technique.

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Authors: Zaheer Ahmad, Jehanzeb Khan Orakzai, Inam Shamsher, Awais Adnan

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This paper discusses the Urdu script characteristics, Urdu Nastaleeq and a simple but a novel and robust technique to recognize the printed Urdu script without a lexicon. Urdu being a family of Arabic script is cursive and complex script in its nature, the main complexity of Urdu compound/connected text is not its connections but the forms/shapes the characters change when it is placed at initial, middle or at the end of a word. The characters recognition technique presented here is using the inherited complexity of Urdu script to solve the problem. A word is scanned and analyzed for the level of its complexity, the point where the level of complexity changes is marked for a character, segmented and feeded to Neural Networks. A prototype of the system has been tested on Urdu text and currently achieves 93.4% accuracy on the average.

Keywords: Cursive Script, OCR, Urdu.

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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: Suparat Niwitpong, Sa-aat Niwitpong

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In this paper we proposed the new confidence interval for the normal population mean with known coefficient of variation. In practice, this situation occurs normally in environment and agriculture sciences where we know the standard deviation is proportional to the mean. As a result, the coefficient of variation of is known. We propose the new confidence interval based on the recent work of Khan [3] and this new confidence interval will compare with our previous work, see, e.g. Niwitpong [5]. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. A numerical method will be used to assess the performance of these intervals based on their expected lengths.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation.

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Authors: Dong Hoon Lim

Abstract:

A series of microarray experiments produces observations of differential expression for thousands of genes across multiple conditions. Principal component analysis(PCA) has been widely used in multivariate data analysis to reduce the dimensionality of the data in order to simplify subsequent analysis and allow for summarization of the data in a parsimonious manner. PCA, which can be implemented via a singular value decomposition(SVD), is useful for analysis of microarray data. For application of PCA using SVD we use the DNA microarray data for the small round blue cell tumors(SRBCT) of childhood by Khan et al.(2001). To decide the number of components which account for sufficient amount of information we draw scree plot. Biplot, a graphic display associated with PCA, reveals important features that exhibit relationship between variables and also the relationship of variables with observations.

Keywords: Principal component analysis, singular value decomposition, microarray data, SRBCT

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Authors: Gomaa N. Abdel-Rahman, Nadia R. A. Nassar, Yehia A. Heikal, Mahmoud A. M. Abou-Donia, Mohamed B. M. Ahmed, Mohamed Fadel

Abstract:

Storage stability is the important factor of baker's yeast quality. Effect of the storage period (fifteen days) on storage sugars and cell viability of baker's yeast, produced from three S. cerevisiae strains (FC-620, FH-620, and FAT-12) as comparison with baker's yeast produced by S. cerevisae F-707 (original strain of baker's yeast factory) were investigated. Studied trehalose and glycogen content ranged from 10.19 to 14.79 % and from 10.05 to 10.69 % (d.w.), respectively before storage. The trehalose and glycogen content of all strains was decreased by increasing the storage period with no significant differences between the reduction rates of trehalose. Meanwhile, reduction rates of glycogen had significant differences between different strains, where the FH-620 and FC-620 strains had lowest rates as 18.12 and 20.70 %, respectively. Also, total viable cells and gassing power of all strains were decreased by increasing the storage period. FH-620 and FC-620 strains had the lowest values of reduction rates as an indicator of storage resistant. Where the reduction rates in total viable cells of FH-620 and FC-620 strains were 22.05 and 24.70%, respectively, while the reduction rates of gassing power were 20.90 and 24.30%, in the same order. On other hand, FAT-12 strain was more sensitive to storage as compared to original strain, where the reduction rates were 35.60 and 35.75%, respectively for total viable cells and gassing power.

Keywords: Baker’s yeast, trehalose, glycogen, gassing power.

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Authors: A. A. Khan, M. Naeem, S. Bashir, S. I. Shah

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In this paper we propose a Particle Swarm heuristic optimized Multi-Antenna (MA) system. Efficient MA systems detection is performed using a robust stochastic evolutionary computation algorithm based on movement and intelligence of swarms. This iterative particle swarm optimized (PSO) detector significantly reduces the computational complexity of conventional Maximum Likelihood (ML) detection technique. The simulation results achieved with this proposed MA-PSO detection algorithm show near optimal performance when compared with ML-MA receiver. The performance of proposed detector is convincingly better for higher order modulation schemes and large number of antennas where conventional ML detector becomes non-practical.

