Search results for: symmetry concepts

Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Mihriban Hacisalihoğlu Karadeniz, Figen Bozkuş, Tuğba Baran, Ümit Akar

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Creating the correct symmetry of conceptual knowledge about students, conceptual information about the symmetry of the instructors is important. However, teachers’, the students should be aware of the existing misconceptions and be able to develop strategies to correct these misconceptions. In this study, the purpose, the prospective teachers’, the students’ explanations for corrections of misconceptions and misconceptions were asked to be introduced. The working group during the 2012-2013 academic year, Kocaeli University Faculty of Education Mathematics Education consists of studying at the twenty-six prospective teachers. The study adopted a qualitative approach. The data prepared by the researchers were obtained with an open-ended test. As a result of analysis of the data, prospective with teaching the concept of symmetry observed in more developed practical solutions. These solutions are focused on the method, students utilization mirrors, paper folding, such as using a square piece of registration of events. Prospective teachers’ who think this way, students observed that overlooked the creation of conceptual knowledge.

Keywords: symmetry concepts, misconceptions, elementary mathematics, prospective teachers-students

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Authors: Michele Sinico

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The present research investigates the effect of symmetry on the perception of happiness and boredom in design products. Three experiments were carried out in order to verify the degree of the visual expressive value on different models of bookcases, wall clocks, and chairs. 60 participants directly indicated the degree of happiness and boredom using 7-point rating scales. The findings show that the participants acknowledged a different value of expressive quality in the different product models. Results show also that symmetry is not a significant constraint for an emotional design project.

Keywords: product experience, emotional design, symmetry, expressive qualities

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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: M. Kamel El-Sayed

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The process of determining the degree of membership for an element to an uncertain concept has been found in many ways, using equivalence and symmetry relations in information systems. In the case of similarity, these methods did not take into account the degree of symmetry between elements. In this paper, we use a new definition for finding the membership based on the degree of symmetry. We provide an example to clarify the suggested methods and compare it with previous methods. This method opens the door to more accurate decisions in information systems.

Keywords: information system, uncertain concept, membership function, similarity relation, degree of similarity

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Authors: Gayatri Ghosh

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In this work, a flavour theory of a neutrino mass model based on A_4 symmetry is considered to explain the phenomenology of neutrino mixing. The spontaneous symmetry breaking of A_4 symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. We consider the effect of Z_2 × Z_2 invariant perturbations in neutrino sector and find the allowed region of correction terms in the perturbation matrix that is consistent with 3σ ranges of the experimental values of the mixing angles. We study the entanglement of this formalism on the other phenomenological observables, such as δ_CP phase, the neutrino oscillation probability P(νµ → νe), the effective Majorana mass |mee| and |meff νe |. A Z_2 × Z_2 invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of θ_13 and CP violation. By changing the magnitudes of perturbations in neutrino sector, one can generate viable values of δ_CP and neutrino oscillation parameters. Next we investigate the feasibility of charged lepton flavour violation in type-I seesaw models with leptonic flavour symmetries at high energy that leads to tribimaximal neutrino mixing. We consider an effective theory with an A_4 × Z_2 × Z_2 symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalization group effects or by a soft breaking of the A_4 symmetry. In this context the implications for charged lepton flavour violation processes like µ → eγ, τ → eγ, τ → µγ are discussed.

Keywords: Z2 × Z2 invariant perturbations, CLFV, delta CP phase, tribimaximal neutrino mixing

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Authors: Jeremy Attard, Jordan François, Serge Lazzarini, Thierry Masson

