Developing Proof Demonstration Skills in Teaching Mathematics in the Secondary School

The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.

Links between Inflammation and Insulin Resistance in Children with Morbid Obesity and Metabolic Syndrome

Obesity is a clinical state associated with low-grade inflammation. It is also a major risk factor for insulin resistance (IR). In its advanced stages, metabolic syndrome (MetS), a much more complicated disease which may lead to life-threatening problems, may develop. Obesity-mediated IR seems to correlate with the inflammation. Human studies performed particularly on pediatric population are scarce. The aim of this study is to detect possible associations between inflammation and IR in terms of some related ratios. 549 children were grouped according to their age- and sex-based body mass index (BMI) percentile tables of WHO. MetS components were determined. Informed consent and approval from the Ethics Committee for Clinical Investigations were obtained. The principles of the Declaration of Helsinki were followed. The exclusion criteria were infection, inflammation, chronic diseases and those under drug treatment. Anthropometric measurements were obtained. Complete blood cell, fasting blood glucose, insulin, and C-reactive protein (CRP) analyses were performed. Homeostasis model assessment of insulin resistance (HOMA-IR), systemic immune inflammation (SII) index, tense index, alanine aminotransferase to aspartate aminotransferase ratio (ALT/AST), neutrophils to lymphocyte (NLR), platelet to lymphocyte, and lymphocyte to monocyte ratios were calculated. Data were evaluated by statistical analyses. The degree for statistical significance was 0.05. Statistically significant differences were found among the BMI values of the groups (p < 0.001). Strong correlations were detected between the BMI and waist circumference (WC) values in all groups. Tense index values were also correlated with both BMI and WC values in all groups except overweight (OW) children. SII index values of children with normal BMI were significantly different from the values obtained in OW, obese, morbid obese and MetS groups. Among all the other lymphocyte ratios, NLR exhibited a similar profile. Both HOMA-IR and ALT/AST values displayed an increasing profile from N towards MetS3 group. BMI and WC values were correlated with HOMA-IR and ALT/AST. Both in morbid obese and MetS groups, significant correlations between CRP versus SII index as well as HOMA-IR versus ALT/AST were found. ALT/AST and HOMA-IR values were correlated with NLR in morbid obese group and with SII index in MetS group, (p < 0.05), respectively. In conclusion, these findings showed that some parameters may exhibit informative differences between the early and late stages of obesity. Important associations among HOMA-IR, ALT/AST, NLR and SII index have come to light in the morbid obese and MetS groups. This study introduced the SII index and NLR as important inflammatory markers for the discrimination of normal and obese children. Interesting links were observed between inflammation and IR in morbid obese children and those with MetS, both being late stages of obesity.

Experimental Analysis of Control in Electric Vehicle Charging Station Based Grid Tied Photovoltaic-Battery System

This work presents an improved strategy of control for charging a lithium-ion battery in an electric vehicle charging station using two charger topologies i.e. single ended primary inductor converter (SEPIC) and forward converter. In terms of rapidity and accuracy, the power system consists of a topology/control diagram that would overcome the performance constraints, for instance the power instability, the battery overloading and how the energy conversion blocks would react efficiently to any kind of perturbations. Simulation results show the effectiveness of the proposed topologies operated with a power management algorithm based on voltage/peak current mode controls. In order to provide credible findings, a low power prototype is developed to test the control strategy via experimental evaluations of the converter topology and its controls.

Re-Visiting Rumi and Iqbal on Self-Enhancement for Social Responsibility

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.

An Overview of the Porosity Classification in Carbonate Reservoirs and Their Challenges: An Example of Macro-Microporosity Classification from Offshore Miocene Carbonate in Central Luconia, Malaysia

Biological and chemical activities in carbonates are responsible for the complexity of the pore system. Primary porosity is generally of natural origin while secondary porosity is subject to chemical reactivity through diagenetic processes. To understand the integrated part of hydrocarbon exploration, it is necessary to understand the carbonate pore system. However, the current porosity classification scheme is limited to adequately predict the petrophysical properties of different reservoirs having various origins and depositional environments. Rock classification provides a descriptive method for explaining the lithofacies but makes no significant contribution to the application of porosity and permeability (poro-perm) correlation. The Central Luconia carbonate system (Malaysia) represents a good example of pore complexity (in terms of nature and origin) mainly related to diagenetic processes which have altered the original reservoir. For quantitative analysis, 32 high-resolution images of each thin section were taken using transmitted light microscopy. The quantification of grains, matrix, cement, and macroporosity (pore types) was achieved using a petrographic analysis of thin sections and FESEM images. The point counting technique was used to estimate the amount of macroporosity from thin section, which was then subtracted from the total porosity to derive the microporosity. The quantitative observation of thin sections revealed that the mouldic porosity (macroporosity) is the dominant porosity type present, whereas the microporosity seems to correspond to a sum of 40 to 50% of the total porosity. It has been proven that these Miocene carbonates contain a significant amount of microporosity, which significantly complicates the estimation and production of hydrocarbons. Neglecting its impact can increase uncertainty about estimating hydrocarbon reserves. Due to the diversity of geological parameters, the application of existing porosity classifications does not allow a better understanding of the poro-perm relationship. However, the classification can be improved by including the pore types and pore structures where they can be divided into macro- and microporosity. Such studies of microporosity identification/classification represent now a major concern in limestone reservoirs around the world.