Keywords: Multi Antenna (MA), Multi-input Multi-output(MIMO), Particle Swarm Optimization (PSO), ML detection.

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Authors: Waseem Khan

Abstract:

In this paper a technique for increasing the convergence rate of fractionally spaced channel equalizer is proposed. Instead of symbol-spaced updating of the equalizer filter, a mechanism has been devised to update the filter at a higher rate. This ensures convergence of the equalizer filter at a higher rate and therefore less time-consuming. The proposed technique has been simulated and tested for two-ray modeled channels with various delay spreads. These channels include minimum-phase and nonminimum- phase channels. Simulation results suggest that that proposed technique outperforms the conventional technique of symbol-spaced updating of equalizer filter.

Keywords: Channel equalization, Fractionally-spaced equalizer

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Authors: Muhammad Murtaza Nasir, Safdar Abbas Zaidi, Kamran Khan

Abstract:

This work is carried out to evaluate the possibility of using to-be-wasted steel as reinforcement after welding together pieces of reinforcing steel bars, left over during construction activities. Tests were performed on a total of nine samples. These were made by welding pieces of reinforcing steel bars purchased from the local scrap steel market. The samples were tested in uniaxial tension using a universal testing machine (UTM). It was found that the failure of the welded bars is governed by the thickness of the weld. It is concluded that suitable design of the weld is essential for achieving the desired level of ductility/elongation of these bars, if they are to be used as conventional reinforcement in reinforced concrete members.

Keywords: Ductility/elongation, low cost housing, reinforced concrete, welding, welded reinforcement, wastage steel.

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Authors: Samee Ullah Khan, C. Ardil

Abstract:

We model the process of a data center as a multi- objective problem of mapping independent tasks onto a set of data center machines that simultaneously minimizes the energy consump¬tion and response time (makespan) subject to the constraints of deadlines and architectural requirements. A simple technique based on multi-objective goal programming is proposed that guarantees Pareto optimal solution with excellence in convergence process. The proposed technique also is compared with other traditional approach. The simulation results show that the proposed technique achieves superior performance compared to the min-min heuristics, and com¬petitive performance relative to the optimal solution implemented in UNDO for small-scale problems.

Keywords: Energy-efficient computing, distributed systems, multi-objective optimization.

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Authors: Vandna Jowaheer, Naushad A. Mamode Khan

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Com Poisson distribution is capable of modeling the count responses irrespective of their mean variance relation and the parameters of this distribution when fitted to a simple cross sectional data can be efficiently estimated using maximum likelihood (ML) method. In the regression setup, however, ML estimation of the parameters of the Com Poisson based generalized linear model is computationally intensive. In this paper, we propose to use quasilikelihood (QL) approach to estimate the effect of the covariates on the Com Poisson counts and investigate the performance of this method with respect to the ML method. QL estimates are consistent and almost as efficient as ML estimates. The simulation studies show that the efficiency loss in the estimation of all the parameters using QL approach as compared to ML approach is quite negligible, whereas QL approach is lesser involving than ML approach.

Keywords: Com Poisson, Cross-sectional, Maximum Likelihood, Quasi likelihood

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Authors: C. A. Gilkeson, C. J. Noakes, P. A. Sleigh, M. A. I. Khan, M. A. Camargo-Valero

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Understanding how airborne pathogens are transported through hospital wards is essential for determining the infection risk to patients and healthcare workers. This study utilizes Computational Fluid Dynamics (CFD) simulations to explore possible pathogen transport within a six-bed partitioned Nightingalestyle hospital ward. Grid independence of a ward model was addressed using the Grid Convergence Index (GCI) from solutions obtained using three fullystructured grids. Pathogens were simulated using source terms in conjunction with a scalar transport equation and a RANS turbulence model. Errors were found to be less than 4% in the calculation of air velocities but an average of 13% was seen in the scalar field. A parametric study of variations in the pathogen release point illustrated that its distribution is strongly influenced by the local velocity field and the degree of air mixing present.

