Search results for: Nabeel Iqbal

Authors: M. Imran Akram, Ahmed Pasha, Nabeel Iqbal

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In this paper a real-time trajectory generation algorithm for computing 2-D optimal paths for autonomous aerial vehicles has been discussed. A dynamic programming approach is adopted to compute k-best paths by minimizing a cost function. Collision detection is implemented to detect intersection of the paths with obstacles. Our contribution is a novel approach to the problem of trajectory generation that is computationally efficient and offers considerable gain over existing techniques.

Keywords: dynamic programming, graph search, path planning.

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Authors: Sadia Iqbal, Faheem Iqbal, Furqan Iqbal

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Efficient utilization of existing water is a pressing need for Pakistan. Due to rising population, reduction in present storage capacity and poor delivery efficiency of 30 to 40% from canal. A study to evaluate an irrigation system in the cotton-wheat zone of Pakistan, after the watercourse lining was conducted. The study is made on the basis of cropping pattern and salinity to evaluate the system. This study employed an index-based approach of using Geographic information system with field data. The satellite images of different years were use to examine the effective area. Several combinations of the ratio of signals received in different spectral bands were used for development of this index. Near Infrared and Thermal IR spectral bands proved to be most effective as this combination helped easy detection of salt affected area and cropping pattern of the study area. Result showed that 9.97% area under salinity in 1992, 9.17% in 2000 and it left 2.29% in year 2005. Similarly in 1992, 45% area is under vegetation it improves to 56% and 65% in 2000 and 2005 respectively. On the basis of these results evaluation is done 30% performance is increase after the watercourse improvement.

Keywords: Salinity, remote sensing index, salinity index, cropping pattern.

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Authors: Javed Y. Uppal

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The background of this study is the great degree of stress that the world is experiencing today, internationally among the countries, within a community among people, and even individually within one’s own self. The significance of the study is the attempt to find a solution of this stress in the philosophy of the olden times of Jalaluddin Rumi and comparatively recently of that of Allama Iqbal. The methodology adopted in this paper is firstly exploration of the perspectives of these philosophers that are being consolidated by a number of psychic and spiritual experts of today, who are being widely read but less followed. This paper further goes on presenting brief life sketches of Rumi and Iqbal. It expounds the key concepts proposed by them and the social change that was resulted in the times of the two above mentioned metaphysical philosophers. It is further amplified that with the recent advancements, in both metaphysics and the physical sciences, the gap between the two is closing down. Both Rumi and Iqbal emphasized their common essence. The old time's concepts, postulates, and philosophies are hence once again becoming valid. The findings of this paper are that the existence of human empathy, affection and mutual social attraction among humans is still valid. The positive inner belief system that dictates our thoughts and actions is vital. As a conclusion, empathy should enable us solving our problems collectively. We need to strengthen our inner communication system, to listen to the messages that come to our inner-selves. We need to get guidance and strength from them. We need to value common needs and purposes collectively to achieve results. Spiritual energy among us is to be harnessed and utilized. Connectivity is to be recognized to unify and strengthen ties among people. Mutual bonding at small and large group levels is to be employed for the survival of the disadvantaged, and sustainability of the empowering trends. With the above guidelines, hopefully, we can define a framework towards a brave and happy new humane world.

Keywords: Belief system, connectivity, human empathy, inner-self, mutual bonding, spiritual energy.

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Authors: M. Nabeel Rashin, J. Hemalatha

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Novel Coconut oil nanofluids of various concentrations have been prepared through ultrasonically assisted sol-gel method. The structural and morphological properties of the copper oxide nanoparticle have been analyzed with respectively and it revealed the monoclinic end-centered structure of crystallite and shuttle like flake morphology of agglomerates. Ultrasonic studies have been made for the nanofluids at different temperatures. The molecular interactions responsible for the changes in acoustical parameter with respect to concentration and temperature are discussed.

Keywords: Cutting Fluid, Molecular Interaction, Nanofluids, Ultrasonic

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Authors: Nabeel A. Qazi, Absaar ul Jabbar, Khalid Parvez

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A code has been developed in Mathematica using Direct Simulation Monte Carlo (DSMC) technique. The code was tested for 2-D air flow around a circular cylinder. Same geometry and flow properties were used in FLUENT 6.2 for comparison. The results obtained from Mathematica simulation indicated significant agreement with FLUENT calculations, hence providing insight into particle nature of fluid flows.