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Gauge theories are the natural background for describing geometrically fundamental interactions using principal and associated fiber bundles as dynamical entities. The central notion of these theories is their local gauge symmetry implemented by the local action of a Lie group H. There exist several methods used to reduce the symmetry of a gauge theory, like gauge fixing, bundle reduction theorem or spontaneous symmetry breaking mechanism (SSBM). This paper is a presentation of another method of gauge symmetry reduction, distinct from those three. Given a symmetry group H acting on a fiber bundle and its naturally associated fields (Ehresmann (or Cartan) connection, curvature, matter fields, etc.) there sometimes exists a way to erase (in whole or in part) the H-action by just reconfiguring these fields, i.e. by making a mere change of field variables in order to get new (‘composite‘) fields on which H (in whole or in part) does not act anymore. Two examples: the re-interpretation of the BEHGHK (Higgs) mechanism, on the one hand, and the top-down construction of Tractor and Penrose's Twistor spaces and connections in the framework of conformal Cartan geometry, one the other, will be discussed. They have, of course, nothing to do with each other but the dressing field method can be applied on both to get a new insight. In the first example, it turns out, indeed, that generation of masses in the Standard Model can be separated from the symmetry breaking, the latter being a mere change of field variables, i.e. a dressing. This offers an interpretation in opposition with the one usually found in textbooks. In the second case, the dressing field method applied to the conformal Cartan geometry offer a way of understanding the deep geometric nature of the so-called Tractors and Twistors. The dressing field method, distinct from a gauge transformation (even if it can have apparently the same form), is a systematic way of finding and erasing artificial symmetries of a theory, by a mere change of field variables which redistributes the degrees of freedom of the theories.

Keywords: BEHGHK (Higgs) mechanism, conformal gravity, gauge theory, spontaneous symmetry breaking, symmetry reduction, twistors and tractors

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Authors: Maba Boniface Matadi

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This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

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Authors: Alpana Tiwari, N. K. Gaur

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We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). The dynamical matrix of ETSM has been applied to compute the phonon frequencies of orientationally disordered mixed crystal (ND4Br)x(KBr)1-x in (q00), (qq0) and (qqq) symmetry directions for compositions 0.10≤x≤0.50 at T=300K.These frequencies are plotted as a function of wave vector k. An unusual acoustic mode softening is found along symmetry directions (q00) and (qq0) as a result of translation-rotation coupling.

Keywords: orientational glass, phonons, TR-coupling, lattice dynamics

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Authors: Narendra Babu Bommenahalli Veerabhadrappa

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Teaching sustainability concepts along with profit maximizing philosophy of business in management education is a challenge. This paper explores and evaluates various learning models to inculcate sustainability concepts in management education. The paper explains about a new pedagogy that was tested in a business management school (Indus Business Academy, Bangalore, India) to teach sustainability. The pedagogy was designed by intertwining concepts related to sustainability with digital marketing concepts. As part of this experimental method, students (in groups) were assigned with various topics of sustainability and were asked to work with concepts of digital marketing and thus market the concepts of sustainability. The paper explains as a case study as to how sustainability was integrated with digital marketing tools and how learning towards sustainability was facilitated. It also explains the outcomes of this pedagogical method, in terms of inculcating sustainability concepts amongst management students as well as marketing and proliferation of sustainability concepts to bring about the behavioral changes amongst target audience towards sustainability.

Keywords: management-education, pedagogy, sustainability, behavior

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Authors: Saleh Elawgali

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In order to present the effect of the dynamic eccentricity on the stator currents of squirrel cage induction machines, the current spectrums of a 550 kW induction motor was calculated for the cases of full symmetry and dynamic eccentricity. The calculations presented in this paper are based on the Poly-Harmonic Model accounting for static and dynamic eccentricity, stator and rotor slotting, parallel branches as well as cage asymmetry. The calculations were followed by Fourier analysis of the stator currents in steady state operation. The paper presents the stator current spectrums for full symmetry and dynamic eccentricity cases, and demonstrates the harmonics present in each case. The effect of dynamic eccentricity is demonstrating via comparing the current spectrums related to dynamic eccentricity cases with the full symmetry one.

Keywords: current spectrum, dynamic eccentricity, harmonics, Induction machine, slot harmonic zone.

