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From the result of the 2016 Ujian Pencapaian Sekolah Rendah (UPSR), it showed that out of the 440496 candidates who sat for the Mathematics paper, 21.6% of them failed the subject. This makes Mathematics one of the critical subjects to be mastered by the primary school students. Previous studies have shown that transforming the teaching and learning (T&L) from a teacher-centered learning to a student-centered learning can improve the performance of students academically. One of the ways to implement this is through the use of information and communication technology (ICT). The use of ICT can help strengthen the T&L process in all areas of learning especially Mathematics. In light of this, a study was done to investigate whether incorporating e-learning in the teaching and learning (T&L) of mathematics can improve students’ performances and also motivate them in Mathematics at the primary level. The research sample consisted of 40 Year 3 students from Sekolah Kebangsaan Khir Johari, Perai. The effectiveness of e-learning was measured through a pre-test and post-test assessment method. The students were also required to answer a questionnaire to find out whether e-learning has impacted their motivations towards learning mathematics. This results indicated that there is significant difference between the achievement of students before and after the use of e-learning. [ABSTRACT FROM AUTHOR]

Applications of knowledge in the real life and practical use of knowledge from natural sciences are typical for current modernization trends in teaching at Slovak schools. In this paper, we focus on emphasizing the interdisciplinary relationship among physics, mathematics and geography. Considering a specific example of Mercator projection, we present close connections of the given subjects via using modern ICT tools, especially dynamical geometry software GeoGebra. We demonstrate how this problem can be useful in school practice as a motivating factor which yields the development of a pupil's intellect. [ABSTRACT FROM AUTHOR]

Currently in Slovakia, there is a strong need to attract more students for their future career in IT or science and technology. The motivation towards these subjects is an important issue at all levels of education and isin the main focus of the national project IT academy. One of its goals at upper secondary level is the introduction of classes with focus on informatics where teaching informatics and science is strengthened a great deal. Except from extra lessons on informatics a new interdisciplinary subject Informatics in science and mathematics is designed. Its main goal is to show interesting problems that can be solved using informatics concepts. For the physics part, we have designed teaching and learning materials on the concept of modeling. Developing models in the physics research cannot be conducted without knowledge of coding in a programming environment. Our main goal is to show students a similar modeling approach on situations that are simple and understandable to them. Students proceed similar way as researchers do, i.e. they get a problem, develop a model, manipulate with it, test the model and improve it to get better correspondence with experimental results. The modeling is conducted in dynamical modeling software where variables are represented by icons that can be a first step to coding in professional programming environment. In the paper we introduce a set of modeling activities designed for the purpose of the presented teaching subject. [ABSTRACT FROM AUTHOR]

In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite numbers. Using the results of the paper we get the known properties of the Bell numbers (Touchard's Congruence for k = 0). [ABSTRACT FROM AUTHOR]

The Nyström-Clenshaw-Curtis (NCC) quadrature, which was proposed in [S. Y. Kang, I. Koltracht, and G. Rawitscher, Math. Comp. 72, 729–756 (2003)], is a highly accurate numerical method for solving integral equations with semi-smooth kernel. In this paper, we introduce the basic idea of the NCC quadrature and derive an NCC quadrature for Volterra integral equations with proportional delays. Numerical results are presented to illustrated the high accuracy of the method. [ABSTRACT FROM AUTHOR]

The idea of I−convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P., Šalát, T. and Wilczyński, W. I−convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray and Ruckle [Nuray, F. and Ruckle, W. H. Generalized statistical convergence and convergence free spaces. J. Math. Anal. Appl. 245(2) (2000), 513–527]. In this paper we introduce I−deferred statistical convergence and strong I−deferred Cesàro convergence and investigate between their relationship. [ABSTRACT FROM AUTHOR]

In this paper, we developed a mathematical model for tuberculosis. In this model, we obtained system of differential equations on fractional order. The results obtained in our model are verified with real data. [ABSTRACT FROM AUTHOR]

