Search results for: emergy algebra
101 Methodological Aspect of Emergy Accounting in Co-Production Branching Systems
Authors: Keshab Shrestha, Hung-Suck Park
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Emergy accounting of the systems networks is guided by a definite rule called ‘emergy algebra’. The systems networks consist of two types of branching. These are the co-product branching and split branching. The emergy accounting procedure for both the branching types is different. According to the emergy algebra, each branch in the co-product branching has different transformity values whereas the split branching has the same transformity value. After the transformity value of each branch is determined, the emergy is calculated by multiplying this with the energy. The aim of this research is to solve the problems in determining the transformity values in the co-product branching through the introduction of a new methodology, the modified physical quantity method. Initially, the existing methodologies for emergy accounting in the co-product branching is discussed and later, the modified physical quantity method is introduced with a case study of the Eucalyptus pulp production. The existing emergy accounting methodologies in the co-product branching has wrong interpretations with incorrect emergy calculations. The modified physical quantity method solves those problems of emergy accounting in the co-product branching systems. The transformity value calculated for each branch is different and also applicable in the emergy calculations. The methodology also strictly follows the emergy algebra rules. This new modified physical quantity methodology is a valid approach in emergy accounting particularly in the multi-production systems networks.Keywords: co-product branching, emergy accounting, emergy algebra, modified physical quantity method, transformity value
Procedia PDF Downloads 284100 Construction Sustainability Improvement through Using Recycled Aggregates in Concrete Production
Authors: Zhiqiang Zhu, Khalegh Barati, Xuesong Shen
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Due to the energy consumption caused by the construction industry, the public is paying more and more attention to the sustainability of the buildings. With the advancement of research on recycled aggregates, it has become possible to replace natural aggregates with recycled aggregates and to achieve a reduction in energy consumption of materials during construction. The purpose of this paper is to quantitatively compare the emergy consumption of natural aggregate concrete (NAC) and recycled aggregate concrete (RAC). To do so, the emergy analysis method is adopted. Using this technique, it can effectively analyze different forms of energy and substance. The main analysis object is the direct and indirect emergy consumption of the stages in concrete production. Therefore, for indirect energy, consumption of production machinery and transportation vehicle also need to be considered. Finally, the emergy values required to produce the two concrete types are compared to analyze whether the RAC can reduce emergy consumption.Keywords: sustainable construction, NAC, RAC, emergy, concrete
Procedia PDF Downloads 14499 Sustainable Manufacturing of Solenoid Valve Housing in Fiji: Fused Deposition Modeling (FDM) and Emergy Analysis
Authors: M. Hisham, S. Cabemaiwai, S. Prasad, T. Dauvakatini, R. Ananthanarayanan
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A solenoid valve is an important part of many fluid systems. Its purpose is to regulate fluid flow in a machine. Due to the crucial role of the solenoid valve and its design intricacy, it is quite expensive to obtain in Fiji and is not manufactured locally. A concern raised by the local health industry is that the housing of the solenoid valve gets damaged when machines are continuously being used and this part of the valve is very costly to replace due to the lack of availability in Fiji and many other South Pacific region countries. This study explores the agile manufacturing of a solenoid coil housing using the Fused Deposition Modeling (FDM) process. An emergy study was carried out to analyze the feasibility and sustainability of producing the part locally after estimating a Unit Emergy Value (or emergy transformity) of 1.27E+05 sej/j for the electricity in Fiji. The total emergy of the process was calculated to be 3.05E+12 sej, of which a majority was sourced from imported services and materials. Renewable emergy sources contributed to just 16.04% of the total emergy. Therefore, the part is suitable to be manufactured in Fiji with a reasonable quality and a cost of $FJ 2.85. However, the loading on the local environment is found to be significant and therefore, alternative raw materials for the filament like recycled PET should be explored or alternative manufacturing processes may be analyzed before committing to fabricating the part using FDM in its analyzed state.Keywords: emergy analysis, fused deposition modeling, solenoid valve housing, sustainable production
Procedia PDF Downloads 198 Ecological-Economics Evaluation of Water Treatment Systems
Authors: Hwasuk Jung, Seoi Lee, Dongchoon Ryou, Pyungjong Yoo, Seokmo Lee
