Search results for: Boolean algebra

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

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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: Ming-Yang Guo, Cheng-Xian Wu, Wei-Xiang Chen, Chun-Yuan Lin, Yen-Jen Lin, Ann-Shyn Chiang

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With more and more Drosophila Driver and Neuron images, it is an important work to find the similarity relationships among them as the functional inference. There is a general problem that how to find a Drosophila Driver image, which can cover a set of Drosophila Driver/Neuron images. In order to solve this problem, the intersection/union region for a set of images should be computed at first, then a comparison work is used to calculate the similarities between the region and other images. In this paper, three encoding schemes, namely Integer, Boolean, Decimal, are proposed to encode each image as a one-dimensional structure. Then, the intersection/union region from these images can be computed by using the compare operations, Boolean operators and lookup table method. Finally, the comparison work is done as the union region computation, and the similarity score can be calculated by the definition of Tanimoto coefficient. The above methods for the region computation are also implemented in the multi-core CPUs environment with the OpenMP. From the experimental results, in the encoding phase, the performance by the Boolean scheme is the best than that by others; in the region computation phase, the performance by Decimal is the best when the number of images is large. The speedup ratio can achieve 12 based on 16 CPUs. This work was supported by the Ministry of Science and Technology under the grant MOST 106-2221-E-182-070.

Keywords: Drosophila driver image, Drosophila neuron images, intersection/union computation, parallel processing, OpenMP

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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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

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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

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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

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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

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Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

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Authors: Ahmed Emad, Ahmed Salah, Abdelrahman Magdy, Omar Rashid, Mohammed Adel

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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

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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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

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Authors: Abigail Gragg

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The goal of this research study was to adjudicate if implementing Howard Gardner’s multiple levels of intelligence would enhance student achievement levels in an Algebra 1 College Preparatory class. This was conducted within every class by incorporating one level of the eight levels of intelligence into small group work in stations. Every class was conducted utilizing small-group instruction. Achievement levels were measured through various forms of collected data that expressed student understandings in class through formative assessments versus student understandings on summative assessments. The data samples included: assessments (i.e. summative and formative assessments), observable data, video recordings, a daily log book, student surveys, and checklists kept during the observation periods. Formative assessments were analyzed during each class period to measure in-class understanding. Summative assessments were dissected per question per accuracy to review the effects of each intelligence implemented. The data was collated into a coding workbook for further analysis to conclude the resulting themes of the research. These themes include 1) there was no correlation to multiple levels of intelligence enhancing student achievement, 2) bodily-kinesthetic intelligence showed to be the intelligence that had the most improvement on test questions and 3) out of all of the bits of intelligence, interpersonal intelligence enhanced student understanding in class.

Keywords: stations, small group instruction, multiple levels of intelligence, Mathematics, Algebra 1, student achievement, secondary school, instructional Pedagogies

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Authors: Natália Maria Rego

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ALeibnizn-algebraGis aK-vector space endowed whit a n-linearbracket operation [-,…-] : GG … G→ Gsatisfying the fundamental identity, which can be expressed saying that the right multiplication map Ry2, …, ᵧₙ: Gn→ G, Rᵧ₂, …, ᵧₙn(ˣ¹, …, ₓₙ) = [[ˣ¹, …, ₓₙ], ᵧ₂, …, ᵧₙ], is a derivation. This structure, together with its skew-symmetric version, named as Lie n-algebra or Filippov algebra, arose in the setting of Nambumechanics, an n-ary generalization of the Hamiltonian mechanics. Thefirst goal of this work is to provide a characterization of various classes of central extensions of Leibniz n-algebras in terms of homological properties. Namely, Commutator extension, Quasi-commutator extension, Stem extension, and Stem cover. These kind of central extensions are characterized by means of the character of the map *(E): nHL1(G) → M provided by the five-term exact sequence in homology with trivial coefficients of Leibniz n-algebras associated to an extension E : 0 → M → K → G → 0. For a free presentation 0 →R→ F →G→ 0of a Leibniz n-algebra G,the term M(G) = (R[F,…n.., F])/[R, F,..n-1..,F] is called the Schur multiplier of G, which is a Baer invariant, i.e., it does not depend on the chosen free presentation, and it is isomorphic to the first Leibniz n-algebras homology with trivial coefficients of G. A central extension of Leibniz n-algebras is a short exact sequenceE : 0 →M→K→G→ 0such that [M, K,.. ⁿ⁻¹.., K]=0. It is said to be a stem extension if M⊆[G, .. n.., G]. Additionally, if the induced map M(K) → M(G) is the zero map, then the stem extension Eis said to be a stem cover. The second aim of this work is to analyze the interplay between stem covers of Leibniz n-algebras and the Schur multiplier. Concretely, in the case of finite-dimensional Leibniz n-algebras, we show the existence of coverings, and we prove that all stem covers with finite-dimensional Schur multiplier are isoclinic. Additionally, we characterize stem covers of perfect Leibniz n-algebras.