Keywords: DSMC algorithm, non continuum gas flows, Monte Carlo methods

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Authors: Muhammad Javid Qadir, Abdul Hameed

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The purpose of the study was to investigate the effectiveness of ICT training workshop of tutors of Allama Iqbal Open University Pakistan. The study was delimited to tutors of Multan region. The total sample comprised of 100 tutors. All the tutors who participated in ICT training workshop in Multan region were taken as sample in the study. A questionnaire having two parts, based on five point rating scale was developed by the researcher. Part one was about the competency level of computer skills while Part two was based on items related to training delivery, structure and content. Part One of questionnaire had five levels of competency about computer skills. The questionnaire was personally administered and collected back by the researcher himself on the last day of workshop. The collected data were analyzed by using descriptive statistics. Through this study it was found that majority of the tutors strongly agreed that training enhanced their computer skills. Majority of the respondents consider themselves to be generally competent in the use of computer. They also agreed that there was appropriate infrastructure and technical support in lab during training workshop. Moreover, it was found that the training imparted the knowledge of pedagogy of using computers for distance education.

Keywords: ICT, Tutors, AIOU.

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Authors: Haroun A.K. Shahad, Nabeel Abdul-Hadi

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Experiments were carried out to evaluate the influence of the addition of hydrogen to the inlet air on the performance of a single cylinder direct injection diesel engine. Hydrogen was injected in the inlet manifold. The addition of hydrogen was done on energy replacement basis. It was found that the addition of hydrogen improves the combustion process due to superior combustion characteristics of hydrogen in comparison to conventional diesel fuels. It was also found that 10% energy replacement improves the engine thermal efficiency by about 40% and reduces the sfc by about 35% however the volumetric efficiency was reduced by about 35%.

Keywords: Hydrogen, Blended fuel, Manifold injection , Performance , Combustion

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Authors: Faruq A. Al-Omari, Nabeel I. Al-Fayoumi

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In this paper, we present a new algorithm for clustering data in large datasets using image processing approaches. First the dataset is mapped into a binary image plane. The synthesized image is then processed utilizing efficient image processing techniques to cluster the data in the dataset. Henceforth, the algorithm avoids exhaustive search to identify clusters. The algorithm considers only a small set of the data that contains critical boundary information sufficient to identify contained clusters. Compared to available data clustering techniques, the proposed algorithm produces similar quality results and outperforms them in execution time and storage requirements.

Keywords: Data clustering, Data mining, Image-mapping, Pattern discovery, Predictive analysis.

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Authors: Iqbal Hossain, Monzur Alam Imteaz, Mohammed Iqbal Hossain

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Estimation of stormwater pollutants is a pre-requisite for the protection and improvement of the aquatic environment and for appropriate management options. The usual practice for the stormwater quality prediction is performed through water quality modeling. However, the accuracy of the prediction by the models depends on the proper estimation of model parameters. This paper presents the estimation of model parameters for a catchment water quality model developed for the continuous simulation of stormwater pollutants from a catchment to the catchment outlet. The model is capable of simulating the accumulation and transportation of the stormwater pollutants; suspended solids (SS), total nitrogen (TN) and total phosphorus (TP) from a particular catchment. Rainfall and water quality data were collected for the Hotham Creek Catchment (HTCC), Gold Coast, Australia. Runoff calculations from the developed model were compared with the calculated discharges from the widely used hydrological models, WBNM and DRAINS. Based on the measured water quality data, model water quality parameters were calibrated for the above-mentioned catchment. The calibrated parameters are expected to be helpful for the best management practices (BMPs) of the region. Sensitivity analyses of the estimated parameters were performed to assess the impacts of the model parameters on overall model estimations of runoff water quality.

Keywords: Calibration, Model Parameters, Suspended Solids, TotalNitrogen, Total Phosphorus.

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Authors: Hamid Alalwany, Nabeel A. Koshak, Mohammad K. Ibrahim

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Both knowledge economy and sustainable development are considered key dimensions in the policy action lines of many developed and developing countries. In this context, universities and other higher education institutes have a vital role in developing and sustaining wellbeing communities.

