Search results for: algebraic fractions

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

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Authors: Abdul Hakim Khan

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The aim of the present paper is to study the Banach Space and Combinatorial Algebraic Structure of R. It is further aimed to study algebraic structure of set of all q-extension of classical formula and function for 0 < q < 1.

Keywords: integral functions, q-extensions, q numbers of metric space, algebraic structure of r and banach space

Procedia PDF Downloads 544

Authors: Liliana O. Martínez, Juan E González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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A serious game category mobile application called Math Dominoes is presented. The main objective of this applications is to strengthen the teaching-learning process of solving algebraic equations and is based on the board game "Double 6" dominoes. Math Dominoes allows the practice of solving first, second-, and third-degree algebraic equations. This application is aimed to students who seek to strengthen their skills in solving algebraic equations in a dynamic, interactive, and fun way, to reduce the risk of failure in subsequent courses that require mastery of this algebraic tool.

Keywords: algebra, equations, dominoes, serious games

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Authors: Shai Sarussi

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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. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: integral domains, Alexandroff topology, prime spectrum of a ring, valuation domains

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Authors: Nur Azlina Mohamed Mokmin, Mona Masood

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Guided by the theory of learning style, this study is based on the development of a multimedia learning application for students with mastery learning style. The learning material was developed by applying a graduated difficulty learning strategy. Algebraic fraction was chosen as the learning topic for this application. The effectiveness of this application in helping students learn is measured by giving a pre- and post-test. The result shows that students who learn using the learning material that matches their preferred learning style performs better than the students with a non-personalized learning material.

Keywords: algebraic fractions, graduated difficulty, mastery learning style, multimedia

Procedia PDF Downloads 473

Authors: F. Belkhiri, A. Baghiani, S. Boumerfeg, N. Charef, S. Khennouf, L. Arrar

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The present study was conducted to evaluate the in vitro antioxidant and antibacterial properties of methanolic extracts from roots of Tamus communis L. (TCRE), which is a plant used in traditional medicine in Algeria. The antioxidant potential of pattern was evaluated using tow complementary techniques, inhibition of free radical DPPH and the test of β-Carotene/linoleic acid. The antioxidant test indicates that non-polar fractions of TCRE (chloroform and ethyl acetate fractions) were more active than the polar fractions. Among these fractions, the chloroform extract appear in the DPPH test an IC50 of (18.89 µg/ml) comparable to that of BHT (18.6 µg/ml). This fraction was able to inhibiting the oxidation of β-Carotene with a percentage of inhibition (89.84 %). In antibacterial test, non-polar fractions showed antibacterial activity very important compared with the polar fractions. These fractions have inhibited the growth of four from nine bacterial strains, causing zones of inhibition from 08 to 23 mm of diameter.

Keywords: antioxidant activity, antibacterial activity, Tamus communis L., polar fractions

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Authors: M. Boháč, R. Novotný, F. Frajkorová, R. S. Yadav, T. Opravil, M. Palou

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Properties of Portland cement mixtures with various fractions of metakaolin were studied. 10 % of Portland cement CEM I 42.5 R was replaced by different fractions of high reactivity metakaolin with defined chemical and mineralogical properties. Various fractions of metakaolin were prepared by jet mill classifying system. There is a clear trend between fineness of metakaolin and hydration heat development. Due to metakaolin presence in mixtures the compressive strength development of mortars is rather slower for coarser fractions but 28-day flexural strengths are improved for all fractions of metakaoline used in mixtures compared to reference sample of pure Portland cement. Yield point, plastic viscosity and adhesion of fresh pastes are considerably influenced by fineness of metakaolin used in cement pastes.

Keywords: calorimetry, cement, metakaolin fineness, rheology, strength

Procedia PDF Downloads 382

Authors: P. S. Jagadeesh Kumar, S. Meenakshi Sundaram, Wenli Hu, Yang Yung

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In 3D video games, the dominance of production is unceasingly growing with a protruding level of affordability in terms of budget. Afterward, the automation of speech-lip synchronization technique is customarily onerous and has advanced a critical research subject in virtual reality based 3D video games. This paper presents one of these automatic tools, precisely riveted on the synchronization of the speech and the lip movement of the game characters. A robust and precise speech recognition segment that systematized with Algebraic Code Excited Linear Prediction method is developed which unconventionally delivers lip sync results. The Algebraic Code Excited Linear Prediction algorithm is constructed on that used in code-excited linear prediction, but Algebraic Code Excited Linear Prediction codebooks have an explicit algebraic structure levied upon them. This affords a quicker substitute to the software enactments of lip sync algorithms and thus advances the superiority of service factors abridged production cost.