Keywords: leibniz n-algebras, central extensions, Schur multiplier, stem cover

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Authors: Yasaman Azarmjoo

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Since ancient times, it has been said that mathematics is the mother of all sciences and the foundation of basic concepts in every field and profession. It would be great if, after learning this subject, we could enable students to create games and activities based on the same mathematical concepts. This article explores the design of various mathematical activities in the form of games, utilizing different mathematical topics such as algebra, equations, binary systems, and one-to-one correspondence. The theoretical significance of this article lies in uncovering alternative approaches to teaching and learning mathematics. By employing creative and interactive methods such as game design, it challenges the traditional perception of mathematics as a difficult and laborious subject. The theoretical significance of this article lies in demonstrating that mathematics can be made more accessible and enjoyable, which can result in heightened interest and engagement in the subject. In general, this article reveals another aspect of mathematics.

Keywords: playing with mathematics, algebra and equations, binary systems, one-to-one correspondence

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Authors: Pascal Roubides

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The presentation proposed herein describes a research case study of a hybrid application of the competency-based education model best exemplified by Western Governor’s University, within the general temporal confines of an accelerated (8-week) term of a College Algebra course at the author’s institution. A competency-based model was applied to an accelerated online College Algebra course, built as an Open Educational Resources (OER) course, seeking quantifiable evidence of any differences in the academic achievement of students enrolled in the competency-based course and the academic achievement of the current delivery of the same course. Competency-based learning has been gaining in support in recent times and the author’s institution has also been involved in its own efforts to design and develop courses based on this approach. However, it is unknown whether there had been any research conducted to quantify evidence of the effect of this approach against traditional approaches prior to the author’s case study. The research question sought to answer in this experimental quantitative study was whether the online College Algebra curriculum at the author’s institution delivered via an OER-based competency-based model can produce statistically significant improvement in retention and success rates against the current delivery of the same course. Results obtained in this study showed that there is no statistical difference in the retention rate of the two groups. However, there was a statistically significant difference found between the rates of successful completion of students in the experimental group versus those in the control group.

Keywords: competency-based learning, online mathematics, online math education, online courses

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Authors: Kailash Ghimire, Manoj Thapa

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This study focuses on early identification of deficiencies in pre-required areas of students who are enrolled in College Algebra and Calculus I classes. The students were given pre-diagnostic tests on the first day of the class before they are provided with the syllabus. The tests consist of prerequisite, uniform and advanced content outlined by the University System of Georgia (USG). The results show that 48% of students in College Algebra are lacking prerequisite skills while 52% of Calculus I students are lacking prerequisite skills but, interestingly these students are prior exposed to uniform content and advanced content. The study is still in progress and this paper contains the outcome from Fall 2017 and Spring 2018. In this paper, early intervention used in these classes: two days vs three days meeting a week and students’ self-assessment using exam wrappers and their effectiveness on students’ learning will also be discussed. A result of this study shows that there is an improvement on Drop, Fail and Withdraw (DFW) rates by 7%-10% compared to those in previous semesters.

Keywords: student at risk, diagnostic tests, identification, intervention, normalization gain, validity of tests