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Authors: Saurabh Basu, Sudin Ganguly

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Conductance in graphene nanoribbons (GNR) in presence of magnetic (for example, Iron) and non-magnetic (for example, Gold) adatoms are explored theoretically within a Kane-Mele model for their possible spintronic applications and topologically non-trivial properties. In our work, we have considered the magnetic adatoms to induce a Rashba spin-orbit coupling (RSOC) and an exchange bias field, while the non-magnetic ones induce an RSOC and an intrinsic spin-orbit (SO) coupling. Even though RSOC is present in both, they, however, represent very different physical situations, where the magnetic adatoms do not preserve the time reversal symmetry, while the non-magnetic case does. This has important implications on the topological properties. For example, the non-magnetic adatoms, for moderately strong values of SO, the GNR denotes a quantum spin Hall insulator as evident from a 2e²/h plateau in the longitudinal conductance and presence of distinct conducting edge states with an insulating bulk. Since the edge states are protected by time reversal symmetry, the magnetic adatoms in GNR yield trivial insulators and do not possess any non-trivial topological property. However, they have greater utility than the non-magnetic adatoms from the point of view of spintronic applications. Owing to the broken spatial symmetry induced by the presence of adatoms of either type, all the x, y and z components of the spin-polarized conductance become non-zero (only the y-component survives in pristine Graphene owing to a mirror symmetry present there) and hence become suitable for spintronic applications. However, the values of the spin polarized conductances are at least two orders of magnitude larger in the case of magnetic adatoms than their non-magnetic counterpart, thereby ensuring more efficient spintronic applications. Further the applications are tunable by altering the adatom densities.

Keywords: magnetic and non-magnetic adatoms, quantum spin hall phase, spintronic applications, spin polarized conductance, time reversal symmetry

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Authors: Hubert Klar

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High double excitation of two-electron atoms has been investigated using hyperpherical coordinates within a modified adiabatic expansion technique. This modification creates a novel fictitious force leading to a spontaneous exchange symmetry breaking at high double excitation. The Pauli principle must therefore be regarded as approximation valid only at low excitation energy. Threshold electron scattering from high Rydberg states shows an unexpected time reversal symmetry breaking. At threshold for double escape we discover a broad (few eV) Cooper pair.

Keywords: correlation, resonances, threshold ionization, Cooper pair

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Authors: Neil Morgan

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The notion of Threshold Concepts has offered a fertile new perspective on the transformative effects of mastery of particular concepts on student understanding of subject matter and their developing identities as inductees into disciplinary discourse communities. Only by successfully traversing key knowledge thresholds, it is claimed, can neophytes gain access to the more sophisticated understandings of subject matter possessed by mature members of a discipline. This paper uses thematic analysis of disciplinary guiding principles to identify nine candidate Threshold Concepts that appear to underpin effective TESOL practice. The relationship between these candidate TESOL Threshold Concepts, TESOL principles, and TESOL instructional techniques appears to be amenable to a schematic representation based on superordinate categories of TESOL practitioner concern and, as such, offers an alternative to the view of Threshold Concepts as a privileged subset of disciplinary core concepts. The paper concludes by exploring the potential of a Threshold Concepts framework to productively inform TESOL initial teacher education (ITE) and in-service education and training (INSET).

Keywords: TESOL, threshold concepts, TESOL principles, TESOL ITE/INSET, community of practice

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Anas Ibrahim Yahaya, Christophe Soligo

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A substantial body of literature has reported on facial symmetry and asymmetry and their role in human mate choice. However, major gaps persist, with nearly all data originating from the WEIRD (Western, Educated, Industrialised, Rich and Developed) populations, and results remaining largely equivocal when compared across studies. This study is aimed at quantifying facial asymmetry from the 3D faces of the Hausa of northern Nigeria and also aimed at determining their (Hausa) perceptions and judgements of standardised facial images with different levels of asymmetry using questionnaires. Data were analysed using R-studio software and results indicated that individuals with lower levels of facial asymmetry (near facial symmetry) were perceived as more attractive, more suitable as marriage partners and more caring, whereas individuals with higher levels of facial asymmetry were perceived as more aggressive. The study conclusively asserts that all faces are asymmetric including the most beautiful ones, and the preference of less asymmetric faces was not just dependent on single facial trait, but rather on multiple facial traits; thus the study supports that physical attractiveness is not just an arbitrary social construct, but at least in part a cue to general health and possibly related to environmental context.