Keywords: algebraic code excited linear prediction, speech-lip synchronization, video games, virtual reality

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Authors: U. M. Swamy

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A compact Hausdorff and totally disconnected topological space are known as Boolean space in view of the stone duality between Boolean algebras and such topological spaces. A sheaf over X is a triple (S, p, X) where S and X are topological spaces and p is a local homeomorphism of S onto X (that is, for each element s in S, there exist open sets U and G containing s and p(s) in S and X respectively such that the restriction of p to U is a homeomorphism of U onto G). Here we mainly concern on sheaves over Boolean spaces. From a given sheaf over a Boolean space, we obtain an algebraic structure in such a way that there is a one-to-one correspondence between these algebraic structures and sheaves over Boolean spaces.

Keywords: Boolean algebra, Boolean space, sheaf, stone duality

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Authors: Chahinez Ait Si Said, Ouassila Touafek, Mohamed Reda Zahi, Smain Sabour, ‎Mohamed El Hattab ‎

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Oil mill wastewater (OMW) is a major effluent of the olive industry resulting from olive ‎oil extraction which is a great source for the development of new drugs. The present ‎study aimed to evaluate the antimicrobial activity of seven different fractions separated ‎from OMW extract. The sample was recovered from an oil mill in the Blida region ‎‎(Algeria). A crude ethyl acetate extract was prepared from OMW according to a well-‎established protocol; the yield of the extract obtained was 4%. From the extract, ‎different fractions were prepared by fractionating the total extract with an open column ‎chromatography. The obtained fractions were submitted to antimicrobial activity ‎screening in a comparative purpose. All the fractions obtained show great antimicrobial ‎potential. ‎Phytochemical study of the different fractions was assessed by evaluating the total ‎phenolic compounds for all fractions studied as the main compounds found in OMW ‎were phenols like hydroxytyrosol, tyrosol, phenolic acids like caffeic, quinic and ferulic ‎acids which show great therapeutic activities. ‎

Keywords: olive mill wastewater, fractionation, total phenolic compound, antimicrobial activity

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Authors: O. M. Bamigbola, A. A. Ibrahim

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Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined a priori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss-Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss-Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: linear algebraic system, Gauss-Seidel iteration, algebraic structure, convergence

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Authors: Malika Elkyal

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We consider an iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm does not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

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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

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Authors: Marc Diesse, Hochschule Heilbronn

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We address the question of identifying the configuration space singularities of linkages, i.e., points where the configuration space is not locally a submanifold of Euclidean space. Because the configuration space cannot be smoothly parameterized at such points, these singularity types have a significantly negative impact on the kinematics of the linkage. It is known that Jacobian methods do not provide sufficient conditions for the existence of CS-singularities. Herein, we present several additional algebraic criteria that provide the sufficient conditions. Further, we use those criteria to analyze certain classes of planar linkages. These examples will also show how the presented criteria can be checked using algorithmic methods.

Keywords: linkages, configuration space-singularities, real algebraic geometry, analytic geometry

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Authors: Mohammad K. Parvez, Ahmed H. Arbab, Mohammed S. Al-Dosari

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Cyperus rotendus rhizomes are used as traditional medicine, including Ayurveda in chronic liver diseases and hepatitis B. We investigated the in vitro hepatoprotective and anti-hepatitis B virus (HBV) potential of Cyperus rotundus rhizome organic and aqueous fractions. Of these, the n-butanol and aqueous fractions showed the most promising, dose-dependent hepatoprotection in DCFH-injured HepG2 cells at 48 h. DCFH-toxicated cells were recovered to about 88% and 96%, upon treatment with n-butanol and aqueous fractions (200 g/ml), respectively compared to DCFH-only treated cells. Further, C. rotundus fractions were tested for anti-HBV activities by measuring the expression levels of viral antigens (HBsAg and HBeAg) in the HepG2.2.15 culture supernatants. At 48 h post-treatment, the ethyl acetate, n-butanol and aqueous fractions showed dose-dependent inhibition wherein at a higher dose (100 g/ml), HBsAg production was reduced to 60.27%, 46.87 and 42.76%, respectively. In a time-course study, HBsAg production was inhibited up to 50% and 40% by ethyl acetate and n-butanol fractions (100 g/ml), respectively on day 5. Three three active fractions were further subjected to time-dependent inhibition of HBeAg expression, an indirect measure of HBV active DNA replication. At day 5 post-treatment, ethyl acetate and n-butanol fractions downregulated HBV replication by 44.14% and 24.70%, respectively. In conclusion, our results showed very promising hepatoprotective and anti-HBV potential of C. rotendus tubers fractions in vitro. Our data could, therefore, provide the basis for the claimed traditional use of C. rotendus for jaundice and hepatitis.