Procedia PDF Downloads 180

Authors: Shouji Yujiro, Memei Dukovic, Mist Yakubu

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Fields are important objects of study in algebra since they provide a useful generalization of many number systems, such as the rational numbers, real numbers, and complex numbers. In particular, the usual rules of associativity, commutativity and distributivity hold. Fields also appear in many other areas of mathematics; see the examples below. When abstract algebra was first being developed, the definition of a field usually did not include commutativity of multiplication, and what we today call a field would have been called either a commutative field or a rational domain. In contemporary usage, a field is always commutative. A structure which satisfies all the properties of a field except possibly for commutativity, is today called a division ring ordivision algebra or sometimes a skew field. Also non-commutative field is still widely used. In French, fields are called corps (literally, body), generally regardless of their commutativity. When necessary, a (commutative) field is called corps commutative and a skew field-corps gauche. The German word for body is Körper and this word is used to denote fields; hence the use of the blackboard bold to denote a field. The concept of fields was first (implicitly) used to prove that there is no general formula expressing in terms of radicals the roots of a polynomial with rational coefficients of degree 5 or higher. An extension of a field k is just a field K containing k as a subfield. One distinguishes between extensions having various qualities. For example, an extension K of a field k is called algebraic, if every element of K is a root of some polynomial with coefficients in k. Otherwise, the extension is called transcendental. The aim of Galois Theory is the study of algebraic extensions of a field. Given a field k, various kinds of closures of k may be introduced. For example, the algebraic closure, the separable closure, the cyclic closure et cetera. The idea is always the same: If P is a property of fields, then a P-closure of k is a field K containing k, having property, and which is minimal in the sense that no proper subfield of K that contains k has property P. For example if we take P (K) to be the property ‘every non-constant polynomial f in K[t] has a root in K’, then a P-closure of k is just an algebraic closure of k. In general, if P-closures exist for some property P and field k, they are all isomorphic. However, there is in general no preferable isomorphism between two closures.

Keywords: field theory, mechanic maths, supertech, rolltech

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Authors: Vasileiou Apostolos, Theodosiou Chrysa, Tsitroulis Ioannis, Maris Fotios

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The severity of extreme phenomena is due to their ability to cause severe damage in a small amount of time. It has been observed that floods affect the greatest number of people and induce the biggest damage when compared to the total of annual natural disasters. The detection of potential flood-prone areas constitutes one of the fundamental components of the European Natural Disaster Management Policy, directly connected to the European Directive 2007/60. The aim of the present paper is to develop a new methodology that combines geographical information, fuzzy logic and multi-criteria evaluation methods so that the most vulnerable areas are defined. Therefore, ten factors related to geophysical, morphological, climatological/meteorological and hydrological characteristics of the basin were selected. Afterwards, two models were created to detect the areas pronest to flooding. The first model defined the gravitas of each factor using Analytical Hierarchy Process (AHP) and the final map of possible flood spots were created using GIS and Boolean Algebra. The second model made use of the fuzzy logic and GIS combination and a respective map was created. The application area of the aforementioned methodologies was in Ardas basin due to the frequent and important floods that have taken place these last years. Then, the results were compared to the already observed floods. The result analysis shows that both models can detect with great precision possible flood spots. As the fuzzy logic model is less time-consuming, it is considered the ideal model to apply to other areas. The said results are capable of contributing to the delineation of high risk areas and to the creation of successful management plans dealing with floods.

Keywords: analytical hierarchy process, flood prone areas, fuzzy logic, geographic information system

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Authors: Verónica Díaz Quezada

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The importance given to the development of the problem solving skill and the requirement to solve problems framed in mathematical or real life contexts, in practice, they are not evidence in relation to the teaching of proportional variations. This qualitative and descriptive study aims to (1) to improve problem solving ability of high school students in Chile, (ii) to elaborate and describe a didactic intervention strategy based on learning situations in proportional variations, focused on solving types of routine problems of various contexts and non-routine problems. For this purpose, participant observation was conducted, test of mathematics problems and an opinion questionnaire to thirty-six high school students. Through the results, the highest academic performance is evidenced in the routine problems of purely mathematical context, realistic, fantasy context, and non-routine problems, except in the routine problems of real context and compound proportionality problems. The results highlight the need to consider in the curriculum different types of problems in the teaching of mathematics that relate the discipline to everyday life situations

Keywords: algebra, high school, proportion variations, nonroutine problem solving, routine problem solving

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Authors: Urbánek Jiří J., Krahulec Josef, Urbánek Jiří F., Johanidesová Jitka

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These Computational assistance for the research and modelling of critical infrastructure subjects continuity deal with this paper. It enables us the using of prevailing operation system MS Office (SmartArt...) for mathematical models, using DYVELOP (Dynamic Vector Logistics of Processes) method. It serves for crisis situations investigation and modelling within the organizations of critical infrastructure. In the first part of the paper, it will be introduced entities, operators and actors of DYVELOP method. It uses just three operators of Boolean algebra and four types of the entities: the Environments, the Process Systems, the Cases and the Controlling. The Process Systems (PrS) have five “brothers”: Management PrS, Transformation PrS, Logistic PrS, Event PrS and Operation PrS. The Cases have three “sisters”: Process Cell Case, Use Case and Activity Case. They all need for the controlling of their functions special Ctrl actors, except ENV – it can do without Ctrl. Model´s maps are named the Blazons and they are able mathematically - graphically express the relationships among entities, actors and processes. In the second part of this paper, the rich blazons of DYVELOP method will be used for the discovering and modelling of the cycling cases and their phases. The blazons need live PowerPoint presentation for better comprehension of this paper mission. The crisis management of energetic crisis infrastructure organization is obliged to use the cycles for successful coping of crisis situations. Several times cycling of these cases is a necessary condition for the encompassment of the both the emergency event and the mitigation of organization´s damages. Uninterrupted and continuous cycling process bring for crisis management fruitfulness and it is a good indicator and controlling actor of organizational continuity and its sustainable development advanced possibilities. The research reliable rules are derived for the safety and reliable continuity of energetic critical infrastructure organization in the crisis situation.