Keywords: face, asymmetry, symmetry, Hausa, preference

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Authors: Alisa Rekunova

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According to the theory of word meaning structure developed by Lev Vygotsky (and later modified by Aaro Toomela), there are several levels of thought: sensory-based concepts, situation concepts, logical concepts, and structural-systemic concepts. There are differences between people who have relatively easy access to logical thought compared to those who mostly tend to think in everyday concepts. Religious beliefs are connected with unprovable concepts (Christian Jesus’s ascension or Pagan energy) that cannot be non-controversially related to scientific concepts. However, many scientists in the research are believers of some kinds. Religious views can be different: there are believers, non-believers (atheists), and undecided (we can call them agnostics). Some of the respondents say that scientific or professional and religious spheres do not overlap. Therefore, we can assume they do not see any conflict. Some of them, on the contrary, hesitate to answer and we can conclude they see the conflicts, but they do not want (or do not believe they are able to) to solve it. Finally, the third category of respondents says that religious beliefs and scientific concepts cannot coexist in the human mind. It can be expected that the third category of respondents should have higher education (or even work in the scientific field) but many scientists in the research answer that religious and scientific spheres do not overlap. Therefore, there are other things besides the level of education that is connected with resolving conflicts.

Keywords: conflicts in thinking, cultural-historical psychology, heterogeneity of thinking, religious thinking

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Authors: Jorge Lopez

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In this work, we introduce fractional calculus in order to study the dynamics of a damped multistory building with some symmetry. Initially we make a review of the dynamics of a free and damped multistory building. Then we introduce those concepts of fractional calculus that will be involved in our study. It has been noticed that fractional calculus provides models with less parameters than those based on classical calculus. In particular, a damped classical oscilator is more naturally described by using fractional derivatives. Accordingly, we model our multistory building as a set of coupled fractional oscillators and compare its dynamics with the results coming from traditional methods.

Keywords: coupled oscillators, fractional calculus, fractional oscillator, structural dynamics

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Authors: Rinku Maji, Joydeep Chakrabortty, Stephen F. King

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The grand unified theory (GUT) rationales the arbitrariness of the standard model (SM) and explains many enigmas of nature at the outset of a single gauge group. The GUTs predict the proton decay and, the spontaneous symmetry breaking (SSB) of the higher symmetry group may lead to the formation of topological defects, which are indispensable in the context of the cosmological observations. The Super-Kamiokande (Super-K) experiment sets sacrosanct bounds on the partial lifetime (τ) of the proton decay for different channels, e.g., τ(p → e+ π0) > 1.6×10³⁴ years which is the most relevant channel to test the viability of the nonsupersymmetric GUTs. The GUTs based on the gauge groups SO(10) and E(6) are broken to the SM spontaneously through one and two intermediate gauge symmetries with the manifestation of the left-right symmetry at least at a single intermediate stage and the proton lifetime for these breaking chains has been computed. The impact of the threshold corrections, as a consequence of integrating out the heavy fields at the breaking scale alter the running of the gauge couplings, which eventually, are found to keep many GUTs off the Super-K bound. The possible topological defects arising in the course of SSB at different breaking scales for all breaking chains have been studied.

Keywords: grand unified theories, proton decay, threshold correction, topological defects

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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: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Wenhao Lan, Ning Li, Qiang Tong

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To improve the registration accuracy of a source point cloud and template point cloud when the initial relative deflection angle is too large, a PointNetLK algorithm combined with an oriented bounding box (PointNetLK-OBB) is proposed. In this algorithm, the OBB of a 3D point cloud is used to represent the macro feature of source and template point clouds. Under the guidance of the iterative closest point algorithm, the OBB of the source and template point clouds is aligned, and a mirror symmetry effect is produced between them. According to the fitting degree of the source and template point clouds, the mirror symmetry plane is detected, and the optimal rotation and translation of the source point cloud is obtained to complete the 3D point cloud registration task. To verify the effectiveness of the proposed algorithm, a comparative experiment was performed using the publicly available ModelNet40 dataset. The experimental results demonstrate that, compared with PointNetLK, PointNetLK-OBB improves the registration accuracy of the source and template point clouds when the initial relative deflection angle is too large, and the sensitivity of the initial relative position between the source point cloud and template point cloud is reduced. The primary contribution of this paper is the use of PointNetLK to avoid the non-convex problem of traditional point cloud registration and leveraging the regularity of the OBB to avoid the local optimization problem in the PointNetLK context.