Keywords: anti-hepatitis B, cyperus rotundus, hepatitis B virus, hepatoprotection

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Authors: Shigeyuki Haruyama, Ken Kaminishi, Junji Kaneko, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physics fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: system model, physical models, empirical models, conservation law, differential algebraic equation, object-oriented

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Authors: Nileshkumar Vishnav, Aditya Tatu

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A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

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Authors: Fatbardhë Kurti, Giangiacomo Beretta, Behxhet Mustafa, Fabrizio Gelmini, Avni Hajdari

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Chemical profile, antioxidant and antimicrobial activity of total and fractionated essential oils (EOs) (F1 – hexane, F2 – hexane/diethyl ether, F3 – diethyl ether) derived from five Pinus species (Pinus heldreichii, P. peuce, P. mugo, Pinus nigra, P. sylvestris), were investigated. The hydrodistilled EOs and their chromatographic fractions (direct solid phase extraction, SPE) were analysed by GC-MS and 112 compounds separated and identified. The main constituents were α-pinene, β-pinene, D-limonene, β-caryophyllene, germacrene D, bornyl acetate and 3-carene. The antioxidant activities of total EOs were lower than those of the corresponding fractions, with F2 the strongest in all cases. EOs and fractions showed different degrees of antibacterial efficacy against different microbial pathogens (moderately strong antimicrobial activity against C. albicans and C. krusei ,while low or no activity against E. faecalis and E. coli strains). The detected inhibition zones and MICs for the EOs and fractions were in the range of 14 -35 mm and 0.125 - 1% (v/v), respectively. The components responsible for the antioxidant and antimicrobial activity were oxygenated monoterpenes and sesquiterpenes recovered in the polar EO fractions. These activities seem to be regulated by reciprocal interactions among the different subclasses of phytochemical species present in the EOs.

Keywords: antagonism, antioxidant activity, antibacterial activity, essential oil, fractions, GC-MS, pinus

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Authors: A. Adetutu, T. M. Awodugba, O. A. Owoade

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The development of resistance to currently known conventional anti-typhoid drugs has necessitated search into cheap, more potent and less toxic anti-typhoid drugs of plant origin. Therefore, this study investigated the anti-typhoid activity of fractions of A. indica in Salmonella typhi infected rats. Leaves of A. indica were extracted in methanol and fractionated into n-hexane, chloroform, ethyl-acetate, and aqueous fractions. The anti-salmonella potentials of fractions of A. indica were assessed via in-vitro inhibition of S. typhi using agar well diffusion, Minimum Inhibitory Concentration (MIC), Minimum Bactericidal Concentration (MBC) and biofilm assays. The biochemical and haematological parameters were determined by spectrophotometric methods. The histological analysis was performed using Haematoxylin and Eosin staining methods. Data analysis was performed by one-way ANOVA. Results of this study showed that S. typhi was sensitive to aqueous and chloroform fractions of A. indica, and the fractions showed biofilm inhibition at concentrations of 12.50, 1.562, and 0.39 mg/mL. In the in-vivo study, the extract and chloroform fraction had significant (p < 0.05) effects on the number of viable S. typhi recovered from the blood and stopped salmonellosis after 6 days of treatment of rats at 500 mg/kg b.w. Treatments of infected rats with chloroform and aqueous fractions of A. indica normalized the haematological parameters in the animals. Similarly, treatment with fractions of the plants sustained a normal antioxidant status when compared with the normal control group. Chloroform and ethyl-acetate fractions of A. indica reversed the liver and intestinal degeneration induced by S. typhi infection in rats. The present investigation indicated that the aqueous and chloroform fractions of A. indica showed the potential to provide an effective treatment for salmonellosis, including typhoid fever. The results of the study may justify the ethno-medicinal use of the extract in traditional medicine for the treatment of typhoid and salmonella infections.