Reverse Logistics in Clothing Recycling: A Case Study in Chengdu

Clothing recycling bin is a traditional way to collect textile waste in many areas. In the clothing recycling business, the transportation cost normally takes over 50% of total costs. This case gives a good way to reduce transportation cost by reverse logistics system. In this reverse logistics system, there are offline strategic alliance partners, such as transport firms, convenience stores, laundries, and post office which are integrated onto the mobile APP. Offline strategic alliance partners provide the service of textile waste collection, and transportation by their vacant vehicles return journey from convenience stores, laundries and post offices to sorting centers. The results of the case study provide the strategic alliance with a valuable and light - asset business model by using the logistics of offline memberships. The company in this case just focuses on textile waste sorting, reuse, recycling etc. The research method of this paper is a case study of a clothing recycling company in Chengdu by field research and interview; the analysis is based on the theory of the reverse logistics system.

Aerodynamic Interaction between Two Speed Skaters Measured in a Closed Wind Tunnel

Team pursuit is a relatively new event in international long track speed skating. For a single speed skater the aerodynamic drag will account for up to 80% of the braking force, thus reducing the drag can greatly improve the performance. In a team pursuit the interactions between athletes in near proximity will also be essential, but is not well studied. In this study, systematic measurements of the aerodynamic drag, body posture and relative positioning of speed skaters have been performed in the low speed wind tunnel at the Norwegian University of Science and Technology, in order to investigate the aerodynamic interaction between two speed skaters. Drag measurements of static speed skaters drafting, leading, side-by-side, and dynamic drag measurements in a synchronized and unsynchronized movement at different distances, were performed. The projected frontal area was measured for all postures and movements and a blockage correction was performed, as the blockage ratio ranged from 5-15% in the different setups. The static drag measurements where performed on two test subjects in two different postures, a low posture and a high posture, and two different distances between the test subjects 1.5T and 3T where T being the length of the torso (T=0.63m). A drag reduction was observed for all distances and configurations, from 39% to 11.4%, for the drafting test subject. The drag of the leading test subject was only influenced at -1.5T, with the biggest drag reduction of 5.6%. An increase in drag was seen for all side-by-side measurements, the biggest increase was observed to be 25.7%, at the closest distance between the test subjects, and the lowest at 2.7% with ∼ 0.7 m between the test subjects. A clear aerodynamic interaction between the test subjects and their postures was observed for most measurements during static measurements, with results corresponding well to recent studies. For the dynamic measurements, the leading test subject had a drag reduction of 3% even at -3T. The drafting showed a drag reduction of 15% when being in a synchronized (sync) motion with the leading test subject at 4.5T. The maximal drag reduction for both the leading and the drafting test subject were observed when being as close as possible in sync, with a drag reduction of 8.5% and 25.7% respectively. This study emphasize the importance of keeping a synchronized movement by showing that the maximal gain for the leading and drafting dropped to 3.2% and 3.3% respectively when the skaters are in opposite phase. Individual differences in technique also appear to influence the drag of the other test subject.

Development and Usability Assessment of a Connected Resistance Exercise Band Application for Strength-Monitoring

Resistance exercise bands are a core component of any physical activity strengthening program. Strength training can mitigate the development of sarcopenia, the loss of muscle mass or strength and function with aging. Yet, the adherence of such behavioral exercise strategies in a home-based setting are fraught with issues of monitoring and compliance. Our group developed a Bluetooth-enabled resistance exercise band capable of transmitting data to an open-source platform. In this work, we developed an application to capture this information in real-time, and conducted three usability studies in two mixed-aged groups of participants (n=6 each) and a group of older adults with obesity participating in a weight-loss intervention (n=20). The system was favorable, acceptable and provided iterative information that could assist in future deployment on ubiquitous platforms. Our formative work provides the foundation to deliver home-based monitoring interventions in a high-risk, older adult population.