In this paper, the authors’ aim is to address the links between the concepts of innovation and entrepreneurial capacity and knowledge economy, and to utilize the approach of intellectual capital development in building a sustainable knowledge economy.

The paper will contribute to two discourses:

1. Developing a common understanding of the intersection aspects between the three concepts: Knowledge economy, Innovation and entrepreneurial system, and sustainable development.
2. Paving the road towards developing an integrated multidimensional framework for sustainable knowledge economy.

Keywords: Innovation and Entrepreneurial Capacity, Intellectual Capital Development, Sustainable Development, Sustainable Knowledge Economy.

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Authors: Nazir Ahmad Zafar, Nabeel Sabir, Amir Ali

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Functionalities and control behavior are both primary requirements in design of a complex system. Automata theory plays an important role in modeling behavior of a system. Z is an ideal notation which is used for describing state space of a system and then defining operations over it. Consequently, an integration of automata and Z will be an effective tool for increasing modeling power for a complex system. Further, nondeterministic finite automata (NFA) may have different implementations and therefore it is needed to verify the transformation from diagrams to a code. If we describe formal specification of an NFA before implementing it, then confidence over transformation can be increased. In this paper, we have given a procedure for integrating NFA and Z. Complement of a special type of NFA is defined. Then union of two NFAs is formalized after defining their complements. Finally, formal construction of intersection of NFAs is described. The specification of this relationship is analyzed and validated using Z/EVES tool.

Keywords: Modeling, Nondeterministic finite automata, Znotation, Integration of approaches, Validation.

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Authors: Tawakal Hasnain Baluch, Adnan Masood, Javaid Iqbal, Umer Izhar, Umar Shahbaz Khan

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This paper will provide the kinematic and dynamic analysis of a lower limb exoskeleton. The forward and inverse kinematics of proposed exoskeleton is performed using Denevit and Hartenberg method. The torques required for the actuators will be calculated using Lagrangian formulation technique. This research can be used to design the control of the proposed exoskeleton.

Keywords: Dynamic Analysis, Exoskeleton, Kinematic Analysis, Lower Limb, Rehabilitation Robotics

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Authors: Muhammad Tahir Qadri, Syed Shafi-Uddin Qadri, Faizan Farid, Nabeel Abid

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This paper discuss the separation of the miscible liquids by means of fractional distillation. For complete separation of liquids, the process of heating, condensation, separation and storage is done automatically to achieve the objective. PIC micro-controller has been used to control each and every process of the work. The controller also controls the storage process by activating and deactivating the conveyors. The liquids are heated which on reaching their respective boiling points evaporate and enter the condensation chamber where they convert into liquid. The liquids are then directed to their respective tanks by means of stepper motor which moves in three directions, each movement into different tank. The tank on filling sends the signal to controller which then opens the solenoid valves. The tank is emptied into the beakers below the nozzle. As the beaker filled, the nozzle closes and the conveyors come into operation. The filled beaker is replaced by an empty beaker from behind. The work can be used in oil industries, chemical industries and paint industries.

Keywords: Miscible Liquid Separation Unit, Distillation, Waste Water Treatment, Organic Liquids Collection.

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Authors: Irfan Hussain, Adnan Masood, Javaid Iqbal, Umar S. Khan

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Above Elbow Prosthesis is one of the most commonly amputated or missing limbs. The research is done for modelling techniques of upper limb prosthesis and design of high torque, light weight and compact in size elbow actuator. The purposed actuator consists of a DC motor, planetary gear set and a harmonic drive. The calculations show that the actuator is good enough to be used in real life powered prosthetic upper limb or rehabilitation exoskeleton.

Keywords: Above Elbow prosthesis, Harmonic drive, Planetarygear set, Sagittal Plane

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Authors: Hina Gull, Farooque Azam, Wasi Haider Butt, Sardar Zafar Iqbal

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The software system goes through a number of stages during its life and a software process model gives a standard format for planning, organizing and running a project. The article presents a new software development process model named as “Divide and Conquer Process Model", based on the idea first it divides the things to make them simple and then gathered them to get the whole work done. The article begins with the backgrounds of different software process models and problems in these models. This is followed by a new divide and conquer process model, explanation of its different stages and at the end edge over other models is shown.

