Search results for: algebraic challenge

Authors: Sibawu Witness Siyepu

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This study explores the effects of instructional design using blended learning in the learning of radian measures among Engineering students. Blended learning is an education programme that combines online digital media with traditional classroom methods. It requires the physical presence of both lecturer and student in a mathematics computer laboratory. Blended learning provides element of class control over time, place, path or pace. The focus was on the use of Khan Academy to supplement traditional classroom interactions. Khan Academy is a non-profit educational organisation created by educator Salman Khan with a goal of creating an accessible place for students to learn through watching videos in a computer assisted computer. The researcher who is an also lecturer in mathematics support programme collected data through instructing students to watch Khan Academy videos on radian measures, and by supplying students with traditional classroom activities. Classroom activities entails radian measure activities extracted from the Internet. Students were given an opportunity to engage in class discussions, social interactions and collaborations. These activities necessitated students to write formative assessments tests. The purpose of formative assessments tests was to find out about the students’ understanding of radian measures, including errors and misconceptions they displayed in their calculations. Identification of errors and misconceptions serve as pointers of students’ weaknesses and strengths in their learning of radian measures. At the end of data collection, semi-structure interviews were administered to a purposefully sampled group to explore their perceptions and feedback regarding the use of blended learning approach in teaching and learning of radian measures. The study employed Algebraic Insight Framework to analyse data collected. Algebraic Insight Framework is a subset of symbol sense which allows a student to correctly enter expressions into a computer assisted systems efficiently. This study offers students opportunities to enter topics and subtopics on radian measures into a computer through the lens of Khan Academy. Khan academy demonstrates procedures followed to reach solutions of mathematical problems. The researcher performed the task of explaining mathematical concepts and facilitated the process of reinvention of rules and formulae in the learning of radian measures. Lastly, activities that reinforce students’ understanding of radian were distributed. Results showed that this study enthused the students in their learning of radian measures. Learning through videos prompted the students to ask questions which brought about clarity and sense making to the classroom discussions. Data revealed that sense making through reinvention of rules and formulae assisted the students in enhancing their learning of radian measures. This study recommends the use of Khan Academy in blended learning to be introduced as a socialisation programme to all first year students. This will prepare students that are computer illiterate to become conversant with the use of Khan Academy as a powerful tool in the learning of mathematics. Khan Academy is a key technological tool that is pivotal for the development of students’ autonomy in the learning of mathematics and that promotes collaboration with lecturers and peers.

Keywords: algebraic insight framework, blended learning, Khan Academy, radian measures

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Authors: Wagneur Edouard

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Tropical algebra is the algebra constructed over an idempotent semifield S. We show here that every m-dimensional tropical module M over S with strongly independent basis can be embedded into Sm, and provide an algebraic invariant -the Γ-matrix of M- which characterises the isomorphy class of M. The strong independence condition also yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier We also show that the strong independence of the basis of M is equivalent to the unique representation of elements of M. Numerous examples illustrate our results.

Keywords: classification, idempotent semi-modules, strong independence, tropical algebra

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Authors: Benjamin Lee Warren

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Many problems exist in additive number theory which is essential to determine the primes that are the sum of two elements from a given single-variable polynomial sequence, and most of them are unattackable in the present day. Here, we determine solutions for this problem to a few certain sequences (certain binomial coefficients and power sums) using only elementary algebra and some algebraic factoring methods (as well as Euclid’s Lemma and Faulhaber’s Formula). In particular, we show that there are finitely many primes as sums of two of these types of elements. Several cases are fully illustrated, and bounds are presented for the cases not fully illustrated.

Keywords: binomial coefficients, power sums, primes, algebra

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Authors: M. H. M. Rashid

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A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl's Theorem, Weyl Spectrum, Polaroid operators, property (gm)

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Authors: Mohsen Zahraei

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‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: ‎‎Rank-k numerical range‎, ‎isometry‎, ‎numerical range‎, ‎rectangular matrix polynomials

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Authors: Younies Saeed Hassan Mahmoud, Mai Mabrouk, Elsayed Sallam

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Analysing DNA microarray data sets is a great challenge, which faces the bioinformaticians due to the complication of using statistical and machine learning techniques. The challenge will be doubled if the microarray data sets contain missing data, which happens regularly because these techniques cannot deal with missing data. One of the most important data analysis process on the microarray data set is feature selection. This process finds the most important genes that affect certain disease. In this paper, we introduce a technique for imputing the missing data in microarray data sets while performing feature selection.