Atanassov recommended the idea of intuitionistic fuzzy set, that is depicted with a membership function and a non-membership function, as an outcome simplifying Zadeh’s fuzzy sets which merely allocate a membership degree to each element. In the present paper, intuitionistic fuzzy divergence measure involving two parameters along with their proofs of validity is introduced. Further, it is shown that intuitionistic fuzzy divergence measure has monotonic decreasing behavior with respect to the two parameters. Finally, a numerical illustration associated to decision making is employed to prove feasibility and efficacy of suggested technique. [ABSTRACT FROM AUTHOR]

This paper provides an optical characterization and numerical prediction of local deformations appearing on the visible side of composite sandwich panels used for interior furniture of business airplanes. During manufacturing of furniture panels, metallic inserts are bonded inside the sandwich panel using an epoxy adhesive. Surface defects appear on the visible side of the panels due to curing of the adhesive, but also because of temperature gradients and humidity during manufacturing and in service. This paper presents an optical characterization based on deflectometry principle, that allows qualitative and quantitative analyses of the surface deformations in 3-dimensions. In addition, this paper presents a parametric model based on finite elements to predict the formation of surface defects using ABAQUS. A comparison is presented between the experimental observations and numerical predictions with good agreement between them. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain explicit expressions of (1 - x)-a 2F1 [ a, b 2b + j ; - 2x /1 - x ] for j = 0, ±1, . . . , ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences. [ABSTRACT FROM AUTHOR]

In “Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial ex- ´ pression recognition based on curvature, Appl. Math. Comput. 344–345 (2019) 150–162”, some statistical evaluations on feature vectors were given in order to analyse their meaningfulness while classifying human facial expressions. In this paper, by using some results arising from SPSS program, we provide some further statistical evaluations and observations which are related to features based on the calculated Hausdorff distances between Bezier curves belonging to the regions that shape human facial expressions. [ABSTRACT FROM AUTHOR]

In this paper, we revisited the elliptic scalar multiplication method namely the Integer Sub-Decomposition (ISD) method. This method was proposed in 2013 and it is an extension from a well-known GLV method. But the original ISD method deals with trivial endomorphism which only works on integer number field. By extending the ISD method into complex quadratic field, more solutions can be obtained. And allowing ISD method to work in complex quadratic field will enable the ISD method to be applicable on special curves, such as curves with j-invariant 0. The curves with j-invariant 0 has one special endomorphism over complex number field. And since in ISD method, three endomorphisms are needed, the second and third endomorphism is chosen in such a way that they belong to the same field as the first endomorphism. [ABSTRACT FROM AUTHOR]

In [10], we have investigated properties of the sum C1(h, k). In this paper, we will give some other arithmetic properties of the sum C1(h, k). Moreover, in the light of the sum B1(h, k), which has also defined in [10], we will give specific values of the sum C1(h, k) when h + k is an odd number. Finally, we will give a relation between the sum C1(h, k) and the Hardy-Berndt sum s5(h, k) for a special case. [ABSTRACT FROM AUTHOR]

In this paper we investigate the performance of a copula type Gumbel-Barnett, for prediction of the dependence between two variables, X and Y. We fit a copula, using a sample of observations collected at time t and we define predictive areas, at different levels, to detect specific changes in a sample at time t +1, both samples are governed by the same law (copula). The study addresses the more general problem of detecting dependence changes during different periods of time. This work is developed under a Bayesian perspective, a procedure that allows working with small sample sizes and under different assumptions introduced in the model through the prior distribution. [ABSTRACT FROM AUTHOR]

Occupational safety health is a multidisciplinary discipline concentrating on the safety, health and welfare of workers in the working place. Healthcare Students undergoing Occupational Safety Health internships are required to apply mathematical in areas such as safety legislation, safety behavior, ergonomics, chemical safety, OSH practices, industrial hygiene, risk management and safety health practices as problem solving. The aim of this paper is to investigate the level of mathematics and logic utilization from these students during their internship looking at areas of Hazard identification, Determining the population exposed to the hazard, Assessing the risk of the exposure to the hazards and Taking preventive and control. A total of 142 returning healthcare students from their Occupational Safety Health, internship were given a questionnaire to measure their perceptions towards mathematical and logic utilization. The overall results indicated a strong positive skewed result towards the use of Mathematics during their internship. The findings showed that mathematics were well delivered by the students during their internship. Mathematics could not be separated from OSH practice as a needed precision in quantifying safety, health and welfare of workers in addition to empiricism. [ABSTRACT FROM AUTHOR]