Keywords: Process Model, Waterfall, divide and conquer, Requirements.

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Authors: Aaqif Afzaal Abbasi, Javaid Iqbal, Akhtar Nawaz Malik

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4G Communication Networks provide heterogeneous wireless technologies to mobile subscribers through IP based networks and users can avail high speed access while roaming across multiple wireless channels; possible by an organized way to manage the Quality of Service (QoS) functionalities in these networks. This paper proposes the idea of developing a novel QoS optimization architecture that will judge the user requirements and knowing peak times of services utilization can save the bandwidth/cost factors. The proposed architecture can be customized according to the network usage priorities so as to considerably improve a network-s QoS performance.

Keywords: QoS, Network Coverage Boundary, ServicesArchives Units (SAU), Cumulative Services Archives Units (CSAU).

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Authors: T. Hussain, M. W. Siddiqi, A. Iqbal

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The study is aimed to test causal relationship between growth and unemployment, using time series data for Pakistan from 1972 to 2006. Growth is considered to be a pathway to decrease the level of unemployment. Unemployment is a social and political issue. It is a phenomenon where human resources are wasted leading to deacceleration in growth. Johanson Cointegration shows that there is long run relationship between growth and unemployment. For short run dynamics and causality, the study utilizes Vector Error Correction Model (VECM). The results of VECM indicate that there is short and long run causal relation between growth and unemployment including capital, labor and human capital as explanatory variables.

Keywords: Economic Growth, Unemployment, Cointegrationand Causality.

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Authors: H. Mahmood, M. W. Siddiqi, A. Iqbal, M. A. Tabassum

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This study examines the relationships between foreign aid, levels of schooling and democracy for Pakistan using the ARDL cointegration approach. The results of study provide strong evidence for fairly robust long run as well as short run relationships among these variables for the period 1973-2008. The results state that foreign aid and primary school enrollments have negative impact on democracy index and high school enrollments have positive impact on democracy index in Pakistan. The study suggests for promotion of education levels and relies on local resources instead of foreign aid for a good quality of political institutions in Pakistan.

Keywords: Cointegration, Democracy, Education, Foreign Aid

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Authors: Tahir Iqbal, Mumtaz Ali, Syed Wajahat Kareem, Muhammad Harris

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Digital information is expanding in exponential order in our life. Information that is residing online and offline are stored in huge repositories relating to every aspect of our lives. Getting the required information is a task of retrieval systems. Content based image retrieval (CBIR) is a retrieval system that retrieves the required information from repositories on the basis of the contents of the image. Time is a critical factor in retrieval system and using indexed views with CBIR system improves the time efficiency of retrieved results.

Keywords: Content based image retrieval (CBIR), Indexed view, Color, Image retrieval, Cross correlation.

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Authors: Anjum Iqbal, Mohd Aizaini Maarof

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Artificial Immune System (AIS) is relatively naive paradigm for intelligent computations. The inspiration for AIS is derived from natural Immune System (IS). Classically it is believed that IS strives to discriminate between self and non-self. Most of the existing AIS research is based on this approach. Danger Theory (DT) argues this approach and proposes that IS fights against danger producing elements and tolerates others. We, the computational researchers, are not concerned with the arguments among immunologists but try to extract from it novel abstractions for intelligent computation. This paper aims to follow DT inspiration for intelligent data processing. The approach may introduce new avenue in intelligent processing. The data used is system calls data that is potentially significant in intrusion detection applications.

Keywords: artificial immune system, danger theory, intelligent processing, system calls

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Authors: Sajid Iqbal, Masood Ahmed, Suhail Aftab Qureshi

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DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.

Keywords: Buck converter, boost converter, period- doubling, chaos, bifurcation, strange attractor.

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Authors: Liyana Zahid, Mohd Fareq Abd Malek, Ee Meng Cheng, Wei Wen Liu, Yeng Seng Lee, Muhammad Nadeem Iqbal, Fwen Hoon Wee, Farrah Salwani Abdullah

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One of the parameters that affect the performance of microwave absorbers is the shape of the absorbers. This paper shows the performance (reflection loss) of truncated pyramidal and truncated wedge microwave absorbers in the range frequency between 8.2 to 12.4 GHz (X-Band) in simulation. The material used is sugarcane bagasse (SCB) which is one of the new materials that used to fabricate the microwave absorber. The complex permittivity was measured using Agilent dielectric probe technique. The designs were simulated using CST Microwave Studio Software. The reflection losses between these two shapes were compared.