Keywords: Azadirachta indica L, salmonella, typhoid, leave fractions

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Authors: Krish Jhurani

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The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications.

Keywords: eigenspaces, eigenvectors, invariant subspaces, near-rings, non-canonical scalar multiplication, semirings, symmetry properties

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Authors: Oscar Corredor, Alexander Guzman, Adan Leon

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Density is a bulk physical property that indicates the quality of a petroleum fraction. It is also a useful property to estimate various physicochemical properties of fraction and petroleum fluids; however, the determination of density of extra heavy residual (EHR) fractions by standard methodologies, (ASTM D70) shows limitations for samples with higher densities than 1.0879 g/cm3. For this reason, a dilution methodology was developed in order to determinate density for those particular fractions, 87 (EHR) fractions were obtained as products of the fractionation of Colombian typical Vacuum Distillation Residual Fractions using molecular distillation (MD) and extraction with Solvent N-hexane in Supercritical Conditions (SFEF) pilot plants. The proposed methodology showed reliable results that can be demonstrated with the standard deviation of repeatability and reproducibility values of 0.0031 and 0.0061 g/ml respectively. In the same way, it was possible to determine densities in fractions EHR up to 1.1647g/cm3 and °API values obtained were ten times less than the water reference value.

Keywords: API, density, vacuum residual, molecular distillation, supercritical fluid extraction

Procedia PDF Downloads 243

Authors: Faiza Abdul Latip

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One of the ultimate goals of any nation is to produce competitive manpower and this includes Philippines. Inclination in the field of Mathematics has a significant role in achieving this goal. However, Mathematics, as considered by most people, is the most difficult subject matter along with its topics to learn. This could be manifested from the low performance of students in national and international assessments. Educators have been widely using learning style models in identifying the way students learn. Moreover, it could be the frontline in knowing the difficulties held by each learner in a particular topic specifically concepts pertaining to fractions. However, as what many educators observed, students show difficulties in doing mathematical tasks and in great degree in dealing with fractions most specifically in the district of Datu Odin Sinsuat, Maguindanao. This study focused on the Datu Odin Sinsuat district grade six pupils’ learning styles along with their achievements and difficulties in learning concepts on fractions. Five hundred thirty-two pupils from ten different public elementary schools of the Datu Odin Sinsuat districts were purposively used as the respondents of the study. A descriptive research using the survey method was employed in this study. Quantitative analysis on the pupils’ learning styles on the Kolb’s Learning Style Inventory (KLSI) and scores on the mathematics diagnostic test on fraction concepts were made using this method. The simple frequency and percentage counts were used to analyze the pupils’ learning styles and their achievements on fractions. To determine the pupils’ difficulties in fractions, the index of difficulty on every item was determined. Lastly, the Kruskal-Wallis Test was used in determining the significant difference in the pupils’ achievements on fractions classified by their learning styles. This test was set at 0.05 level of significance. The minimum H-Value of 7.82 was used to determine the significance of the test. The results revealed that the pupils of Datu Odin Sinsuat districts learn fractions in varied ways as they are of different learning styles. However, their achievements in fractions are low regardless of their learning styles. Difficulties in learning fractions were found most in the area of Estimation, Comparing/Ordering, and Division Interpretation of Fractions. Most of the pupils find it very difficult to use fraction as a measure, compare or arrange series of fractions and use the concept of fraction as a quotient.

Keywords: difficulties in fraction, fraction, Kolb's model, learning styles

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Authors: Duygu Özdemir, Bilal Özçakır

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Usage of augmented reality in education helps students to make sense of the three-dimensional world of mathematics. In this study, it was aimed to develop activities about fractions for 5th-grade students by augmented reality and also aimed to assess these activities in terms of students’ understanding and views. Data obtained from 60 students in a private school in Marmaris, Turkey was obtained through classroom observations, students’ worksheets and semi-structured interviews during two weeks. Data analysis was conducted by using constant-comparative analysis which leads to meaningful categories of findings. Findings of this study indicated that usage of augmented reality is a facilitator to make concretize and provide real-life application for fractions. Moreover, students’ opinions about its usage were lead to categories as benefit for learning, enjoyment and creating awareness of usage of augmented reality in mathematics education. In general, this study could be a bridge to show the contributions of augmented reality applications to mathematics education and also highlights that augmented reality could be used with subjects like fractions rather than subjects only in geometry learning domain.