Some Issues of Measurement of Impairment of Non-Financial Assets in the Public Sector

The economic value of the asset impairment process is quite large. Impairment reflects the reduction of future economic benefits or service potentials itemized in the asset. The assets owned by public sector entities bring economic benefits or are used for delivery of the free-of-charge services. Consequently, they are classified as cash-generating and non-cash-generating assets. IPSAS 21 - Impairment of non-cash-generating assets, and IPSAS 26 - Impairment of cash-generating assets, have been designed considering this specificity.  When measuring impairment of assets, it is important to select the relevant methods. For measurement of the impaired Non-Cash-Generating Assets, IPSAS 21 recommends three methods: Depreciated Replacement Cost Approach, Restoration Cost Approach, and  Service Units Approach. Impairment of Value in Use of Cash-Generating Assets (according to IPSAS 26) is measured by discounted value of the money sources to be received in future. Value in use of the cash-generating asserts (as per IPSAS 26) is measured by the discounted value of the money sources to be received in the future. The article provides classification of the assets in the public sector  as non-cash-generating assets and cash-generating assets and, deals also with the factors which should be considered when evaluating  impairment of assets. An essence of impairment of the non-financial assets and the methods of measurement thereof evaluation are formulated according to IPSAS 21 and IPSAS 26. The main emphasis is put on different methods of measurement of the value in use of the impaired Cash-Generating Assets and Non-Cash-Generation Assets and the methods of their selection. The traditional and the expected cash flow approaches for calculation of the discounted value are reviewed. The article also discusses the issues of recognition of impairment loss and its reflection in the financial reporting. The article concludes that despite a functional purpose of the impaired asset, whichever method is used for measuring the asset, presentation of realistic information regarding the value of the assets should be ensured in the financial reporting. In the theoretical development of the issue, the methods of scientific abstraction, analysis and synthesis were used. The research was carried out with a systemic approach. The research process uses international standards of accounting, theoretical researches and publications of Georgian and foreign scientists.

Monitoring of Belt-Drive Defects Using the Vibration Signals and Simulation Models

The main aim of this paper is to dedicate the belt drive system faults like cogs missing, misalignment and belt worm using vibration analysis technique. Experimentally, the belt drive test-rig is equipped to measure vibrations signals under different operating conditions. Finite element 3D model of belt drive system is created and vibration response analyzed using commercial finite element software ABAQUS/CAE.  Root mean square (RMS) and Crest Factor will serve as indicators of average amplitude of envelope analysis signals. The vibration signals pattern obtained from the simulation model and experimental data have the same characteristics. It can be concluded that each case of the RMS is more effective in detecting the defect for acceleration response. While Crest Factor parameter has a response with the displacement and velocity of vibration signals. Also it can be noticed that the model has difficulty in completing the solution when the misalignment angle is higher than 1 degree.

The Effects of Production, Transportation and Storage Conditions on Mold Growth in Compound Feeds

The objective of the present study is to determine the critical control points during the production, transportation and storage conditions of compound feeds to be used in the Hazard Analysis Critical Control Point (HACCP) feed safety management system. A total of 40 feed samples were taken after 20 and 40 days of storage periods from the 10 dairy and 10 beef cattle farms following the transportation of the compound feeds from the factory. In addition, before transporting the feeds from factory immediately after production of dairy and beef cattle compound feeds, 10 from each total 20 samples were taken as 0 day. In all feed samples, chemical composition and total aflatoxin levels were determined. The aflatoxin levels in all feed samples with the exception of 2 dairy cattle feeds were below the maximum acceptable level. With the increase in storage period in dairy feeds, the aflatoxin levels were increased to 4.96 ppb only in a BS8 dairy farm. This value is below the maximum permissible level (10 ppb) in beef cattle feed. The aflatoxin levels of dairy feed samples taken after production varied between 0.44 and 2.01 ppb. Aflatoxin levels were found to be between 0.89 and 3.01 ppb in dairy cattle feeds taken on the 20th day of storage at 10 dairy cattle farm. On the 40th day, feed aflatoxin levels in the same dairy cattle farm were found between 1.12 and 7.83 ppb. The aflatoxin levels were increased to 7.83 and 6.31 ppb in 2 dairy farms, after a storage period of 40 days. These obtained aflatoxin values are above the maximum permissible level in dairy cattle feeds. The 40 days storage in pellet form in the HACCP feed safety management system can be considered as a critical control point.

