Search results for: co-prime numbers

Authors: Kazuyoshi Mori

Abstract:

Examples of parameterization of stabilizing controllers that require only one of right-/left-coprime factorizations are presented. One parameterization method requires one side coprime factorization. The other requires no coprime factorization. The methods are based on the factorization approach so that a number of models can be applied the method we use in this paper.

Keywords: parametrization, coprime factorization, factorization approach, linear systems

Procedia PDF Downloads 373

Authors: Martins Olatunbosun Babatunde, Muhammed Bashir Muazu, Emmanuel Adewale Adedokun

Abstract:

This paper presents the development of a double-loop trajectory-tracking controller for the ball and plate system (BPS) using the Normalized Right Coprime Factorization (NRCF) scheme.The Linear Algebraic (LA) method is used to design the inner loop required to stabilize the ball, while H-infinity NRCF method, that involved the lead-lag compensator design approach, is used to develop the outer loop that controls the plate. Simulation results show that the plate was stabilized at 0.2989 seconds and the ball was able to settle after 0.9646 seconds, with a trajectory tracking error of 0.0036. This shows that the controller has good adaptability and robustness.

Keywords: ball and plate system, normalized right coprime factorization, linear algebraic method, compensator, controller, tracking.

Procedia PDF Downloads 141

Authors: Kazuyoshi Mori

Abstract:

In this paper, we consider the number of parameters for the parametrization of stabilizing controllers for RHinf systems with size 2 × 2. Fortunately, any plant of this model can admit doubly coprime factorization. Thus we can use the Youla parameterization to parametrize the stabilizing contollers . However, Youla parameterization does not give itself the minimal number of parameters. This paper shows that the minimal number of parameters is four. As a result, we show that the Youla parametrization naturally gives the parameterization of stabilizing controllers with minimal numbers.

Keywords: RHinfo, parameterization, number of parameters, multi-input, multi-output systems

Procedia PDF Downloads 407

Authors: Melvin Ballera, Aldrich Olivar, Mary Soriano

Abstract:

Digital computers nowadays must be able to have a utility that is capable of generating random numbers. Usually, computer-generated random numbers are not random given predefined values such as starting point and end points, making the sequence almost predictable. There are many applications of random numbers such business simulation, manufacturing, services domain, entertainment sector and other equally areas making worthwhile to design a unique method and to allow unpredictable random numbers. Applying stochastic simulation using linear congruential algorithm, it shows that as it increases the numbers of the seed and range the number randomly produced or selected by the computer becomes unique. If this implemented in an environment where random numbers are very much needed, the reliability of the random number is guaranteed.

Keywords: stochastic simulation, random numbers, linear congruential algorithm, pseudorandomness

Procedia PDF Downloads 316

Authors: Wiem Gadri

Abstract:

This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral charac-teristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this new setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a novel characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, formal power series, over a finite field

Procedia PDF Downloads 51

Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

Abstract:

The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

Procedia PDF Downloads 206

Authors: M. Tiachachat, M. Mihoubi

Abstract:

The Bell polynomials are special polynomials in combinatorial analysis that have a wide range of applications in mathematics. They have interested many authors. The exponential partial Bell polynomials have been well reduced to some special combinatorial sequences. Numerous researchers had already been interested in the above polynomials, as evidenced by many articles in the literature. Inspired by this work, in this work, we propose a family of special polynomials named after the 2-successive partial Bell polynomials. Using the combinatorial approach, we prove the properties of these numbers, derive several identities, and discuss some special cases. This family includes well-known numbers and polynomials such as Stirling numbers, Bell numbers and polynomials, and so on. We investigate their properties by employing generating functions

Keywords: 2-associated r-Stirling numbers, the exponential partial Bell polynomials, generating function, combinatorial interpretation

Procedia PDF Downloads 110

Authors: Iryna Shevchenko

Abstract:

The science of mathematics was originated at the order of count of objects and subsequently for the measurement of size and quality of objects using the logical or abstract means. The laws of mathematics are based on the study of absolute values. The number 0 or "nothing" is the purely logical (as the opposite to absolute) value as the "nothing" should always assume the space for the something that had existed there; otherwise the "something" would never come to existence. In this work we are going to prove that the number "0" is the abstract (logical) and not an absolute number and it has the absolute value of “∞” (infinity). Therefore, the number "0" might not stand in the row of numbers that symbolically represents the absolute values, as it would be the mathematically incorrect. The symbolical value of number "0" in the row of numbers could be represented with symbol "∞" (infinity). As a result, we have the mathematical row of numbers: epsilon, ...4, 3, 2, 1, ∞. As the conclusions of the theory of number “0” we presented the statements: multiplication and division by fractions of numbers is illegal operation and the mathematical division by number “0” is allowed.