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The Nakdong River being used as drinking water sources for Pusan metropolitan city has the vulnerability of water management due to the fact that industrial areas are located in the upper Nakdong River. Most citizens of Busan think that the water quality of Nakdong River is not good, so they boil or use home filter to drink tap water, which causes unnecessary individual costs to Busan citizens. We need to diversify water intake to reduce the cost and to change the weak water source. Under this background, this study was carried out for the environmental accounting of Namgang dam water treatment system compared to Nakdong River water treatment system by using emergy analysis method to help making reasonable decision. Emergy analysis method evaluates quantitatively both natural environment and human economic activities as an equal unit of measure. The emergy transformity of Namgang dam’s water was 1.16 times larger than that of Nakdong River’s water. Namgang Dam’s water shows larger emergy transformity than that of Nakdong River’s water due to its good water quality. The emergy used in making 1 m3 tap water from Namgang dam water treatment system was 1.26 times larger than that of Nakdong River water treatment system. Namgang dam water treatment system shows larger emergy input than that of Nakdong river water treatment system due to its construction cost of new pipeline for intaking Namgang daw water. If the Won used in making 1 m3 tap water from Nakdong river water treatment system is 1, Namgang dam water treatment system used 1.66. If the Em-won used in making 1 m3 tap water from Nakdong river water treatment system is 1, Namgang dam water treatment system used 1.26. The cost-benefit ratio of Em-won was smaller than that of Won. When we use emergy analysis, which considers the benefit of a natural environment such as good water quality of Namgang dam, Namgang dam water treatment system could be a good alternative for diversifying intake source.Keywords: emergy, emergy transformity, Em-won, water treatment system
Procedia PDF Downloads 29497 Quantum Algebra from Generalized Q-Algebra
Authors: Muna Tabuni
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The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given.Keywords: Q-algebras, BCI, BCK, BCH-algebra, quantum mechanics
Procedia PDF Downloads 19296 On the Framework of Contemporary Intelligent Mathematics Underpinning Intelligent Science, Autonomous AI, and Cognitive Computers
Authors: Yingxu Wang, Jianhua Lu, Jun Peng, Jiawei Zhang
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The fundamental demand in contemporary intelligent science towards Autonomous AI (AI*) is the creation of unprecedented formal means of Intelligent Mathematics (IM). It is discovered that natural intelligence is inductively created rather than exhaustively trained. Therefore, IM is a family of algebraic and denotational mathematics encompassing Inference Algebra, Real-Time Process Algebra, Concept Algebra, Semantic Algebra, Visual Frame Algebra, etc., developed in our labs. IM plays indispensable roles in training-free AI* theories and systems beyond traditional empirical data-driven technologies. A set of applications of IM-driven AI* systems will be demonstrated in contemporary intelligence science, AI*, and cognitive computers.Keywords: intelligence mathematics, foundations of intelligent science, autonomous AI, cognitive computers, inference algebra, real-time process algebra, concept algebra, semantic algebra, applications
Procedia PDF Downloads 4695 Conspicuous and Significant Learner Errors in Algebra
Authors: Michael Lousis
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The kind of the most important and conspicuous errors the students made during the three-years of testing of their progress in Algebra are presented in this article. The way these students’ errors changed over three-years of school Algebra learning also is shown. The sample is comprised of two hundred (200) English students and one hundred and fifty (150) Greek students, who were purposefully culled according to their participation in each occasion of testing in the development of the three-year Kassel Project in England and Greece, in both domains at once of Arithmetic and Algebra. Hence, for each of these English and Greek students, six test-scripts were available and corresponded to the three occasions of testing in both Arithmetic and Algebra respectively.Keywords: algebra, errors, Kassel Project, progress of learning
Procedia PDF Downloads 29694 Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra
Authors: Zuhier Altawallbeh
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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra
Procedia PDF Downloads 39993 Fuzzy Implicative Pseudo-Ideals of Pesudo-BCK Algebras
Authors: Alireza Gilani
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In this paper, we consider the fuzzification of implicative pseudo-ideal in a pseudo-BCK algebra, and then we investigate some of their properties. We prove that the family of fuzzy implicative pseudo-ideal is completely distributive lattice.Keywords: BCK-algebra, pseudo-BCK algebra, pseudo-ideal, implicative pseudo-ideal
Procedia PDF Downloads 38392 Non Commutative Lᵖ Spaces as Hilbert Modules
Authors: Salvatore Triolo