Keywords: augmented reality, mathematics, fractions, students

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Authors: Marek Dlapa

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The algebraic approach is applied to the control of the HiMAT (Highly Maneuverable Aircraft Technology). The objective is to find a robust controller which guarantees robust stability and decoupled control of longitudinal model of a scaled remotely controlled vehicle version of the advanced fighter HiMAT. Control design is performed by decoupling the nominal MIMO (multi-input multi-output) system into two identical SISO (single-input single-output) plants which are approximated by a 4th order transfer function. The algebraic approach is then used for pole placement design, and the nominal closed-loop poles are tuned so that the peak of the µ-function is minimal. As an optimization tool, evolutionary algorithm Differential Migration is used in order to overcome the multimodality of the cost function yielding simple controller with decoupling for nominal plant which is compared with the D-K iteration through simulations of standard longitudinal manoeuvres documenting decoupled control obtained from algebraic approach for nominal plant as well as worst case perturbation.

Keywords: algebraic approach, evolutionary computation, genetic algorithms, HiMAT, robust control, structured singular value

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Authors: Tanwi Priya, Brijesh Kumar Mishra

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Occurrence of aromatic fractions of Natural Organic Matter (NOM) led to formation of carcinogenic disinfection by products such as trihalomethanes in chlorinated water. In the present study, the efficiency of aluminium based electrocoagulation on the removal of prominent aromatic groups such as phenol, hydrophobic auxochromes, and carboxyl groups from NOM enriched synthetic water has been evaluated using various spectral indices. The effect of electrocoagulation on turbidity has also been discussed. The variation in coagulation performance as a function of pH has been studied. Our result suggests that electrocoagulation can be considered as appropriate remediation approach to reduce trihalomethanes formation in water. It has effectively reduced hydrophobic fractions from NOM enriched low turbid water. The charge neutralization and enmeshment of dispersed colloidal particles inside metallic hydroxides is the possible mechanistic approach in electrocoagulation.

Keywords: aromatic fractions, electrocoagulation, natural organic matter, spectral indices

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Authors: Vakamalla Teja Reddy, Narasimha Mangadoddy

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Hydrocyclones are used to separate particles into different size fractions in the mineral processing, chemical and metallurgical industries. High speed video imaging, Laser Doppler Anemometry (LDA), X-ray and Gamma ray tomography are previously used to measure the two-phase flow characteristics in the cyclone. However, investigation of solids flow characteristics inside the cyclone is often impeded by the nature of the process due to slurry opaqueness and solid metal wall vessels. In this work, a dual-plane high speed Electrical resistance tomography (ERT) is used to measure hydrocyclone internal flow dynamics in situ. Experiments are carried out in 3 inch hydrocyclone for feed solid concentrations varying in the range of 0-50%. ERT data analysis through the optimized FEM mesh size and reconstruction algorithms on air-core and solid concentration tomograms is assessed. Results are presented in terms of the air-core diameter and solids volume fraction contours using Maxwell’s equation for various hydrocyclone operational parameters. It is confirmed by ERT that the air core occupied area and wall solids conductivity levels decreases with increasing the feed solids concentration. Algebraic slip mixture based multi-phase computational fluid dynamics (CFD) model is used to predict the air-core size and the solid concentrations in the hydrocyclone. Validation of air-core size and mean solid volume fractions by ERT measurements with the CFD simulations is attempted.

Keywords: air-core, electrical resistance tomography, hydrocyclone, multi-phase CFD

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Authors: Mohammad Esmaeilpour

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One of the important open problems in the field of medical image processing is detection and quantification of small changes. In this poster, we try to investigate that, how the algebraic decomposition techniques can be used for semiautomatically detecting and quantifying subtle changes in Magnetic Resonance (MR) neuroimaging volumes. We mostly focus on the low-rank values of the matrices achieved from decomposing MR image pairs during a period of time. Besides, a skillful neuroradiologist will help the algorithm to distinguish between noises and small changes.