Keywords: illegal operation of division and multiplication by fractions of number, infinity, mathematical row of numbers, theory of number “0”

Procedia PDF Downloads 552

Authors: Rosy Joseph

Abstract:

From an algebraic point of view, Semirings provide the most natural generalization of group theory and ring theory. In the absence of additive inverse in a semiring, one had to impose a weaker condition on the semiring, i.e., the additive cancellative law to study interesting structural properties. In many practical situations, fuzzy numbers are used to model imprecise observations derived from uncertain measurements or linguistic assessments. In this connection, a special class of fuzzy numbers whose shape is symmetric with respect to a vertical line called the symmetric fuzzy numbers i.e., for α ∈ (0, 1] the α − cuts will have a constant mid-point and the upper end of the interval will be a non-increasing function of α, the lower end will be the image of this function, is suitable. Based on this description, arithmetic operations and a ranking technique to order the symmetric fuzzy numbers were dealt with in detail. Wherein it was observed that the structure of the class of symmetric fuzzy numbers forms a commutative semigroup with cancellative property. Also, it forms a multiplicative monoid satisfying sub-distributive property.In this paper, we introduce the algebraic structure, sub-distributive semiring and discuss its various properties viz., ideals and prime ideals of sub-distributive semiring, sub-distributive ring of difference etc. in detail. Symmetric fuzzy numbers are visualized as an illustration.

Keywords: semirings, subdistributive ring of difference, subdistributive semiring, symmetric fuzzy numbers

Procedia PDF Downloads 212

Authors: Kairat T. Mynbaev, Elena N. Lomakina

Abstract:

We consider a Hardy-type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion, and bounds for its approximation numbers. Previously, bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness earlier have been found using different methods by G. Sinnamon and K. Mynbaev. Our approach is different in that we use domain partitions for all problems under consideration.

Keywords: approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space

Procedia PDF Downloads 104

Authors: F. Berna Benli, Özgür Keskin

Abstract:

Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

Procedia PDF Downloads 477

Authors: Kazuyoshi Mori

Abstract:

In this paper, we consider the parametrization of Anantharam’s model within the framework of the factorization approach. In the parametrization, we investigate the number of required parameters of Anantharam’s model. We consider single-input single-output systems in this paper. By the investigation, we find three cases that are (1) there exist plants which require only one parameter and (2) two parameters, and (3) the number of parameters is at most three.

Keywords: linear systems, parametrization, coprime factorization, number of parameters

Procedia PDF Downloads 213

Authors: Won-Gon Kim

Abstract:

A standardized system to describe the pressure-flow characteristics of a given cannula has recently been proposed and has been termed ‘the M-number’. Using three different sizes of aortic cannulas in 50 pediatric cardiac patients on hypothermic cardiopulmonary bypass, we analyzed the correlation between experimentally and clinically derived M-numbers, and found this was positive. Clinical M-numbers were typically 0.35 to 0.55 greater than experimental M-numbers, and correlated inversely with a patient's temperature change; this was most probably due to increased blood viscosity, arising from hypothermia. This inverse relationship was more marked in higher M-number cannulas. The clinical data obtained in this study suggest that experimentally derived M-numbers correlate strongly with clinical performance of the cannula, and that the influence of temperature is significant.

Keywords: cardiopulmonary bypass, M-number, aortic cannula, pressure-flow characteristics

Procedia PDF Downloads 244

Authors: Tanveer Rasool, A. K. Dhiman

Abstract:

The paper reports 2-D numerical study used to investigate the effect of changing working fluids with Prandtl numbers 0.71, 10 and 50 on the flow and convective heat transfer across an equilateral triangular cylinder placed in a horizontal channel with its apex facing the flow. Numerical results have been generated for fixed blockage ratio of 50% and for three Reynolds numbers of 50, 75, and 100 for each Prandtl numbers respectively. The studies show that for above range of Reynolds numbers, the overall drag coefficient is insensitive to the Prandtl number changes while as the heat transfer characteristics change drastically with changing Prandtl number of the working fluid. The results generated are in complete agreement with the previous literature available.