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We discuss the possibility of extending the well-known Gelfand-Naimark-Segal representation to modules over a C*algebra. We focus our attention on the case of Hilbert modules. We consider, in particular, the problem of the existence of a faithful representation. Non-commutative Lᵖ-spaces are shown to constitute examples of a class of CQ*-algebras. Finally, we have shown that any semisimple proper CQ*-algebra (X, A#), with A# a W*-algebra can be represented as a CQ*-algebra of measurable operators in Segal’s sense.Keywords: Gelfand-Naimark-Segal representation, CQ*-algebras, faithful representation, non-commutative Lᵖ-spaces, operator in Hilbert spaces
Procedia PDF Downloads 24491 The Weights of Distinguished sl2-Subalgebras in Dn
Authors: Yassir I. Dinar
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We computed the weights of the adjoint action of distinguished sl2-triples in Lie algebra of type Dn using mathematical induction.Keywords: lie algebra, root systems, representation theory, nilpotent orbits
Procedia PDF Downloads 29290 From Equations to Structures: Linking Abstract Algebra and High-School Algebra for Secondary School Teachers
Authors: J. Shamash
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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development
Procedia PDF Downloads 14189 Math Rally Proposal for the Teaching-Learning of Algebra
Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera
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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.Keywords: algebra, algebraic challenge, algebraic puzzle, math rally
Procedia PDF Downloads 15988 On Lie-Central Derivations and Almost Inner Lie-Derivations of Leibniz Algebras
Authors: Natalia Pacheco Rego
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The Liezation functor is a map from the category of Leibniz algebras to the category of Lie algebras, which assigns a Leibniz algebra to the Lie algebra given by the quotient of the Leibniz algebra by the ideal spanned by the square elements of the Leibniz algebra. This functor is left adjoint to the inclusion functor that considers a Lie algebra as a Leibniz algebra. This environment fits in the framework of central extensions and commutators in semi-abelian categories with respect to a Birkhoff subcategory, where classical or absolute notions are relative to the abelianization functor. Classical properties of Leibniz algebras (properties relative to the abelianization functor) were adapted to the relative setting (with respect to the Liezation functor); in general, absolute properties have the corresponding relative ones, but not all absolute properties immediately hold in the relative case, so new requirements are needed. Following this line of research, it was conducted an analysis of central derivations of Leibniz algebras relative to the Liezation functor, called as Lie-derivations, and a characterization of Lie-stem Leibniz algebras by their Lie-central derivations was obtained. In this paper, we present an overview of these results, and we analyze some new properties concerning Lie-central derivations and almost inner Lie-derivations. Namely, a Leibniz algebra is a vector space equipped with a bilinear bracket operation satisfying the Leibniz identity. We define the Lie-bracket by [x, y]lie = [x, y] + [y, x] , for all x, y . The Lie-center of a Leibniz algebra is the two-sided ideal of elements that annihilate all the elements in the Leibniz algebra through the Lie-bracket. A Lie-derivation is a linear map which acts as a derivative with respect to the Lie-bracket. Obviously, usual derivations are Lie-derivations, but the converse is not true in general. A Lie-derivation is called a Lie-central derivation if its image is contained in the Lie-center. A Lie-derivation is called an almost inner Lie-derivation if the image of an element x is contained in the Lie-commutator of x and the Leibniz algebra. The main results we present in this talk refer to the conditions under which Lie-central derivation and almost inner Lie-derivations coincide.Keywords: almost inner Lie-derivation, Lie-center, Lie-central derivation, Lie-derivation
Procedia PDF Downloads 13287 Classification of Tropical Semi-Modules
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
Procedia PDF Downloads 36686 Incomplete Existing Algebra to Support Mathematical Computations
Authors: Ranjit Biswas
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The existing subject Algebra is incomplete to support mathematical computations being done by scientists of all areas: Mathematics, Physics, Statistics, Chemistry, Space Science, Cosmology etc. even starting from the era of great Einstein. A huge hidden gap in the subject ‘Algebra’ is unearthed. All the scientists today, including mathematicians, physicists, chemists, statisticians, cosmologists, space scientists, and economists, even starting from the great Einstein, are lucky that they got results without facing any contradictions or without facing computational errors. Most surprising is that the results of all scientists, including Nobel Prize winners, were proved by them by doing experiments too. But in this paper, it is rigorously justified that they all are lucky. An algebraist can define an infinite number of new algebraic structures. The objective of the work in this paper is not just for the sake of defining a distinct algebraic structure, but to recognize and identify a major gap of the subject ‘Algebra’ lying hidden so far in the existing vast literature of it. The objective of this work is to fix the unearthed gap. Consequently, a different algebraic structure called ‘Region’ has been introduced, and its properties are studied.Keywords: region, ROR, RORR, region algebra