Keywords: Microwave Absorber, Reflection Loss, Sugarcane Bagasse (SCB), X- Band.

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Authors: Bilal Saeed Raja, M. Ali Iqbal, Imran Ihsan

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Extracting and elaborating software requirements and transforming them into viable software architecture are still an intricate task. This paper defines a solution architecture which is based on the blurred amalgamation of problem space and solution space. The dependencies between domain constraints, requirements and architecture and their importance are described that are to be considered collectively while evolving from problem space to solution space. This paper proposes a revised version of Twin Peaks Model named Win Peaks Model that reconciles software requirements and architecture in more consistent and adaptable manner. Further the conflict between stakeholders- win-requirements is resolved by proposed Voting methodology that is simple adaptation of win-win requirements negotiation model and QARCC.

Keywords: Functional Requirements, Non Functional Requirements, Twin Peaks Model, QARCC.

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Authors: Chandrakala Varatharajoo, Adelina Binti Asmawi, Nabeel Abdallah Mohammad Abedalaziz

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The research explored the effect of morphemic analysis awareness on ESL secondary school students’ vocabulary acquisition. The quasi-experimental study was conducted with 100 ESL secondary school students in two experimental groups (inflectional and derivational) and one control group. The students’ vocabulary acquisition was assessed through two measures: Morph-Analysis Test and Morph-Vocabulary Test in the pretest and posttest before and after an intervention programme. Results of ANCOVA revealed that both the experimental groups achieved a significant score in Morph- Analysis Test and Vocabulary-Morphemic Test. However, the inflectional group obtained a fairly higher score than the derivational group. Thus, the findings of the research are discussed in two main areas. First, individual instructions of two types of morphemic awareness have contributed significant results on inflectional and derivational awareness among the ESL secondary school students. Nevertheless, derivational morphology achieved a significant but relatively smaller amount of effect on secondary school students’ morphological awareness compared to inflectional morphology in this research. Second finding showed that the awareness of inflectional and derivational morphology was found significantly related to vocabulary achievement of ESL secondary school students. Nevertheless, inflectional morphemic awareness had higher significant effect on ESL secondary school students’ vocabulary acquisition. Despite these findings, the study implies that morphemic analysis awareness can serve as an alternative strategy for ESL secondary school students in acquiring English vocabulary.

Keywords: Morphemic analysis, vocabulary, ESL students.

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Authors: Humaira Liaquat, Nadeem Iftikhar, Shaukat Ali, Zohaib Zafar Iqbal

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In the current age, retrieval of relevant information from massive amount of data is a challenging job. Over the years, precise and relevant retrieval of information has attained high significance. There is a growing need in the market to build systems, which can retrieve multimedia information that precisely meets the user's current needs. In this paper, we have introduced a framework for refining query results before showing it to the user, using ambient intelligence, user profile, group profile, user location, time, day, user device type and extracted features. A prototypic tool was also developed to demonstrate the efficiency of the proposed approach.

Keywords: Context aware retrieval, Information retrieval, Ambient Intelligence, Multimedia databases, User and group profile.

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Authors: Yongkui Cui, Fengping Wang, Hailai Zhao, Muhammad Zubair Iqbal, Ziya Wang, Yan Li, Pengpeng L. V.

Abstract:

The novel 3D SnO cabbages self-assembled by nanosheets were successfully synthesized via template-free hydrothermal growth method under facile conditions. The XRD results manifest that the as-prepared SnO is tetragonal phase. The TEM and HRTEM results show that the cabbage nanosheets are polycrystalline structure consisted of considerable single-crystalline nanoparticles. Two typical Raman modes A1g=210 and Eg=112 cm-1 of SnO are observed by Raman spectroscopy. Moreover, galvanostatic cycling tests has been performed using the SnO cabbages as anode material of lithium ion battery and the electrochemical results suggest that the synthesized SnO cabbage structures are a promising anode material for lithium ion batteries.

Keywords: Hydrothermal process, lithium ion battery, Raman spectroscopy, stannous oxide.