Study on Wireless Transmission for Reconnaissance UAV with Wireless Sensor Network and Cylindrical Array of Microstrip Antennas

It is important for a commander to have real-time information to aware situations and to make decision in the battlefield. Results of modern technique developments have brought in this kind of information for military purposes. Unmanned aerial vehicle (UAV) is one of the means to gather intelligence owing to its widespread applications. It is still not clear whether or not the mini UAV with short-range wireless transmission system is used as a reconnaissance system in Taiwanese. In this paper, previous experience on the research of the sort of aerial vehicles has been applied with a data-relay system using the ZigBee modulus. The mini UAV developed is expected to be able to collect certain data in some appropriate theaters. The omni-directional antenna with high gain is also integrated into mini UAV to fit the size-reducing trend of airborne sensors. Two advantages are so far obvious. First, mini UAV can fly higher than usual to avoid being attacked from ground fires. Second, the data will be almost gathered during all maneuvering attitudes.

The Two Layers of Food Safety and GMOs in the Hungarian Agricultural Law

The study presents the complexity of food safety dividing it into two layers. Beyond the basic layer of requirements, there is a more demanding higher level linked with quality and purity aspects. It would be important to give special prominence to both layers, given that massive illnesses are caused by foods even though officially licensed. Then the study discusses an exciting safety challenge stemming from the risks of genetically modified organisms (GMOs). Furthermore, it features legal case examples that illustrate how certain liability questions are solved or not yet decided in connection with the production of genetically modified crops. In addition, a special kind of land grabbing, more precisely land grabbing from non-GMO farming systems can also be noticed as well as a new phenomenon eroding food sovereignty. Coexistence, the state where organic, conventional, and GM farming systems are standing alongside each other is an unsuitable experiment that cannot be successful, because of biophysical reasons (such as cross-pollination). Agricultural and environmental lawyers both try to find the optimal solution. Agri-environmental measures are introduced as a special subfield of law maintaining also food safety. The important steps of agri-environmental legislation are aiming at the protection of natural values, the environmental media and strengthening food safety as well, practically the quality of agricultural products intended for human consumption. The major findings of the study focus on searching for the appropriate approach capable of solving the security and safety problems of food production. The most interesting concepts of the Hungarian national and EU food law legislation are analyzed in more detail with descriptive, analytic and comparative methods.

Designing an Integrated Platform for Real-Time Recommendations Sharing among the Aged and People Living with Cancer

The world is expected to experience growth in the number of ageing population, and this will bring about high cost of providing care for these valuable citizens. In addition, many of these live with chronic diseases that come with old age. Providing adequate care in the face of rising costs and dwindling personnel can be challenging. However, advances in technologies and emergence of the Internet of Things are providing a way to address these challenges while improving care giving. This study proposes the integration of recommendation systems into homecare to provide real-time recommendations for effective management of people receiving care at home and those living with chronic diseases. Using the simplified Training Logic Concept, stakeholders and requirements were identified. Specific requirements were gathered from people living with cancer. The solution designed has two components namely home and community, to enhance recommendations sharing for effective care giving. The community component of the design was implemented with the development of a mobile app called Recommendations Sharing Community for Aged and Chronically Ill People (ReSCAP). This component has illustrated the possibility of real-time recommendations, improved recommendations sharing among care receivers and between a physician and care receivers. Full implementation will increase access to health data for better care decision making.

The Carbon Footprint Model as a Plea for Cities towards Energy Transition: The Case of Algiers Algeria

Environmental sustainability rather than a trans-disciplinary and a scientific issue, is the main problem that characterizes all modern cities nowadays. In developing countries, this concern is expressed in a plethora of critical urban ills: traffic congestion, air pollution, noise, urban decay, increase in energy consumption and CO2 emissions which blemish cities’ landscape and might threaten citizens’ health and welfare. As in the same manner as developing world cities, the rapid growth of Algiers’ human population and increasing in city scale phenomena lead eventually to increase in daily trips, energy consumption and CO2 emissions. In addition, the lack of proper and sustainable planning of the city’s infrastructure is one of the most relevant issues from which Algiers suffers. The aim of this contribution is to estimate the carbon deficit of the City of Algiers, Algeria, using the Ecological Footprint Model (carbon footprint). In order to achieve this goal, the amount of CO2 from fuel combustion has been calculated and aggregated into five sectors (agriculture, industry, residential, tertiary and transportation); as well, Algiers’ biocapacity (CO2 uptake land) has been calculated to determine the ecological overshoot. This study shows that Algiers’ transport system is not sustainable and is generating more than 50% of Algiers total carbon footprint which cannot be sequestered by the local forest land. The aim of this research is to show that the Carbon Footprint Assessment might be a relevant indicator to design sustainable strategies/policies striving to reduce CO2 by setting in motion the energy consumption in the transportation sector and reducing the use of fossil fuels as the main energy input.