Keywords: Prandtl number, Reynolds number, drag coefficient, flow and isothermal patterns

Procedia PDF Downloads 397

Authors: Nicolás Rudas

Abstract:

Sociologists have brought to light the fascination of contemporary societies with numbers but fall short of explaining it. In their accounts, people generally misunderstand the technical intricacies of statistical knowledge and therefore accept numbers as unassailable “facts”. It is due to such pervasive fascination, furthermore, that both old and new forms of social control find fertile ground. By focusing on the process whereby the fetishization of numbers reaches its zenith, i.e., when specific statistics become emblematic of an entire society, it is asserted that numbers primarily function as moral symbols with immense potential for galvanizing collective action. Their “facticity” is not solely a cognitive problem but one that is deeply rooted in myth and connected with social experiences of epiphany and ritual. Evidence from Colombia is used to illustrate how certain quantifications become canonical. In 2021, Colombia’s Peace Court revealed that the national army had executed 6,402 innocent civilians to later report them as members of illegal armed groups. Rapidly, “6,402” transformed into a prominent item in the country’s political landscape. This article reconstructs such a process by following the first six months of the figure’s circulation, both in traditional and social media. In doing so, it is developed a new cultural-sociological conceptualization of numbers as “fact-icons” that departs from traditional understandings of statistics as “technical” objects. Numbers are icons whose appropriation is less rational than aesthetic.

Keywords: culture, statistics, collective memory, social movements

Procedia PDF Downloads 71

Authors: Sabrina Nouri, Abderahmane Ghezal, Said Abboudi, Pierre Spiteri

Abstract:

This paper deals with the numerical study of heat and mass transfer of laminar flow transition at low Prandtl numbers. The model includes the two-directional momentum, the energy and mass transfer equations. These equations are discretized by the finite volume method and solved by a self-made simpler like Fortran code. The effect of governing parameters, namely the Lewis and Prandtl numbers, on the transition of the flow and solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are derived for of Prandtl [10⁻²-10¹] and Lewis numbers [1-10⁴]. The results show unicell and multi-cell flow. Solute and flow boundary layers appear for low Prandtl number.

Keywords: natural convection, low Prandtl number, heat and mass transfer, finite volume method

Procedia PDF Downloads 198

Authors: R. M. Kashim

Abstract:

The study investigated primary school teachers’ conceptual and procedural knowledge of rational numbers and its effects on pupil’s achievement in rational numbers. Specifically, primary school teachers’ level of conceptual knowledge about rational numbers, primary school teachers’ level of procedural knowledge about rational numbers, and the effects of teachers conceptual and procedural knowledge on their pupils understanding of rational numbers in primary schools is investigated. The study was carried out in Bauchi metropolis in the Bauchi state of Nigeria. The design of the study was a multi-stage design. The first stage was a descriptive design. The second stage involves a pre-test, post-test only quasi-experimental design. Two instruments were used for the data collection in the study. These were Conceptual and Procedural knowledge test (CPKT) and Rational number achievement test (RAT), the population of the study comprises of three (3) mathematics teachers’ holders of Nigerian Certificate in Education (NCE) teaching primary six and 210 pupils in their intact classes were used for the study. The data collected were analyzed using mean, standard deviation, analysis of variance, analysis of covariance and t- test. The findings indicated that the pupils taught rational number by a teacher that has high conceptual and procedural knowledge understand and perform better than the pupil taught by a teacher who has low conceptual and procedural knowledge of rational number. It is, therefore, recommended that teachers in primary schools should be encouraged to enrich their conceptual knowledge of rational numbers. Also, the superiority performance of teachers in procedural knowledge in rational number should not become an obstruction of understanding. Teachers Conceptual and procedural knowledge of rational numbers should be balanced so that primary school pupils will have a view of better teaching and learning of rational number in our contemporary schools.

Keywords: conceptual, procedural knowledge, rational number, pupils

Procedia PDF Downloads 451

Authors: Feddaoui Amina

Abstract:

Through this study we will try to shed light on the theoretical framework proposed for understanding creative accounting as a financial numbers game and one of the most important techniques of accounts manipulation, its main actors and its practices. We will discover the role of the modified Jones model (1995) in detecting creative accounting practices using discretionary accruals. Finally we will try to confirm the importance and the need to address this type of practices using corporate governance as a main control system and an important defense line to reduce these dangerous accounts manipulation.

Keywords: financial numbers game, creative accounting, modified Jones model, accounts manipulation

Procedia PDF Downloads 477

Authors: Md. Shah Alam

Abstract:

Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.

Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix

Procedia PDF Downloads 363

Authors: Peter Jean-Paul, Shanaz Wahid

Abstract:

The problem of division by zero can be stated as: “what is the value of 0 x 1/0?” This expression has been considered undefined by mathematicians because it can have two equally valid solutions either 0 or 1. Recently semi-structured complex number set was invented to solve “division by zero”. However, whilst the number set had some merits it was considered to have a poor theoretical foundation and did not provide a quality solution to “division by zero”. Moreover, the set lacked consistency in simple algebraic calculations producing contradictory results when dividing by zero. To overcome these issues this research starts by treating the expression " 0 x 1/0" as a quantum mechanical system that produces two tangled results 0 and 1. Dirac Notation (a tool from quantum mechanics) was then used to redefine the unstructured unit p in semi-structured complex numbers so that p represents the superposition of two results (0 and 1) and collapses into a single value when used in algebraic expressions. In the process, this paper describes a new number set called Quantum Semi-structured Complex Numbers that provides a valid solution to the problem of “division by zero”. This research shows that this new set (1) forms a “Field”, (2) can produce consistent results when solving division by zero problems, (3) can be used to accurately describe systems whose mathematical descriptions involve division by zero. This research served to provide a firm foundation for Quantum Semi-structured Complex Numbers and support their practical use.

Keywords: division by zero, semi-structured complex numbers, quantum mechanics, Hilbert space, Euclidean space

Procedia PDF Downloads 157

Authors: Hisyam Hidayatullah

Abstract:

This world events consciously or not realize everything has a pattern, until the events of the universe according to the Big Bang theory of the solar system which makes so regular in the rotation. The author would like to create a results curve area between the quadratic function y=kx2 and line y=ka2 using GeoGebra application version 4.2. This paper can provide a series that is no less interesting with Fourier series, so that will add new material about the series can be calculated with sigma notation. In addition, the ranks of the unique natural numbers of extensive changes in established areas. Finally, this paper provides analytical and geometric proof of the vast area in between the lines and curves that give the area is formed by y=ka2 dan kurva y=kx2, x-axis, line x=√a and x=-√a make a series of numbers for k=1 and a ∈ original numbers. ∑_(i=0)^n=(4n√n)/3=0+4/3+(8√2)/3+4√3+⋯+(4n√n)/3. The author calls the series “H154M”.

Keywords: sequence, series, sigma notation, application GeoGebra

Procedia PDF Downloads 376

Authors: Peng Li, Chuanri Li, Tao Li

Abstract:

Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method and gives concrete processes on determining the factor set, the factor weight set, judgment set, and multi-grade fuzzy comprehensive evaluation. To determine the weight of factor set, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in the fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: reliability allocation, fuzzy arithmetic, allocation weight, linear programming

Procedia PDF Downloads 341

Authors: Hosein Shokoohmand, Mohamad Esmaeil Jomeh

Abstract:

The present thesis studies the effect of different factors such as frequency of oscillatory flow, change in constant wall heat flux and two-phase current state, on heat transfer in a pipe in presence of porous medium. In this experimental study is conducted for Reynolds numbers in a range of Re=850 to Re=10000 and oscillatory frequencies of 5, 20, 10, 30 and 40 Hz with constant heat flux of 585 w/m2 and 819 w/m2. The results indicate that increase in oscillation frequency in higher frequencies for heat flux of 585 w/m2 leads to an increase in heat transfer; however, in the rest of tests it results in a heat transfer decrease. Increasing Reynolds number in a pulsation mist flow causes an increase in average Nusselt number values. The effect of oscillation frequencies in a pulsation mist flow for different Reynolds numbers has revealed different results, in a way that for some Reynolds numbers an increase of frequency has led to a heat transfer decrease.

Keywords: Reynolds numbers, frequency of oscillatory flow, constant heat flux, mist flow

Procedia PDF Downloads 494

Authors: Raliatu Mohammed Kashim

Abstract:

The study investigated primary school teachers conceptual and procedural knowledge of rational numbers to determine how it effects on pupil’s achievement on rational number. Specifically, primary school teachers’ level of conceptual and procedural knowledge about rational number and its effects on their pupils understanding of rational number in primary school was explored. The study was carried out in Bauchi state of Nigeria, Using a multistage design. The first stage was a descriptive design. The second stage involves a pre-test post-test only quasi experiment design. The population of the study comprises of six mathematics teachers holding the Nigerian Certificate in Education (NCE) teaching primary six and their two hundred and ten pupils in intact class. Two instrument namely Conceptual and Procedural knowledge Test (CPKT) and Rational number Achievement Test (RAT) were used for data collection. Data collected was analyzed using ANCOVA and Scheffe’s Test. The result revealed a significant differences between pupils taught by teachers with high conceptual and procedural knowledge and those target by teachers with low conceptual and procedural knowledge.