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Authors: Basant H. El-Refay, Nabeel T. Faiad

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Background: The high prevalence of obesity in Egypt has a great impact on the health care system, economic and social situation. Evidence suggests that even a moderate amount of weight loss can be useful. Aim of the study: To analyze the effects of lower body positive pressure supported treadmill training, conducted with hypocaloric diet, on body composition of obese children. Methods: Thirty children aged between 8 and 14 years, were randomly assigned into two groups: intervention group (15 children) and control group (15 children). All of them were evaluated using body composition analysis through bioelectric impedance. The following parameters were measured before and after the intervention: body mass, body fat mass, muscle mass, body mass index (BMI), percentage of body fat and basal metabolic rate (BMR). The study group exercised with antigravity treadmill three times a week during 2 months, and participated in a hypocaloric diet program. The control group participated in a hypocaloric diet program only. Results: Both groups showed significant reduction in body mass, body fat mass and BMI. Only study group showed significant reduction in percentage of body fat (p = 0.0.043). Changes in muscle mass and BMR didn't reach statistical significance in both groups. No significant differences were observed between groups except for muscle mass (p = 0.049) and BMR (p = 0.042) favoring study group. Conclusion: Both programs proved effective in the reduction of obesity indicators, but lower body positive pressure supported treadmill training was more effective in improving muscle mass and BMR.

Keywords: Children, Hypocaloric diet, Lower body positive pressure supported treadmill, obesity.

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Authors: Kashif Bilal, Tassawar Iqbal, Asad Ali Safi, Nadeem Daudpota

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This paper deals with dynamic load balancing using PVM. In distributed environment Load Balancing and Heterogeneity are very critical issues and needed to drill down in order to achieve the optimal results and efficiency. Various techniques are being used in order to distribute the load dynamically among different nodes and to deal with heterogeneity. These techniques are using different approaches where Process Migration is basic concept with different optimal flavors. But Process Migration is not an easy job, it impose lot of burden and processing effort in order to track each process in nodes. We will propose a dynamic load balancing technique in which application will intelligently balance the load among different nodes, resulting in efficient use of system and have no overheads of process migration. It would also provide a simple solution to problem of load balancing in heterogeneous environment.

Keywords: PVM, load balancing, task allocation, intelligent application.

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Authors: M. Yasin, A. Tanveer, Z. Iqbal, A. Ali

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This study was conducted to investigate the efficacy of five herbicides on narrow leaved weeds and growth and yield of wheat. An experiment was conducted at Agronomic Research Farm, University of Agriculture Faisalabad. The experiment was laid out in randomized complete block designee (RCBD) with three replications. Treatments studied were clodinafop (Topic-15 WG) at 37 g a.i. ha-1, clodinafop (Topaz-15 WG) at 45 g a.i. ha-1, fenoxaprop-p-ethyl (Puma Super-75 EW) at 45 g a.i. ha-1, fenoxaprop-p-ethyl (Gramicide-6.9 EW) at 85 g a.i. ha-1, fenoxaprop-p-ethyl (Chinlima-6.9 EW) at 85 g a.i. ha-1 and weedy check. Plots treated with fenoxaprop-p-ethyl (Puma Super-75 EW) at 45 g a.i. ha-1 produced relatively less weed biomass, more plant height, number of spike bearing tillers, number of grains per spike, 1000-grain weight and grain yield (4.20 t ha-1).

Keywords: clodinafop, fenoxaprop-p-ethyl, weeds, wheat

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Authors: T. Hussain, A. Iqbal, M. W. Siddiqi

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The objective of this study is to examine the validity of Wagner-s law and relationship between economic growth, population and export for Pakistan. The ARDL Bounds cointegration and ECM are utilized for long and short run equilibrium for the period of 1972-2007. Population has considerable role in an economy and exports are the main source to raise the GDP. With the increase in GDP, the government expenditures may or may not increase. The empirical results indicate that the Wagner-s Law does hold, as economic growth is significantly and positively correlated with government expenditures. However, population and exports have also significant and positive impact on government expenditures both in short and long run. The significant and negative coefficient of error correction term in ECM indicates that after a shock, the long rum equilibrium will again converge towards equilibrium about 70.82 percent within a year.

Keywords: ARDL Cointegration, Growth, Pakistan, Wagner's law.

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