Procedia PDF Downloads 4485 Mixed Number Algebra and Its Application
Authors: Md. Shah Alam
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Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix
Procedia PDF Downloads 35584 Formex Algebra Adaptation into Parametric Design Tools: Dome Structures
Authors: Réka Sárközi, Péter Iványi, Attila B. Széll
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The aim of this paper is to present the adaptation of the dome construction tool for formex algebra to the parametric design software Grasshopper. Formex algebra is a mathematical system, primarily used for planning structural systems such like truss-grid domes and vaults, together with the programming language Formian. The goal of the research is to allow architects to plan truss-grid structures easily with parametric design tools based on the versatile formex algebra mathematical system. To produce regular structures, coordinate system transformations are used and the dome structures are defined in spherical coordinate system. Owing to the abilities of the parametric design software, it is possible to apply further modifications on the structures and gain special forms. The paper covers the basic dome types, and also additional dome-based structures using special coordinate-system solutions based on spherical coordinate systems. It also contains additional structural possibilities like making double layer grids in all geometry forms. The adaptation of formex algebra and the parametric workflow of Grasshopper together give the possibility of quick and easy design and optimization of special truss-grid domes.Keywords: parametric design, structural morphology, space structures, spherical coordinate system
Procedia PDF Downloads 24983 Learners’ Reactions to Writing Activities in an Elementary Algebra Classroom
Authors: Early Sol A. Gadong, Lourdes C. Zamora, Jonny B. Pornel, Aurora Fe C. Bautista
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Various research has shown that writing allows students to engage in metacognition and provides them with a venue to communicate their disposition towards what they are learning. However, few studies have explored students’ feelings about the incorporation of such writing activities in their mathematics classes. Through reflection sheets, group discussions, and interviews, this mixed-methods study explored students’ perceptions and insights on supplementary writing activities in their Elementary Algebra class. Findings revealed that while students generally have a positive regard for writing activities, they have conflicting views about how writing activities can help them in their learning. A big majority contend that writing activities can enhance the learning of mathematical content and attitudes towards mathematics if they allow students to explore and synthesize what they have learned and reflected on their emotional disposition towards mathematics. Also, gender does not appear to play a significant role in students’ reactions to writing activities.Keywords: writing in math, metacognition, affective factors in learning, elementary algebra classroom
Procedia PDF Downloads 43382 Mathematical Anxiety and Misconceptions in Algebra of Grade Vii Students in General Emilio Aguinaldo National High School
Authors: Nessa-Amie T. Peñaflor, Antonio Cinto
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This is a descriptive research on the level of math anxiety and mathematics misconceptions in algebra. This research is composed of four parts: (1) analysis of the level of anxiety of the respondents; (2) analysis of the common mathematical misconceptions in algebra; (3) relationship of socio-demographic profile in math anxiety and mathematical misconceptions and (4) analysis of the relationship of math anxiety and misconceptions in algebra. Through the demographic profile questionnaire it was found out that most of the respondents were female. Majority had ages that ranged from 13-15. Most of them had parents who finished secondary education. The biggest portion of Grade Seven students where from families with annual family income ranging from PhP 100, 000 to PhP 299, 999. Most of them came from public school. Mathematics Anxiety Scale for Secondary and Senior Secondary School Students (MAS) and set of 10 open-ended algebraic expressions and polynomials were also administered to determine the anxiety level and the common misconceptions in algebra. Data analysis revealed that respondents had high anxiety in mathematics. Likewise, the common mathematical misconceptions of the Grade Seven students were: combining unlike terms; multiplying the base and exponents; regarding the variable x as 0; squaring the first and second terms only in product of two binomials; wrong meaning attached to brackets; writing the terms next to each other but not simplifying in using the FOIL Method; writing the literal coefficient even if the numerical coefficient is 0; and dividing the denominator by the numerator when the numerical coefficient in the numerator is smaller than the numerical coefficient of the denominator. Results of the study show that the socio-demographic characteristics were not related to mathematics anxiety and misconceptions. Furthermore, students from higher section had high anxiety than those students on the lower section. Thus, belonging to higher or lower section may affect the mathematical misconceptions of the respondents.Keywords: algebra, grade 7 math, math anxiety, math misconceptions