Keywords: magnetic resonance neuroimaging, subtle change detection and quantification, algebraic decomposition, basis functions

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Authors: Mohd Farooq Naqshbandi

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The four fractions of aqueous extract of Sesame Seeds (Sesamum indicum L.) were studied for invitro DNA fragmentation, cell migration, and cellular apoptosis on SW480 and HTC116 human colorectal cancer cell lines. The seeds of Sesamum indicum were extracted with six solvents, including Methanol, Ethanol, Aqueous, Chloroform, Acetonitrile, and Hexane. The aqueous extract (IC₅₀ value 154 µg/ml) was found to be the most active in terms of cytotoxicity with SW480 human colorectal cancer cell lines. Further fractionation of this aqueous extract on flash chromatography gave four fractions. These four fractions were studied for anticancer and DNA binding studies. Cell viability was assessed by colorimetric assay (MTT). IC₅₀ values for all these four fractions ranged from 137 to 548 µg/mL for the HTC116 cancer cell line and 141 to 402 µg/mL for the SW480 cancer cell line. The four fractions showed good anticancer and DNA binding properties. The DNA binding constants ranged from 10.4 ×10⁴ 5 to 28.7 ×10⁴, showing good interactions with DNA. The DNA binding interactions were due to intercalative and π-π electron forces. The results indicate that aqueous extract fractions of sesame showed inhibition of cell migration of SW480 and HTC116 human colorectal cancer cell lines and induced DNA fragmentation and apoptosis. This was demonstrated by calculating the low wound closure percentage in cells treated with these fractions as compared to the control (80%). Morphological features of nuclei of cells treated with fractions revealed chromatin compression, nuclear shrinkage, and apoptotic body formation, which indicate cell death by apoptosis. The flow cytometer of fraction-treated cells of SW480 and HTC116 human colorectal cancer cell lines revealed death due to apoptosis. The results of the study indicate that aqueous extract of sesame seeds may be used to treat colorectal cancer.

Keywords: Sesamum indicum, cell migration inhibition, apoptosis induction, anticancer activity, colorectal cancer

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Authors: S. R. Nayaka, Putta Swamy

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Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

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Authors: S. R. Santhanam

Abstract:

A gifted child is one who gives evidence of creativity, good memory, rapid learning. In mathematics, a teacher often comes across some gifted children and they exhibit the following characteristics: unusual alertness, enjoying solving problems, getting bored on repetitions, self-taught, going beyond what teacher taught, ask probing questions, connecting unconnected concepts, vivid imagination, readiness for research work, perseverance of a topic. There are two main areas of research carried out on them: 1)identifying gifted children, 2) interacting and channelizing them. A lack of appropriate recognition will lead the gifted child demotivated. One of the main findings is if proper attention and nourishment are not given then it leads a gifted child to become depressed, underachieving, fail to reach their full potential and sometimes develop negative attitude towards school and study. After identifying them, a mathematics teacher has to develop them into a fall fledged achiever. The responsibility of the teacher is enormous. The teacher has to be resourceful and patient. But interacting with them one finds a lot of surprises and awesomeness. The elementary algebraic identities like (a+b)(a-b)=a²-b², expansion of like (a+b)²(a-b)² and others are taught to students, of age group 13-15 in India. An average child will be satisfied with a single proof and immediate application of these identities. But a gifted child expects more from the teacher and at one stage after a little training will surpass the teacher also. In this short paper, the author shares his experience regarding teaching algebraic identities to gifted children. The following problem was given to a set of 10 gifted children of the specified age group: If a natural number ‘n’ to expressed as the sum of the two squares, will 2n also be expressed as the sum of two squares? An investigation has been done on what multiples of n satisfying the criterion. The attempts of the gifted children were consolidated and conclusion was drawn. A second problem was given to them as: can two natural numbers be found such that the difference of their square is 3? After a successful solution, more situations were analysed. As a third question, the finding of the sign of an algebraic expression in three variables was analysed. As an example: if a,b,c are real and unequal what will be sign of a²+4b²+9c²-4ab-12bc-6ca? Apart from an expression as a perfect square what other methods can be employed to prove an algebraic expression as positive negative or non negative has been analysed. Expressions like 4x²+2y²+13y²-2xy-4yz-6zx were given, and the children were asked to find the sign of the expression for all real values of x,y and z. In all investigations, only basic algebraic identities were used. As a next probe, a divisibility problem was initiated. When a,b,c are natural numbers such that a+b+c is at least 6, and if a+b+c is divisible by 6 then will 6 divide a³+b³+c³. The gifted children solved it in two different ways.

Keywords: algebraic identities, gifted children, Indian scenario, research

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