Using Divergent Nozzle with Aerodynamic Lens to Focus Nanoparticles

ANSYS Fluent will be used to simulate Computational Fluid Dynamics (CFD) for an efficient lens and nozzle design which will be explained in this paper. We have designed and characterized an aerodynamic lens and a divergent nozzle for focusing flow that transmits sub 25 nm particles through the aerodynamic lens. The design of the lens and nozzle has been improved using CFD for particle trajectories. We obtained a case for calculating nanoparticles (25 nm) flowing through the aerodynamic lens and divergent nozzle. Nanoparticles are transported by air, which is pumped into the aerodynamic lens through the nozzle at 1 atmospheric pressure. We have also developed a computational methodology that can determine the exact focus characteristics of aerodynamic lens systems. Particle trajectories were traced using the Lagrange approach. The simulation shows the ability of the aerodynamic lens to focus on 25 nm particles after using a divergent nozzle.

A Prediction Model Using the Price Cyclicality Function Optimized for Algorithmic Trading in Financial Market

After the widespread release of electronic trading, automated trading systems have become a significant part of the business intelligence system of any modern financial investment company. An important part of the trades is made completely automatically today by computers using mathematical algorithms. The trading decisions are taken almost instantly by logical models and the orders are sent by low-latency automatic systems. This paper will present a real-time price prediction methodology designed especially for algorithmic trading. Based on the price cyclicality function, the methodology revealed will generate price cyclicality bands to predict the optimal levels for the entries and exits. In order to automate the trading decisions, the cyclicality bands will generate automated trading signals. We have found that the model can be used with good results to predict the changes in market behavior. Using these predictions, the model can automatically adapt the trading signals in real-time to maximize the trading results. The paper will reveal the methodology to optimize and implement this model in automated trading systems. After tests, it is proved that this methodology can be applied with good efficiency in different timeframes. Real trading results will be also displayed and analyzed in order to qualify the methodology and to compare it with other models. As a conclusion, it was found that the price prediction model using the price cyclicality function is a reliable trading methodology for algorithmic trading in the financial market.

Design and Performance Analysis of a Hydro-Power Rim-Driven Superconducting Synchronous Generator

The technology of superconductivity has developed in many power system devices such as transmission cable, transformer, current limiter, motor and generator. Superconducting wires can carry high density current without loss, which is the capability that is used to design the compact, lightweight and more efficient electrical machines. Superconducting motors have found applications in marine and air propulsion systems as well as superconducting generators are considered in low power hydraulic and wind generators. This paper presents a rim-driven superconducting synchronous generator for hydraulic power plant. The rim-driven concept improves the performance of hydro turbine. Furthermore, high magnetic field that is produced by superconducting windings allows replacing the rotor core. As a consequent, the volume and weight of the machine is decreased significantly. In this paper, a 1 MW coreless rim-driven superconducting synchronous generator is designed. Main performance characteristics of the proposed machine are then evaluated using finite elements method and compared to an ordinary similar size synchronous generator.

Development of Tools for Multi Vehicles Simulation with Robot Operating System and ArduPilot

One of the main difficulties in developing multi-robot systems (MRS) is related to the simulation and testing tools available. Indeed, if the differences between simulations and real robots are too significant, the transition from the simulation to the robot won’t be possible without another long development phase and won’t permit to validate the simulation. Moreover, the testing of different algorithmic solutions or modifications of robots requires a strong knowledge of current tools and a significant development time. Therefore, the availability of tools for MRS, mainly with flying drones, is crucial to enable the industrial emergence of these systems. This research aims to present the most commonly used tools for MRS simulations and their main shortcomings and presents complementary tools to improve the productivity of designers in the development of multi-vehicle solutions focused on a fast learning curve and rapid transition from simulations to real usage. The proposed contributions are based on existing open source tools as Gazebo simulator combined with ROS (Robot Operating System) and the open-source multi-platform autopilot ArduPilot to bring them to a broad audience.

Cryptographic Attack on Lucas Based Cryptosystems Using Chinese Remainder Theorem

Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC3 cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC4,6 cryptosystem than LUC3 and LUC cryptosystems. Current study concludes that LUC4,6 cryptosystem is more secure than LUC and LUC3 cryptosystems in sustaining against Lenstra’s attack.