Procedia PDF Downloads 40781 Generalized π-Armendariz Authentication Cryptosystem
Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi
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Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.Keywords: cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol
Procedia PDF Downloads 20880 Effect of Digital Technology on Students Interest, Achievement and Retention in Algebra in Abia State College of Education (Technical) Arochukwu
Authors: Stephen O. Amaraihu
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This research investigated the effect of Computer Based Instruction on Students’ interest, achievement, and retention in Algebra in Abia State College of Education (Technical), Arochukwu. Three research questions and two hypotheses guided the study. Two instruments, Maths Achievement Test (MAT) and Maths Interest Inventory were employed, to test a population of three hundred and sixteen (316) NCE 1 students in algebra. It is expected that this research will lead to the improvement of students’ performance and enhance their interest and retention of basic algebraic concept. It was found that the majority of students in the college are not proficient in the use of ICT as a result of a lack of trained personnel. It was concluded that the state government was not ready to implement the usage of mathematics in Abia State College of Education. The paper recommends, amongst others, the employment of mathematics Lectures with competent skills in ICT and the training of lecturers of mathematics.Keywords: achievement, computer based instruction, interest, retention
Procedia PDF Downloads 20179 Performance-Based Quality Evaluation of Database Conceptual Schemas
Authors: Janusz Getta, Zhaoxi Pan
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Performance-based quality evaluation of database conceptual schemas is an important aspect of database design process. It is evident that different conceptual schemas provide different logical schemas and performance of user applications strongly depends on logical and physical database structures. This work presents the entire process of performance-based quality evaluation of conceptual schemas. First, we show format. Then, the paper proposes a new specification of object algebra for representation of conceptual level database applications. Transformation of conceptual schemas and expression of object algebra into implementation schema and implementation in a particular database system allows for precise estimation of the processing costs of database applications and as a consequence for precise evaluation of performance-based quality of conceptual schemas. Then we describe an experiment as a proof of concept for the evaluation procedure presented in the paper.Keywords: conceptual schema, implementation schema, logical schema, object algebra, performance evaluation, query processing
Procedia PDF Downloads 28678 Primes as Sums and Differences of Two Binomial Coefficients and Two Powersums
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
Procedia PDF Downloads 9377 Students' Errors in Translating Algebra Word Problems to Mathematical Structure
Authors: Ledeza Jordan Babiano
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Translating statements into mathematical notations is one of the processes in word problem-solving. However, based on the literature, students still have difficulties with this skill. The purpose of this study was to investigate the translation errors of the students when they translate algebraic word problems into mathematical structures and locate the errors via the lens of the Translation-Verification Model. Moreover, this qualitative research study employed content analysis. During the data-gathering process, the students were asked to answer a six-item algebra word problem questionnaire, and their answers were analyzed by experts through blind coding using the Translation-Verification Model to determine their translation errors. After this, a focus group discussion was conducted, and the data gathered was analyzed through thematic analysis to determine the causes of the students’ translation errors. It was found out that students’ prevalent error in translation was the interpretation error, which was situated in the Attribute construct. The emerging themes during the FGD were: (1) The procedure of translation is strategically incorrect; (2) Lack of comprehension; (3) Algebra concepts related to difficulty; (4) Lack of spatial skills; (5) Unprepared for independent learning; and (6) The content of the problem is developmentally inappropriate. These themes boiled down to the major concept of independent learning preparedness in solving mathematical problems. This concept has subcomponents, which include contextual and conceptual factors in translation. Consequently, the results provided implications for instructors and professors in Mathematics to innovate their teaching pedagogies and strategies to address translation gaps among students.Keywords: mathematical structure, algebra word problems, translation, errors
Procedia PDF Downloads 4676 Learners’ Conspicuous and Significant Errors in Arithmetic
Authors: Michael Lousis