Keywords: blazons, computational assistance, DYVELOP method, critical infrastructure

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Authors: Sanjeev Sharma, Suman Lata

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With the availability of diverse printed, electronic literature and web sites on medical and health related information, it is impossible for the medical professional to get the information he seeks in the shortest possible time. For all these problems information literacy is the only solution. Thus, information literacy is recognized as an important aspect of medical education. In the present study, an attempt has been made to know the information literacy skills of the faculty and students at medical colleges of Haryana, Punjab and Chandigarh. The scope of the study was confined to the 12 selected medical colleges of three States (Haryana, Punjab, and Chandigarh). The findings of the study were based on the data collected through 1018 questionnaires filled by the respondents of the medical colleges. It was found that Online Medical Websites (such as WebMD, eMedicine and Mayo Clinic etc.) were frequently used by 63.43% of the respondents of Chandigarh which is slightly more than Haryana (61%) and Punjab (55.65%). As well, 30.86% of the respondents of Chandigarh, 27.41% of Haryana and 27.05% of Punjab were familiar with the controlled vocabulary tool; 25.14% respondents of Chandigarh, 23.80% of Punjab, 23.17% of Haryana were familiar with the Boolean operators; 33.05% of the respondents of Punjab, 28.19% of Haryana and 25.14% of Chandigarh were familiar with the use and importance of the keywords while searching an electronic database; and 51.43% of the respondents of Chandigarh, 44.52% of Punjab and 36.29% of Haryana were able to make effective use of the retrieved information. For accessing information in electronic format, 47.74% of the respondents rated their skills high, while the majority of respondents (76.13%) were unfamiliar with the basic search technique i.e. Boolean operator used for searching information in an online database. On the basis of the findings, it was suggested that a comprehensive training program based on medical professionals information needs should be organized frequently. Furthermore, it was also suggested that information literacy may be included as a subject in the health science curriculum so as to make the medical professionals information literate and independent lifelong learners.

Keywords: information, information literacy, medical professionals, medical colleges

Procedia PDF Downloads 115

Authors: David C. Ni

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The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: general relativity, quantum mechanics, string theory, duality, symmetry, correspondence, algebra, momentum-angular-momentum

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Authors: Saqib Rasool, Adnan N. Mian

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Web components are introduced as the latest standard of HTML5 for writing modular web interfaces for ensuring maintainability through the isolated scope of web components. Reusability can also be achieved by sharing plug-and-play web components that can be used as off-the-shelf components by other developers. A web component encapsulates all the required HTML, CSS and JavaScript code as a standalone package which must be imported for integrating a web component within an existing web interface. It is then followed by the integration of web component with the web services for dynamically populating its content. Since web components are reusable as off-the-shelf components, these must be equipped with some mechanism for ensuring their proper integration with web services. The consistency of a service behavior can be verified through type-checking. This is one of the popular solutions for improving the quality of code in many programming languages. However, HTML does not provide type checking as it is a markup language and not a programming language. The contribution of this work is to introduce a new extension of HTML called Service Type-checking Markup Language (STML) for adding support of type checking in HTML for JSON based REST services. STML can be used for defining the expected data types of response from JSON based REST services which will be used for populating the content within HTML elements of a web component. Although JSON has five data types viz. string, number, boolean, object and array but STML is made to supports only string, number and object. This is because of the fact that both object and array are considered as string, when populated in HTML elements. In order to define the data type of any HTML element, developer just needs to add the custom STML attributes of st-string, st-number and st-boolean for string, number and boolean respectively. These all annotations of STML are used by the developer who is writing a web component and it enables the other developers to use automated type-checking for ensuring the proper integration of their REST services with the same web component. Two utilities have been written for developers who are using STML based web components. One of these utilities is used for automated type-checking during the development phase. It uses the browser console for showing the error description if integrated web service is not returning the response with expected data type. The other utility is a Gulp based command line utility for removing the STML attributes before going in production. This ensures the delivery of STML free web pages in the production environment. Both of these utilities have been tested to perform type checking of REST services through STML based web components and results have confirmed the feasibility of evaluating service behavior only through HTML. Currently, STML is designed for automated type-checking of integrated REST services but it can be extended to introduce a complete service testing suite based on HTML only, and it will transform STML from Service Type-checking Markup Language to Service Testing Markup Language.