Keywords: DNA microarray, feature selection, missing data, bioinformatics

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Authors: Marcin Kowalski, Tomasz Wiktor, Piotr Ladonski, Krzysztof Bortnowski, Szymon Przybyl, Mateusz Grzesiak

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This paper provides a detailed overview of the so-called smart grid or vehicle-to-grid idea, including a description of our way of implementation. The primary targets of this paper are technical students, young constructors, visionaries, however more experienced designers may find useful ideas for developing their vehicles. The publication will also be useful for home-grown builders who want to save on electricity. This article as well summarizes the advantages and disadvantages of V2G solution and might be helpful for students teams planning to participate in Bridgestone World Solar Challenge.

Keywords: solar powered vehicle, vehicle to grid, electric car, v2g, bridgestone world solar challenge

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Authors: Catherine Cheetam, Alan Harper, Melody Elliott, Mika Ito

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This paper describes a pilot study conducted with English as a foreign language (EFL) students at a private university in Japan who used graded readers and the MReader website in class or independently to enhance their English reading skills. Each semester students who read 100,000 words with MReader quizzes passed enter into the ‘MReader Challenge,’ a reading contest that recognizes students for their achievement. The study focused specifically on the attitudes of thirty-six EFL students who successfully completed the Challenge in the 2015 spring semester using graded readers and MReader, and their motivation to continue using English in the future. The attitudes of these students were measured using their responses to statements on a Likert scaled survey. Follow-up semi-structured interviews were conducted with eleven students to gain additional insight into their opinions. The results from this study suggest that reading graded readers in general promoted intrinsic motivation among a majority of the participants. This study is preliminary and needs to be expanded and continued to assess the lasting impact of the extensive reading program. Limitations and future directions of the study are also summarized and discussed.

Keywords: attitudes, extensive, intrinsic, methodolgies, motivation, reading

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Authors: Fola John Adeyeye

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In this paper, we propose a cryptosystem private and public key base on symmetric group Pn and validates its theoretical formulation. This proposed system benefits from the algebraic properties of Pn such as noncommutative high logical, computational speed and high flexibility in selecting key which makes the discrete permutation multiplier logic (DPML) resist to attack by any algorithm such as Pohlig-Hellman. One of the advantages of this scheme is that it explore all the possible triangular symmetries. Against these properties, the only disadvantage is that the law of permutation multiplicity only allow an operation from left to right. Many other cryptosystems can be transformed into their symmetric group.

Keywords: cryptosystem, private and public key, DPML, symmetric group Pn

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Authors: Mohammad Ayub Khan

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With increased market segmentation and competition in the hotel industry, a hotel’s ability to constantly renovate its services and amenities is a business practice that can be termed as an attitude that is not only flexible but also malleable as a result of which a hotel/property is continually poised to face the ever-changing nature of the hospitality industry and upgrades that keep the hotel or brand in competition with current competitors. One such challenge is to competitively and creatively market value-added amenities, upgraded technology, and marketing all of these as a package to not only stay relevant in the market but also to retain and enhance revenues to ensure the future financial health of a hotel. This delicate balance between staying relevant and financially viable is a crucial challenge that this poster will explore, analyze, and present by specifically looking at the ability of a hotel/brand to effectively translate its theoretical need and practice of constantly staying updated, including strategically renovating, upgrading, modifying its services, into a tangible business practice. In what ways do hotels face this challenge? In what areas of the hotel is this business concept/action most effective and profitable are just some questions that this paper will attempt to answer.

Keywords: hospitality theory, renovations, value-added amenities, strategic planning

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Authors: Siddhant Rao

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Studies estimate that there will be 266,120 new cases of invasive breast cancer and 40,920 breast cancer induced deaths in the year of 2018 alone. Despite the pervasiveness of this affliction, the current process to obtain an accurate breast cancer prognosis is tedious and time consuming. It usually requires a trained pathologist to manually examine histopathological images and identify the features that characterize various cancer severity levels. We propose MITOS-RCNN: a region based convolutional neural network (RCNN) geared for small object detection to accurately grade one of the three factors that characterize tumor belligerence described by the Nottingham Grading System: mitotic count. Other computational approaches to mitotic figure counting and detection do not demonstrate ample recall or precision to be clinically viable. Our models outperformed all previous participants in the ICPR 2012 challenge, the AMIDA 2013 challenge and the MITOS-ATYPIA-14 challenge along with recently published works. Our model achieved an F- measure score of 0.955, a 6.11% improvement in accuracy from the most accurate of the previously proposed models.