In this paper, we introduce notations of neutrosophic soft graphs, neutrosophic soft subgraphs and strong neutrosophic soft graphs. We also give some properties and related examples of them. [ABSTRACT FROM AUTHOR]

In this paper, we consider the spectral problem for the equation -u″(x) + (A + λI)u(x) = f (x) on the two disjoint intervals (-1, 0) and (0, 1) together with multi-point boundary conditions and supplementary transmission conditions at the point of interaction x = 0, where A is an abstract linear operator. So, our problem is not a pure differential boundary-value one. Starting with the analysis of the principal part of the problem, the coercive estimates, the Fredholmness and isomorphism are established for the main problem. The obtained results are new even in the case of boundary conditions without internal points. [ABSTRACT FROM AUTHOR]

This paper gives a graphical representation of a subclass of complex filiform Leibniz algebras. This class is split into three subclasses called first, second and third class denoted, in dimension n over a field of complex numbersℂ, by FLbn(ℂ), SLbn(ℂ) and TLbn(ℂ), respectively. Here, the combinatorial structures associated with FLbn(ℂ), and SLbn(ℂ), in low dimensions are considered and some structural properties of the combinatorial structures are given. [ABSTRACT FROM AUTHOR]

In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]

In this paper, the aim of this work is to study theorem for the one-dimensional space-time fractional deriative, generalize some function for the one-dimensional fractional by table represents the fractional Laplace transforms of some elementary functions to be valid for the multi-dimensional fractional Laplace transform and give the definition of the multi-dimensional fractional Laplace transform. This study includes that, dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable and develop of the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform based on the modified Riemann-Liouville derivative. [ABSTRACT FROM AUTHOR]

The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are known for a particular family of doubly connected regions and a particular triply connected region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded multiply connected regions with smooth boundaries. The method depends on the values of S (z(t), a), S'(z(t), a) and θ'(t), where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S'(z(t), a). An integral equation for θ'(t) is used for finding the zeros of Ahlfors map. The numerical examples presented here demonstrate the method. [ABSTRACT FROM AUTHOR]

In this paper, we give an alternative formula of total norms for Τ-Adic Non-adjacent Forms (Τ-NAF) expansion for an integer n element of ℤ(Τ) in Koblitz curve.We apply the geometric series formula to simplify some series involving floor functions in total norms formula. With this approach, we can evaluate the total norm by using the length of Τ-NAF expansion. [ABSTRACT FROM AUTHOR]

As pointed out by Professor Berndt that the following two interesting summations due to Ramanujan [1] 1 + ( x/1!)2 x/3x + (x(x - 1)/2! )2 x(x - 1)/3x(3x - 1) + ... = г3(2x + 1)/ г3(x + 1)г(3x + 1) 1 + x/1! (x - 1)(x + 1) x /(4x - 1) + x(x - 1)/2! (x - 1)(x - 2)/(x + 1)(x + 2) x(x - 1) (4x - 1)(4x - 2) + . . . = 8 г3(3x + 1) г(x + 1) 9г3(2x + 1)г(4x + 1) can be obtained quite simply by employing the classical Saalschutz's summation theorem. Recently an interesting extension of the classical Saalschutzs summation theorem has been given by Rakha and Rathie. The aim of this paper is to provide entensions of the above summation formulae due to Ramanujan. The results obtained in this paper are interesting, easily established and useful. [ABSTRACT FROM AUTHOR]

There are many practical applications based on the Least Square Error (LSE) or Total Least Square Error (TLSE) methods. Usually the standard least square error is used due to its simplicity, but it is not an optimal solution, as it does not optimize distance, but square of a distance. The TLSE method, respecting the orthogonality of a distance measurement, is computed in ɖ-dimensional space, i.e. for points given in E2 a line ∏ in E2, resp. for points given in E3 a plane Þ in E3, fitting the TLSE criteria are found. However, some tasks in physical sciences lead to a slightly different problem. In this paper, a new TSLE method is introduced for solving a problem when data are given in E3 a line ∏ ∊ E3 is to be found fitting the TLSE criterion. The presented approach is applicable for a general ɖ-dimensional case, i.e. when points are given in Ed a line ∏ ∊ Ed is to be found. This formulation is different from the TLSE formulation. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model, based on finite element theory, useful to model the stress-strain state for a bonded single lap joint under peeling load has been presented. The numerical FE model has been developed by means of Abaqus® code in order to reproduce some experimental tests. For FE model validation purpose, the numerical results have been compared with the experimental ones and a good correlation has been achieved. In more detail, the adhesive layer has been modeled by means of cohesive elements. Such elements present some numerical difficulties related to the dependence from the own element size. So, a procedure useful to solve such mesh-dependence has been proposed. [ABSTRACT FROM AUTHOR]