Keywords: Natural, Ventilation, Pathogen, Transport

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Authors: Muhammad Sohail Khan, Rehan Ali Shah

Abstract:

The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l₁₀, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.

Keywords: Wire coating die, Corotational Maxwell model, optimal homotopy asymptotic method, optimal homotopy perturbation method.

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Authors: Asfar Ali Khan, Ekram Husain

Abstract:

Modern Society is strongly dependent on a reliable power supply. The availability of cheap and reliable supply of electrical energy is an indicator of societal welfare. Uninterrupted reliable operation of a modern power system depends to a great extent on reliable and satisfactory performance of insulators under different environmental conditions. This paper reports result of natural pollution tests that have been done at sites around city of Aligarh (India). Flashover voltage per insulation distance (FOVUID) of porcelain disc insulator for different pH values, ESDD has been recorded for proper correlation between electrical and chemical parameters. The pH of the contaminants has been suggested to be an effective pollution severity indicator and may be used as a diagnostic parameter for proper maintenance of porcelain insulators.

Keywords: Porcelain insulators, Flashover Voltage, pH value, Conductivity, ESDD.

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Authors: Md. Sohidul Islam, Ahmad Fartheen Khan

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In recent times, Non-Orthogonal Multiple Access (NOMA) has received significant attention as an upcoming candidate in the world of 5G systems. The main reason for getting NOMA in 5G is because of its capacity to provide services to many users who have the same time and frequency resources. It is best used as "multiple-input, multiple-output" (MIMO) technology. In this paper, we are going to investigate outage probability as a function of signal-to-noise ratio (SNR) and target rate user. These methods will be implemented using cooperative communication and fair power allocation, respectively.

Keywords: Non-orthogonal Multiple Access, Fair Power Allocation, Outage Probability, Target Rate User, Cooperative Communication, massive multiple input multiple output, MIMO, Successive Interference Cancellation.

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Authors: Mateen Abbas, Abdul Muqeet Khan, Muhammad Rafique Asi, Javed Akhtar

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Mycotoxin (aflatoxins) contamination of peanuts is a great concern for human health. A total of 72 samples of unripe, roasted, and salty peanuts were collected randomly from Pothohar plateau of Pakistan for the assessment of aflatoxin. Samples were dried, ground and extracted by acetonitrile (84%). The filtered extracts were cleaned up by MycoSep-226 and analyzed by high performance liquid chromatography with flourescence detector. Quantification limit of Aflatoxin was 1 μg/kg and 70% Recovery was observed in spiked samples in the range 1–10 μg/kg. The screening of mycotoxins indicated that aflatoxins were present in most of the samples being detected in 82%, in concentrations from 14.25 μg/kg to 98.80 μg/kg. Optimal conditions for mycotoxin production and fungal growth are frequently found in the crop fields as well as in store houses. Human exposure of such toxin can be controlled by pointed out such awareness and implemented the regulations.

Keywords: Aflatoxin, HPLC, Pakistan, Peanuts, Punjab

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Authors: Salwa Hagag Abdelaziz, Naglaa Fathy Youssef, Nadia Abdel Latif Hassan, Rasha Wesam Abdel Rahman

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Breast cancer is considered as a substantial health concern and practicing mammography screening [MS] is important in minimizing its related morbidity. So it is essential to have a better understanding of breast cancer screening behaviors of women and factors that influence utilization of them. The aim of this study is to identify the factors that are linked to MS behaviors among the Egyptian women. A cross-sectional descriptive design was carried out to provide a snapshot of the factors that are linked to MS behaviors. A convenience sample of 311 women was utilized and all eligible participants admitted to the Women Imaging Unit who are 40 years of age or above, coming for mammography assessment, not pregnant or breast feeding and who accepted to participate in the study were included. A structured questionnaire was developed by the researchers and contains three parts; Socio-demographic data; Motivating factors associated with MS; and association between MS and model of behavior change. The analyzed data indicated that most of the participated women (66.6%) belonged to the age group of 40- 49.A high proportion of participants (58.1%) of group having previous MS influenced by their neighbors to practice MS, whereas 32.7 % in group not having previous MS were influenced by family members which indicated significant differences (P <0.05). Doctors and media shown to be the least influence of others to practice MS. Women with intention to have a future mammogram had higher OR (1.404) for practicing MS compared with women with no intention. Further studies are needed to examine the relation between Transtheoretical Model [TTM] and practicing MS.