Keywords: conceptual knowledge, procedural knowledge, rational numbers, multistage design

Procedia PDF Downloads 387

Authors: Hamed Sanei, Mohammad Bagher Ayani

Abstract:

Optimizations of Plate Heat Exchangers (PHS) have received great attention in the past decade. In this study, heat transfer and pressure drop coefficients are compared for rectangular and circular PHS employing numerical simulations. Plates are designed to have equivalent areas. Simulations were implemented to investigate the efficiency of PHSs considering heat transfer, friction factor and pressure drop. Amount of heat transfer and pressure drop was obtained for different range of Reynolds numbers. These two parameters were compared with aim of F "weighting factor correlation". In this comparison, the minimum amount of F indicates higher efficiency. Results reveal that the F value for rectangular shape is less than circular plate, and hence using rectangular shape of PHS is more efficient than circular one. It was observed that, the amount of friction factor is correlated to the Reynolds numbers, such that friction factor decreased in both rectangular and circular plates with an increase in Reynolds number. Furthermore, such simulations revealed that the amount of heat transfer in rectangular plate is more than circular plate for different range of Reynolds numbers. The difference is more distinct for higher Reynolds number. However, amount of pressure drop in circular plate is less than rectangular plate for the same range of Reynolds numbers which is considered as a negative point for rectangular plate efficiency. It can be concluded that, while rectangular PHSs occupy more space than circular plate, the efficiency of rectangular plate is higher.

Keywords: Chevron corrugated plate heat exchanger, heat transfer, friction factor, Reynolds numbers

Procedia PDF Downloads 300

Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava

Abstract:

This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

Procedia PDF Downloads 472

Authors: R. M. Kashim

Abstract:

The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

Keywords: conceptual knowledge, primary school teachers, procedural knowledge, rational numbers

Procedia PDF Downloads 328

Authors: Y. El Khchine, M. Sriti

Abstract:

In the present work, the forced convection heat transfer and fluid flow past an unconfined semi-circular cylinder is investigated. The two-dimensional simulation is employed for Reynolds numbers ranging from 10 ≤ Re ≤ 200, employing air (Pr = 0.71) as an operating fluid with Newtonian constant physics property. Continuity, momentum, and energy equations with appropriate boundary conditions are solved using the Computational Fluid Dynamics (CFD) solver Ansys Fluent. Various parameters flow such as lift, drag, pressure, skin friction coefficients, Nusselt number, Strouhal number, and vortex strength are calculated. The transition from steady to time-periodic flow occurs between Re=60 and 80. The effect of the Reynolds number on heat transfer is discussed. Finally, a developed correlation of Nusselt and Strouhal numbers is presented.

Keywords: forced convection, semi-circular cylinder, Nusselt number, Prandtl number

Procedia PDF Downloads 109

Authors: Ana Rahma Yuniarti, Ki Moo Lim

Abstract:

Slowed myocardial conduction velocity (CV) and shortened action potential duration (APD) due to some reason are associated with an increased risk of re-entrant excitation, predisposing to cardiac arrhythmia. That is because both of CV reduction and APD shortening induces shortening of wavelength. In this study, we investigated quantitatively the cardiac mechanical responses under various CV and APD using multi-scale computational model of the heart. The model consisted of electrical model coupled with the mechanical contraction model together with a lumped model of the circulatory system. The electrical model consisted of 149.344 numbers of nodes and 183.993 numbers of elements of tetrahedral mesh, whereas the mechanical model consisted of 356 numbers of nodes and 172 numbers of elements of hexahedral mesh with hermite basis. We performed the electrical simulation with two scenarios: 1) by varying the CV values with constant APD and 2) by varying the APD values with constant CV. Then, we compared the electrical and mechanical responses for both scenarios. Our simulation showed that faster CV and longer APD induced largest resultants wavelength and generated better cardiac pumping efficacy by increasing the cardiac output and consuming less energy. This is due to the long wave propagation and faster conduction generated more synchronous contraction of whole ventricle.

Keywords: conduction velocity, action potential duration, mechanical contraction model, circulatory model

Procedia PDF Downloads 204

Authors: Meiqun Yin, Jidong Zhang, Fan Liu

Abstract:

The paper investigates the impact of social media on audit opinion. The numbers of posting and reposting negative reports from SINA Micro-blog are collected to measure the influence of social media. The research collected the samples from Chinese public firms from 2012 to 2014. It is found that the numbers of posting and reposting negative reports in SINA Micro-Blog would significantly relate to the qualified opinion while controlling firm size. Another finding is that the numbers of posting and reposting negative reports would be much more significantly impact on audit opinion if the firm received a qualified opinion in the previous period. It is also found that the involvement of more independent directors has no relationship with the influence of social media on audit opinion.

Keywords: association, social media, audit opinion, SINA Micro-Blog

Procedia PDF Downloads 265