Keywords: mirror symmetry, oriented bounding box, point cloud registration, PointNetLK-OBB

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Authors: B. F. Nteumagne, E. Pindza, E. Mare

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We apply Lie symmetries analysis to price and hedge options in the fractional Brownian framework. The reputation of Lie groups is well spread in the area of Mathematical sciences and lately, in Finance. In the presence of transactions costs and under fractional Brownian motions, analytical solutions become difficult to obtain. Lie symmetries analysis allows us to simplify the problem and obtain new analytical solution. In this paper, we investigate the use of symmetries to reduce the partial differential equation obtained and obtain the analytical solution. We then proposed a hedging procedure and calibration technique for these types of options, and test the model on real market data. We show the robustness of our methodology by its application to the pricing of digital options.

Keywords: fractional brownian model, symmetry, transaction cost, option pricing

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Authors: Suleiman Bashir Adamu, Lawan Sani Taura

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We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schrödinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained.

Keywords: Eigenvalues, Eigenfunction, Hamiltonian, Klein- Gordon equation, PT-symmetric quantum mechanics

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Authors: Rizky Oktaviana

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The main purpose of studying lies in improving students’ understanding. Teachers usually use written test to measure students’ understanding about learning material especially mathematical learning material. This common method actually has a lack point, such that in mathematics content, written test only show procedural steps to solve mathematical problems. Therefore, teachers unable to see whether students actually understand about mathematical concepts and the relation between concepts or not. One of the best tools to observe students’ understanding about the mathematical concepts is concept map. The goal of this research is to describe junior high school students understanding about mathematical concepts through Concept Maps based on the difference of mathematical ability. There were three steps in this research; the first step was choosing the research subjects by giving mathematical ability test to students. The subjects of this research are three students with difference mathematical ability, high, intermediate and low mathematical ability. The second step was giving concept mapping training to the chosen subjects. The last step was giving concept mapping task about the function to the subjects. Nodes which are the representation of concepts of function were provided in concept mapping task. The subjects had to use the nodes in concept mapping. Based on data analysis, the result of this research shows that subject with high mathematical ability has formal understanding, due to that subject could see the connection between concepts of function and arranged the concepts become concept map with valid hierarchy. Subject with intermediate mathematical ability has relational understanding, because subject could arranged all the given concepts and gave appropriate label between concepts though it did not represent the connection specifically yet. Whereas subject with low mathematical ability has poor understanding about function, it can be seen from the concept map which is only used few of the given concepts because subject could not see the connection between concepts. All subjects have instrumental understanding for the relation between linear function concept, quadratic function concept and domain, co domain, range.

Keywords: concept map, concept mapping, mathematical concepts, understanding

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Authors: Olga V. Korotkaya

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This article is devoted to an important problem of calculation of deflected mode of the combustion chamber and the nozzle end of a new liquid-propellant rocket cruise engine. A special attention is given to the methodology of calculation. Three operating modes are considered. The analysis has been conducted in ANSYS software. The methods of conducted research are mathematical modelling, substructure method, cyclic symmetry, and finite element method. The calculation has been carried out to order of S. P. Korolev Rocket and Space Corporation «Energia». The main results are practical. Proposed methodology and created models would be able to use for a wide range of strength problems.