Keywords: Breast cancer, mammography, screening behaviors.

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Authors: Soukaina Motia, Nadia El Alami El Hassani, Alassane Diouf, Benachir Bouchikhi, Nezha El Bari

Abstract:

Parabens are the antimicrobial molecules largely used in cosmetic products as a preservative agent. Among them, the methylparaben (MP) is the most frequently used ingredient in cosmetic preparations. Nevertheless, their potential dangers led to the development of sensible and reliable methods for their determination in environmental samples. Firstly, a sensitive and selective molecular imprinted polymer (MIP) based on screen-printed gold electrode (Au-SPE), assembled on a polymeric layer of carboxylated poly(vinyl-chloride) (PVC-COOH), was developed. After the template removal, the obtained material was able to rebind MP and discriminate it among other interfering species such as glucose, sucrose, and citric acid. The behavior of molecular imprinted sensor was characterized by Cyclic Voltammetry (CV), Differential Pulse Voltammetry (DPV) and Electrochemical Impedance Spectroscopy (EIS) techniques. Then, the biosensor was found to have a linear detection range from 0.1 pg.mL^-1 to 1 ng.mL^-1 and a low limit of detection of 0.12 fg.mL^-1 and 5.18 pg.mL^-1 by DPV and EIS, respectively. For applications, this biosensor was employed to determine MP content in four wastewaters in Meknes city and two cosmetic products (shower gel and shampoo). The operational reproducibility and stability of this biosensor were also studied. Secondly, another MIP biosensor based on tungsten trioxide (WO₃) functionalized by gold nanoparticles (Au-NPs) assembled on a polymeric layer of PVC-COOH was developed. The main goal was to increase the sensitivity of the biosensor. The developed MIP biosensor was successfully applied for the MP determination in wastewater samples and cosmetic products.

Keywords: Cosmetic products, methylparaben, molecularly imprinted polymer, wastewater.

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Authors: Amir Rashid, M. Saleem Khan, Freeha Zafar

Abstract:

This work presents a new approach of securing a wireless network. The configuration is focused on securing & Protecting wireless network traffic for a small network such as a home or dorm room. The security Mechanism provided both authentication, allowing only known authorized users access to the wireless network, and encryption, preventing anyone from reading the wireless traffic. The mentioned solution utilizes the open source free S/WAN software which implements the Internet Protocol Security –IPSEC. In addition to wireless components, wireless NIC in PC and wireless access point needs a machine running Linux to act as security gateway. While the current configuration assumes that the wireless PC clients are running Linux, Windows XP/VISTA/7 based machines equipped with VPN software which will allow to interface with this configuration.

Keywords: Wireless network security, security network, authentication, encryption and internet protocol security.

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Authors: Muhammad Tahir, Muhammad H. Sayyad, Dil N. Khan, Fazal Wahab

Abstract:

Herein, the organic semiconductor methyl orange (MO), is investigated for the first time for its electronic applications. For this purpose, Al/MO/n-Si heterojunction is fabricated through economical cheap and simple “drop casting” technique. The currentvoltage (I-V) measurements of the device are made at room temperature under dark conditions. The I-V characteristics of Al/MO/n-Si junction exhibits asymmetrical and rectifying behavior that confirms the formation of diode. The diode parameters such as rectification ratio (RR), turn on voltage (Vturn on), reverse saturation current (I0), ideality factor (n), barrier height ( b f ), series resistance (Rs) and shunt resistance (Rsh) are determined from I-V curves using Schottky equations. These values of these parameters are also extracted and verified by applying Cheung’s functions. The conduction mechanisms are explained from the forward bias I-V characteristics using the power law.

Keywords: Electrical properties, Organic/inorganic heterojunction diode, Methyl Orange, Cheungs Functions

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