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The systematic identification of the most conspicuous and significant errors made by learners during three-years of testing of their progress in learning Arithmetic are presented in this article. How these errors have changed over three-years of school instruction of Arithmetic also is shown. The sample is comprised of two hundred (200) English students and one hundred and fifty (150) Greek students. These students were purposefully selected according to their participation in each testing session in the development of the three-year Kassel Project in England and Greece, in both domains simultaneously in Arithmetic and Algebra. The data sample includes six test-scripts corresponding to three testing sessions in both Arithmetic and Algebra respectively.Keywords: arithmetic, errors, Kassel Project, progress of learning
Procedia PDF Downloads 25975 Integral Domains and Alexandroff Topology
Authors: Shai Sarussi
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Let S be an integral domain which is not a field, let F be its field of fractions, and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R ∩ F = S and F R = A. A topological space whose set of open sets is closed under arbitrary intersections is called an Alexandroff space. Inspired by the well-known Zariski-Riemann space and the Zariski topology on the set of prime ideals of a commutative ring, we define a topology on the set of all S-nice subalgebras of A. Consequently, we get an interplay between Algebra and topology, that gives us a better understanding of the S-nice subalgebras of A. It is shown that every irreducible subset of S-nice subalgebras of A has a supremum; and a characterization of the irreducible components is given, in terms of maximal S-nice subalgebras of A.Keywords: Alexandroff topology, integral domains, Zariski-Riemann space, S-nice subalgebras
Procedia PDF Downloads 10374 Instructional Game in Teaching Algebra for High School Students: Basis for Instructional Intervention
Authors: Jhemson C. Elis, Alvin S. Magadia
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Our world is full of numbers, shapes, and figures that illustrate the wholeness of a thing. Indeed, this statement signifies that mathematics is everywhere. Mathematics in its broadest sense helps people in their everyday life that is why in education it is a must to be taken by the students as a subject. The study aims to determine the profile of the respondents in terms of gender and age, performance of the control and experimental groups in the pretest and posttest, impact of the instructional game used as instructional intervention in teaching algebra for high school students, significant difference between the level of performance of the two groups of respondents in their pre–test and post–test results, and the instructional intervention can be proposed. The descriptive method was also utilized in this study. The use of the certain approach was to that it corresponds to the main objective of this research that is to determine the effectiveness of the instructional game used as an instructional intervention in teaching algebra for high school students. There were 30 students served as respondents, having an equal size of the sample of 15 each while a greater number of female teacher respondents which totaled 7 or 70 percent and male were 3 or 30 percent. The study recommended that mathematics teacher should conceptualize instructional games for the students to learn mathematics with fun and enjoyment while learning. Mathematics education program supervisor should give training for teachers on how to conceptualize mathematics intervention for the students learning. Meaningful activities must be provided to sustain the student’s interest in learning. Students must be given time to have fun at the classroom through playing while learning since mathematics for them was considered as difficult. Future researcher must continue conceptualizing some mathematics intervention to suffice the needs of the students, and teachers should inculcate more educational games so that the discussion will be successful and joyful.Keywords: instructional game in algebra, mathematical intervention, joyful, successful
Procedia PDF Downloads 59173 Vehicle to Vehicle Communication: Collision Avoidance Scenarios
Authors: Ahmed Emad, Ahmed Salah, Abdelrahman Magdy, Omar Rashid, Mohammed Adel
Abstract:
This research paper discusses vehicle-to-vehicle technology as an important application of linear algebra. This communication technology represents an efficient and promising application to help to ensure the safety of the drivers by warning them when a crash possibility is close. The major link that combines our topic with linear algebra is the Laplacian matrix. Some main definitions used in the V2V were illustrated, such as VANET and its characteristics. The V2V technology could be applied in different applications with different traffic scenarios and various ways to warn car drivers. These scenarios were simulated programs such as MATLAB and Python to test how the V2V system would respond to the different scenarios and warn the car drivers exposed to the threat of collisions.Keywords: V2V communication, vehicle to vehicle scenarios, VANET, FCW, EEBL, IMA, Laplacian matrix
Procedia PDF Downloads 14972 A Proof of the N. Davydov Theorem for Douglis Algebra Valued Functions
Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes
Abstract:
The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae
Procedia PDF Downloads 245