Despite of a lot of attempts during recent years, complex mechanical behaviour of polymers remains incompletely modelled, making industrial design of structures under complex, cyclic and hard loadings not totally reliable. The non linear and dissipative viscoelastic, viscoplastic behaviour of those materials impose to take into account non linear and combined effects of mechanical and thermal phenomena. In this view, a visco-hyperelastic, viscoplastic model, based on network description of the material has recently been developed and designed in a complete thermodynamic frame in order to take into account those main thermo-mechanical couplings . Also, a way to account for coupled effects of strain-rate and temperature was suggested. First experimental validations conducted in the 1D limit on amorphous rubbery like PMMA in isothermal conditions led to pretty goods results. In this paper a more complete formalism is presented and validated in the case of a semi crystalline polymer, a PA66 and a PET (either amorphous or semi crystalline) are used. Protocol for identification of constitutive parameters is described. It is concluded that this new approach should be the route to accurately model thermo-mechanical behaviour of polymers using a reduced number of parameters of some physicl meaning. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of composition of two arbitrary rotations in SO(3,ℝ) given in their vector-parameter form. The cases when one or two half-turns are involved in the composition or the resulting rotation is a half turn receive also rigorous treatment. Technically, this is done by lifting the problem to the covering group SU(2). Systematization of the results is made and relying on them, some applications are discussed. A convenient and economic computational method for composing rotations in vector-parameter form is proposed. It is such that the composition of two arbitrary (including half-turns) rotations can be done with at most 12 multiplications. Finally, we present an explicit variant of the construction behind Cartan's theorem in the case of SO(3,ℝ). [ABSTRACT FROM AUTHOR]

The concept of 'Isotopy' as formulated by Ruggero Maria Santilli plays a vital role in the development of Iso mathematics. Santilli defined iso-fields of characteristic zero. In this paper we extend this definition to define Iso-Galois fields which are essentially of non-zero characteristic. Isotopically isomorphic realizations of a group define isopermutation group which gives a clear cut distinction between automorphic groups and isotopic groups. [ABSTRACT FROM AUTHOR]

This paper describes instruments' validation process to identify the suitability and accuracy of the final examination questions for engineering mathematics. As a compulsory subject for second year students from 4 departments in Faculty of Engineering and Built Environment Universiti Kebangsaan Malaysia, the Differential Equations 1 course (KKKQ2124) was considered in this study. The data used in this study consists of the raw marks for final examination of semester 2, 2012/2013 session. The data then will be run and analyzed using the Rasch measurement model. Rasch model can also examine the ability of students and redundancy of instrument constructs. [ABSTRACT FROM AUTHOR]

Students have difficulties to appreciate the role of mathematics in their daily life. Failure to understand how mathematics is relevant in life might hinder learning. An online web magazine entitled Dunia Matematik has been published to share mathematics that beyond the classrooms. This paper discusses students' rating of the articles which portray statistics in real life that made available at one section of the web magazine. Students' motivate on were assesed based on four components of ARCS model: Attention, Relevance, Confidence and Satisfaction. The thirty-seven form four students who participated in the study were given one hour to review on some selected articles on statistics that have been published in Dunia Matematik. At the end of the one hour session the participants were required to respond to 20 survey items. Findings showed that the students rated highest for Confidence while Attention was rated lowest. Meanwhile, the overall rating for the articles on Statistics of the online web magazine Dunia Matematik was rated considerably high. The study shows that form four students viewed the articles on applications of statistics published in Dunia Matematik has the potential to motivate the learning of statistics. It is hoped that students take advantage to what is offered by this local web magazine to attain learning and experience beyond classrooms. [ABSTRACT FROM AUTHOR]