Keywords: combustion chamber, cyclic symmetry, finite element method, liquid-propellant rocket engine, nozzle end, substructure

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Authors: Vojo George Fasinu, Nadaraj Govender, Predeep Kumar

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An Antenna, which remains the hub of technological development in Africa had been found to be a course that is been taught and designed in an abstract manner in some universities. One of the reasons attached to this is that the appropriate approach of teaching antenna design is not yet understood by many engineering academics in some universities in South Africa. Also, another problem reported is the main difficulty encountered when interpreting and applying some of the mathematical concepts learned into their practical antenna design course. As a result of this, some engineering experts classified antenna as a mysterious technology that could not be described by anybody using mathematical concepts. In view of this, this paper takes it as its point of departure in explaining what an antenna is all about with a strong emphasis on its mathematical modelling. It also argues that the place of modelling mathematical concepts into the teaching of engineering design cannot be overemphasized. Therefore, it explains the mathematical concepts adopted during the teaching of an antenna design course, the Strategies of modelling those mathematics concepts, the behavior of antennas, and their mathematics usage were equally discussed. More so, the paper also sheds more light on mathematical modelling in South Africa context, and also comparative analysis of mathematics concepts taught in mathematics class and mathematics concepts taught in engineering courses. This paper focuses on engineering academics teaching selected topics in electronic engineering (Antenna design), with special attention on the mathematical concepts they teach and how they teach them when teaching the course. A qualitative approach was adopted as a means of collecting data in order to report the naturalistic views of the engineering academics teaching Antenna design. The findings of the study confirmed that some mathematical concepts are being modeled into the teaching of an antenna design with the adoption of some teaching approaches. Furthermore, the paper reports a didactical-realistic mathematical model as a conceptual framework used by the researchers in describing how academics teach mathematical concepts during their teaching of antenna design. Finally, the paper concludes with the importance of mathematical modelling to the engineering academics and recommendations for further researchers.

Keywords: modelling, mathematical concepts, engineering, didactical, realistic model

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Authors: Ece Çelikçapa Özinan

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It is possible to see the effects of both approaches in the acting method of Yoshi Oida, who has experience in Eastern and Western theater understandings. Integrating the two understandings with cultural differences in theater was mostly preferred in order to eliminate the deadlocks of the Western understanding. Yoshi Oida wanted to make the acting concepts acquired in traditional Japanese theater available to Western actors as well. The usefulness of these concepts, which offer advice for the actor's mind control and focus, is debatable. The concepts that have been experienced for many years in the training of actors in traditional Japanese theater should perhaps go through an education process with the same discipline in order to be useful for a Western actor. Although the importance of intercultural exchange of these educational teachings is known, it should be considered that it can cause the concepts to be emptied. In this study, Yoshi Oida's concepts related to the control of the actor's mind, which he used in his acting method, will be explained, examples of his exercises will be presented and their competencies will be discussed.

Keywords: Yoshi Oida, acting, mind, Eastern, Western

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Authors: Fetah Eren, Ismail Sahin, Ismail Celik, Ahmet Oguz Akturk

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The aim of this study is to discover secondary school students’ perceptions related to information technologies and the connections between concepts in their cognitive structures. A word association test consisting of six concepts related to information technologies is used to collect data from 244 secondary school students. Concept maps that present students’ cognitive structures are drawn with the help of frequency data. Data are analyzed and interpreted according to the connections obtained as a result of the concept maps. It is determined students associate most with these concepts—computer, Internet, and communication of the given concepts, and associate least with these concepts—computer-assisted education and information technologies. These results show the concepts, Internet, communication, and computer, are an important part of students’ cognitive structures. In addition, students mostly answer computer, phone, game, Internet and Facebook as the key concepts. These answers show students regard information technologies as a means for entertainment and free time activity, not as a means for education.

Keywords: word association test, cognitive structure, information technology, secondary school

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Authors: Nellie Nosisi Feza

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Developing young students' number sense is a priority if the aim is to build a rich mathematical foundation for successful schooling and future innovative careers. Capturing students’ interests is crucial while mediating counting concepts. This paper reports South African young children number concepts demonstrated before entering the reception class. It indicates the diverse knowledge attained in different settings before entering formal schooling. The findings indicate that their start is uneven with fully and partly attained number concepts. The findings suggest pre-schooling stimulation that provides rich mathematical experiences and purposeful play towards the attainment of core foundational concepts. Literature directs practice on important core concepts that are foundational in developing number sense.

Keywords: numeracy, learning trajectories, innate abilities, counting, Grade R/reception class

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