Keywords: REST, STML, type checking, web component

Procedia PDF Downloads 224

Authors: Soofia Malik

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The purpose of this study is to develop an instrument to measure undergraduate students’ attitudes toward mathematics (MAT) and to assess the data collected from the instrument for validity and reliability. The instrument is developed using five subscales: anxiety, enjoyment, self-confidence, value, and technology. The technology dimension is added as the fifth subscale of attitude toward mathematics because of the recent trend of incorporating online homework in mathematics courses as well as due to heavy reliance of higher education on using online learning management systems, such as Blackboard and Moodle. The sample consists of 163 (M = 82, F = 81) undergraduates enrolled in College Algebra course in the summer 2017 semester at a university in the USA. The data is analyzed to answer the research question: if and how do undergraduate students’ attitudes toward mathematics load using Principal Components Analysis (PCA)? As a result of PCA, three subscales emerged namely: anxiety/self-confidence scale, enjoyment, and value scale. After deleting the last five items or the last two subscales from the initial MAT scale, the Cronbach’s alpha was recalculated using the scores from 20 items and was found to be α = .95. It is important to note that the reliability of the initial MAT form was α = .93. This means that employing the final MAT survey form would yield consistent results in repeated uses. The final MAT form is, therefore, more reliable as compared to the initial MAT form.

Keywords: college algebra, Cronbach's alpha reliability coefficient, Principal Components Analysis, PCA, technology in mathematics

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Authors: M. H. M. Rashid

Abstract:

Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge transform

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Authors: A. Belmeguenai, K. Mansouri, R. Djemili

Abstract:

This work present a new algorithm based on the nonlinear filter generator for speech encryption and decryption. The proposed algorithm consists on the use a linear feedback shift register (LFSR) whose polynomial is primitive and nonlinear Boolean function. The purpose of this system is to construct Keystream with good statistical properties, but also easily computable on a machine with limited capacity calculated. This proposed speech encryption scheme is very simple, highly efficient, and fast to implement the speech encryption and decryption. We conclude the paper by showing that this system can resist certain known attacks.

Keywords: nonlinear filter generator, stream ciphers, speech encryption, security analysis

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Authors: Shai Sarussi

Abstract:

Suppose F is a field with valuation v and valuation domain Oᵥ, and R is an Oᵥ-algebra. It is known that there exists a filter quasi-valuation on R; the existence of a quasi-valuation yields several important connections between Oᵥ and R, in particular with respect to their prime spectra. In this paper, the notion of a module valuation is introduced. It is shown that any torsion-free module over Oᵥ has an induced module valuation. Moreover, several results connecting the filter quasi-valuation and module valuations are presented.

Keywords: valuations, quasi-valuations, prime spectrum, algebras over valuation domains

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Authors: Kankeyanathan Kannan

Abstract:

On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

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Authors: Abdelkader Hadjoudja, Hajar Bouazza

Abstract:

The PLD/CPLD devices are widely used for logic synthesis since several decades. Based on sum of product terms (PTs) architecture, the PLD/CPLD offer a high degree of flexibility to support various application requirements. They are suitable for large combinational logic, finite state machines as well as intensive I/O designs. CPLDs offer very predictable timing characteristics and are therefore ideal for critical control applications. This paper describes how the logic synthesis techniques, such as 1) XOR detection, 2) logic doubling, 3) complement of a Boolean function are combined, applied and used to optimize the CPLDs devices architecture that is based on PAL-like macrocells. Our goal is to use these techniques for minimizing the number of macrocells required to implement a circuit and minimize the delay of mapped circuit.

Keywords: CPLD, doubling, optimization, XOR

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Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. A characterization of the property of immediate neighbors in an Alexandroff topological space is given, in terms of closed and open subsets of appropriate subspaces. Moreover, two special subspaces of W are introduced, and a way in which their closed and open subsets induce W is presented.

Keywords: integral domains, Alexandroff topology, immediate neighbors, valuation domains

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