Keywords: breast cancer, mitotic count, machine learning, convolutional neural networks

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Authors: Puttaswamy, Anwar Alwardi, Nayaka S. R.

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One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs.

Keywords: domination polynomial, paired dominating set, paired domination number, paired domination polynomial

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Authors: Scarlet Alejandra Romano, Joni Kareco

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The three pillars of sustainability (social, economic and environmental) are relevant concepts to the Architecture, Engineering, and Construction (AEC) industry because of the increase of international agreements and guidelines related to this topic during the last years. Considering these three pillars, the AEC industry faces important challenges, for instance, to decrease the carbon emissions (environmental challenge), design sustainable spaces for people (social challenge), and improve the technology of this field to reduce costs and environmental problems (economic and environmental challenge). One alternative to overcome these challenges is Building Information Modelling program (BIM) because according to several authors, this technology improves the performance of the sustainable buildings in all their lifecycle phases. The main objective of this paper is to explore and analyse the current advantages and disadvantages of the BIM implementation in the life-cycle of sustainable buildings considering the three pillars of sustainability as analysis parameters. The methodology established to achieve this objective is exploratory-descriptive with the literature review technique. The partial results illustrate that despite the BIM disadvantages and the lack of information about its social sustainability advantages, this software represents a significant opportunity to improve the three sustainable pillars of the sustainable buildings.

Keywords: building information modelling, building lifecycle analysis, sustainability, sustainable buildings

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Authors: Jonathan A. Sánchez Muñoz, Gustavo Flores Eraña, Juan M. Silva

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Mexican Mezcal industry has reached attention during the last decade due to it has been a popular beverage demanded by North American and European markets, reaching popularity due to its crafty character. Despite its wide demand, productive processes are still made with rudimentary equipment, and there is a lack of evidence to improve kiln energy efficiency. Tec21 is a challenge-based learning curricular model implemented by Tecnológico de Monterrey since 2019, where each formation unit requires an industrial partner. “Problem processes solution” is a formation unity designed for mechatronics engineers, where students apply the acquired knowledge in thermofluids and apply electronic. During five weeks, students are immersed in an industrial problem to obtain a proper level of competencies according to formation unit designers. This work evaluates the competencies acquired by the student through qualitative research methodology. Several evaluation instruments (report, essay, and poster) were selected to evaluate etic argumentation, principles of sustainability, implemented actions, process modelling, and redesign feasibility.

Keywords: applied electronic, challenge based learning, competencies, mezcal industry, thermofluids

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Swapna Bhargavi Gantasala

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If teamwork is the key to organizational learning, productivity, and growth, then, why do some teams succeed in achieving these, while others falter at different stages? Building teams in higher education institutions has been a challenge and an open-ended constructivist approach was considered on an experimental basis for this study to address this challenge. For this research, teams of students from the MBA program were chosen to study the effect of teamwork in learning, the motivation levels among student team members, and the effect of collaboration in achieving team goals. The teams were built on shared vision and goals, cohesion was ensured, positive induction in the form of faculty mentoring was provided for each participating team and the results have been presented with conclusions and suggestions.

Keywords: teamwork, leadership, motivation and reinforcement, collaboration

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Authors: Sukrat Sinha, Abhay Kumar, Shanthy Sundaram

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The Leishmania homologue of activated C kinase (LACK) is known T cell epitope from soluble Leishmania antigens (SLA) that confers protection against Leishmania challenge. This antigen has been found to be highly conserved among Leishmania strains. LACK has been shown to be protective against L. donovani challenge. A comprehensive analysis of several LACK sequences was completed. The analysis shows a high level of conservation, lower variability and higher antigenicity in specific portions of the LACK protein. This information provides insights for the potential consideration of LACK as a putative candidate in the context of visceral Leishmaniasis vaccine target.

Keywords: bioinformatics, genome assembly, leishmania activated protein kinase c (lack), next-generation sequencing

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Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

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Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

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Authors: Ladznar S. Laja, Rosalio G. Artes, Jr.

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This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established.

Keywords: convex subgraph, convex index, generating function, polynomial ring

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Authors: Odewumi Olatunde, Adegun Sunday

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Linguistic diversity is seen to complicate attempts to build a stable and cohesive political community. Hence, the challenge of integration is enormous in a multi-ethno-lingual country like Nigeria. In the same vein, justification for minority language rights claims in relation to broader political theories of justice, freedom and democracy cannot be ignored. It is in the light of the fore-going that this paper explores Nigeria’s experiments at language policy and planning(LPP) and the long drawn agitations for self-determination and linguistic freedom by the minority ethnic groups in the polity which has been exacerbated by the National Policy on Education language provisions. The paper succinctly reviews Nigeria’s LPP efforts and its attendant theater of conflicts; explores international attempts at evolving normative principles of freedom and equality for language policy and finally evaluates the position of the Nigerian LPP in the light of evolving international conventions. On this premise, it is concluded that giving a conscientious and honest implementation of the Nigerian language provisions as assessed from their face validity, the nation’s efforts could be exonerated from running afoul of any known civilized values and best practices. It is, therefore, recommended that an effectual and consistent commitment to implementation driven by a renewed political will is what is required for the nation to succeed in this direction.

Keywords: integration, rights, challenge, conventions, policy

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Authors: Mohammed Hussaini

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This paper discusses insecurity as a challenge to the nutritional Status of children and mothers in Dansadau, Maru Local Government area of Zamfara state, Northwestern Nigeria. A Descriptive survey design was used in the study. Objectives of the study were formulated to guide the study. 20 Health workers and 100 mothers were used as population of the study; the instrument validation for data collection was interview. The interview structure was validated by 3 experts, the data collected was analyzed and presented using descriptive standard score (Z-score). The study revealed that, Nutritional Status of children and mothers in Northwest Nigeria specifically Zamfara state is low. This mostly affect children and mother as a result of serious insecurity challenge in the region, consisting of banditry and kidnapping, killing of farmers, destruction of farmland, burning of farm products. The study recommended that the focus is on implementing strong communication strategies to enhance short-term relief initiatives, both governmental and non-governmental organizations should actively play a role in initiating lasting change, especially when tackling issues of insecurity and effectively addressing the rise of armed banditry and other security concerns requires a sophisticated and nuanced strategy.

Keywords: insecurity, malnutrition, children, mothers

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Authors: Crin N. Marcean, Mihaela A. Alexandru, Eugenia S. Cristescu

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By definition, nursing means caring. It is a profession within the health care sector focused on the care of individuals, families, and communities so they may attain, maintain or recover optimal health and quality of life. However, there is a subtle difference between the two: nursing is widely considered as an art and a science, wherein caring forms the theoretical framework of nursing. Nursing and caring are grounded in a relational understanding, unity, and connection between the professional nurse and the patient. Task-oriented approaches challenge nurses in keeping care in nursing. This challenge is on-going as professional nurses strive to maintain the concept, art, and act of caring as the moral centre of the nursing profession. Keeping the care in nursing involves the application of art and science through theoretical concepts, scientific research, conscious commitment to the art of caring as an identity of nursing, and purposeful efforts to include caring behaviours during each nurse-patient interaction. The competencies, abilities, as well as the psycho-motor, cognitive, and relational skills necessary for the nursing practice are conveyed and improved by the nursing teachers’ art of teaching. They must select and use the teaching methods which shape the personalities of the trainers or students, enabling them to provide individualized, personalized care in real-world context of health problems. They have the ultimate responsibility of shaping the future health care system by educating skilful nurses.

Keywords: art of nursing, health care, teacher-student relationship, teaching innovations

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Hamoud Al-Hadrami, Hossein Emadi, Athar Hussain

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Green hydrogen is quickly emerging as a new source of renewable energy for the world. Hydrogen production using water electrolysis is deemed as an environmentally friendly and safe source of energy for transportation and other industries. However, storing a high volume of hydrogen seems to be a significant challenge. Abandoned hydrocarbon reservoirs are considered as viable hydrogen storage options because of the availability of the required infrastructure such as wells and surface facilities. However, long-term wellbore integrity in these wells could be a serious challenge. Hydrogen reduces the compressive strength of a set cement if it gets in contact with the cement slurry. Also, mixing hydrogen with cement slurry slightly increases its density and rheological properties, which need to be considered to have a successful primary cementing operation.

Keywords: hydrogen, well bore integrity, clean energy, cementing

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Authors: Sartaj Singh, Amar Singh, Ashok Sharma, Sandeep Kaur

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With upcoming threats in a digital world, we need to work continuously in the area of security in all aspects, from hardware to software as well as data modelling. The rise in social media activities and hunger for data by various entities leads to cybercrime and more attack on the privacy and security of persons. Cryptography has always been employed to avoid access to important data by using many processes. Symmetric key and asymmetric key cryptography have been used for keeping data secrets at rest as well in transmission mode. Various cryptosystems have evolved from time to time to make the data more secure. In this research article, we are studying various cryptosystems in asymmetric cryptography and their application with usefulness, and much emphasis is given to Elliptic curve cryptography involving algebraic mathematics.

Keywords: cryptography, symmetric key cryptography, asymmetric key cryptography

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Authors: John Abubakar

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Access to decent housing is a global challenge. An estimated one billion people currently live in slum settlements globally. About 80 percent of these slum dwellers are in Asia and Africa. Nigeria accounts for a significant percentage of African slum dwellers because of its size. Addressing the challenge of slum settlement in Nigeria can have far reaching positive implications in Africa. A major slum settlement in Nigeria is Mararaba slum in Karu local government of Nasarawa state. The importance of this slum settlement hinges on its proximity to Abuja, Nigeria’s capital city. This study is an attempt at identifying the impact of self-help housing and government mass housing scheme in addressing the problem of housing access in Mararaba area of Karu local government, Nasarawa state. The research method used is the content analysis of existing literature. After the review of existing literature, the paper argues that self-help house is more impactful in addressing housing access in Mararaba area of Karu local government. Therefore, self-help housing should be recognized and incorporated into the housing policy of Nasarawa state. Both self-help housing and government mass housing programs are reviewed comparatively, and their strengths and weaknesses analyses.

Keywords: slum settlement, informal settlement, progressive improvement, holistic planning

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Authors: Dan Ohev Zion, Alon Cohen

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In recent years, the presence of short-range millimeter-wave radar in civil application has increased significantly. Autonomous driving, security, 3D imaging and high data rate communication systems are a few examples. The next challenge is the integration inside small form-factor devices, such as smartphones (e.g. gesture recognition). The main challenge is implementation of a truly low-power, low-complexity high-resolution radar. The most popular approach is the Frequency Modulated Continuous Wave (FMCW) radar, with an analog multiplication front-end. In this paper, we present an approach for adaptive estimation and correction of impairments of such front-end, specifically implemented using the Six-Port Device (SPD) as the multiplier element. The proposed algorithm was simulated and implemented on a 60 GHz radar lab prototype.

Keywords: radar, FMCW Radar, IQ mismatch, six port

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Authors: Shadi Janbabaei, Hossein Gharaee Garakani, Naser Mohammadzadeh

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Internet of things is a new concept that its emergence has caused ubiquity of sensors in human life, so that at any time, all data are collected, processed and transmitted by these sensors. In order to establish a secure connection, the first challenge is authentication between sensors. However, this challenge also requires some features so that the authentication is done properly. Anonymity, untraceability, and being lightweight are among the issues that need to be considered. In this paper, we have evaluated the authentication protocols and have analyzed the security vulnerabilities found in them. Then an improved light weight authentication protocol for sensor-to-sensor communications is presented which uses the hash function and logical operators. The analysis of protocol shows that security requirements have been met and the protocol is resistant against various attacks. In the end, by decreasing the number of computational cost functions, it is argued that the protocol is lighter than before.

Keywords: anonymity, authentication, Internet of Things, lightweight, un-traceability

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Authors: Sana Ansari, Sirus Mohammadi

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In distribution systems, shunt capacitors are used to reduce power losses, to improve voltage profile, and to increase the maximum flow through cables and transformers. This paper presents a new method to determine the optimal locations and economical sizing of fixed and/or switched shunt capacitors with a view to power losses reduction and voltage stability enhancement. General Algebraic Modeling System (GAMS) has been used to solve the maximization modules using the MINOS optimization software with Linear Programming (LP). The proposed method is tested on 33 node distribution system and the results show that the algorithm suitable for practical implementation on real systems with any size.

Keywords: power losses, voltage stability, radial distribution systems, capacitor

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