Abstract: The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.
Abstract: In this paper, effectiveness of a machine design process is evaluated on the basis of the specific output calculus. Concretely, a screw-worm gear mechanical transmission is designed by using the classical and the 3D-CAD methods. Strength analysis and drawing of the designed parts is substantially aided by employing the SolidWorks software. Quality of the design process is assessed by manufacturing (printing) the parts, and by computing the efficiency, specific load, as well as the specific output (work) of the mechanical transmission. Influence of the stroke, travelling velocity and load on the mechanical output, is emphasized. Optimal design of the mechanical transmission becomes possible by the appropriate usage of the acquired results.
Abstract: This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.
Abstract: Classical matrix calculus and Routh-Hurwitz stability conditions, applied to the snake-like motion of the conical wheel axle, lead to the conclusion that the hunting mode is inherently unstable, and its natural frequency is a complex number. In order to analytically solve such a complicated vibration model, either the inertia terms were neglected, in the model designated as geometrical, or restrictions on the creep coefficients and yawing diameter were imposed, in the so-called dynamical model. Here, an alternative solution is proposed to solve the hunting mode, based on the observation that the bullet train wheel axle is equipped with cylindrical wheels. One argues that for such wheel treads, the geometrical hunting is irrelevant, since its natural frequency becomes nil, but the dynamical hunting is significant since its natural frequency reduces to a real number. Moreover, one illustrates that the geometrical simplification of the wheel causes the stabilization of the hunting mode, since the characteristic quartic equation, derived for conical wheels, reduces to a quadratic equation of positive coefficients, for cylindrical wheels. Quite simple analytical expressions for the damping ratio and natural frequency are obtained, without applying restrictions into the model of contact. Graphs of the time-depending hunting lateral perturbation, including the maximal and inflexion points, are presented both for the critically-damped and the over-damped wheel axles.
Abstract: The paper discusses the subinterval-based numerical
method for fractional derivative computations. It is now referred
to by its acronym – SubIval. The basis of the method is briefly
recalled. The ability of the method to be applied in time stepping
solvers is discussed. The possibility of implementing a time step size
adaptive solver is also mentioned. The solver is tested on a transient
circuit example. In order to display the accuracy of the solver –
the results have been compared with those obtained by means of a
semi-analytical method called gcdAlpha. The time step size adaptive
solver applying SubIval has been proven to be very accurate as
the results are very close to the referential solution. The solver is
currently able to solve FDE (fractional differential equations) with
various derivative orders for each equation and any type of source
time functions.
Abstract: We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in Lq space to infinite in non-Lq space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.
Abstract: The paper reviews design and implementation of a Calculus Course required for the Biomedical Competency Based Program developed as a joint project between The University of Texas Rio Grande Valley, and the University of Texas’ Institute for Transformational Learning, from the theoretical perspective as presented in scholarly work on active learning, formative assessment, and on-line teaching. Following a four stage curriculum development process (objective, content, delivery, and assessment), and theoretical recommendations that guarantee effectiveness and efficiency of assessment in active learning, we discuss the practical recommendations on how to incorporate a strong formative assessment component to address disciplines’ needs, and students’ major needs. In design and implementation of this project, we used Constructivism and Stage-by-Stage Development of Mental Actions Theory recommendations.
Abstract: The present paper deals with the flexural vibrations
of homogeneous, isotropic, generalized micropolar microstretch
thermoelastic thin Euler-Bernoulli beam resonators, due to
Exponential time varying load. Both the axial ends of the
beam are assumed to be at simply supported conditions. The
governing equations have been solved analytically by using Laplace
transforms technique twice with respect to time and space variables
respectively. The inversion of Laplace transform in time domain
has been performed by using the calculus of residues to obtain
deflection.The analytical results have been numerically analyzed with
the help of MATLAB software for magnesium like material. The
graphical representations and interpretations have been discussed
for Deflection of beam under Simply Supported boundary condition
and for distinct considered values of time and space as well. The
obtained results are easy to implement for engineering analysis and
designs of resonators (sensors), modulators, actuators.
Abstract: This paper reviews the crucial situation in higher education in Taiwan due to the rapid decline of the birth rate in the past three decades, and how the government and local colleges/universities work to face the challenge. Recruiting international students is one of the possible ways to resolve the problem, but offering enough courses in English is one of the main obstacles when the majority of learners are still Taiwanese students. In the academic year of 2012, Chung Yuan Christian University determined to make its campus international and began to enforce two required courses for freshmen taught in English. It failed in the beginning, but succeeded in the following academic year of 2013. Using the teaching evaluations accumulated in the past three years, this paper aims to clarify the myths which had been bothering most faculties. It also offers some suggestions for college/university teachers interested in giving lectures in English to English as Second Language (ESL) learners. A conclusion is presented at the end of the paper, in which the author explained why Taiwanese students could learn their profession in English.
Abstract: The goal of this project is to investigate constant
properties (called the Liouville-type Problem) for a p-stable map
as a local or global minimum of a p-energy functional where
the domain is a Euclidean space and the target space is a
closed half-ellipsoid. The First and Second Variation Formulas
for a p-energy functional has been applied in the Calculus
Variation Method as computation techniques. Stokes’ Theorem,
Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and
the Bochner Formula as estimation techniques have been used to
estimate the lower bound and the upper bound of the derived
p-Harmonic Stability Inequality. One challenging point in this project
is to construct a family of variation maps such that the images
of variation maps must be guaranteed in a closed half-ellipsoid.
The other challenging point is to find a contradiction between the
lower bound and the upper bound in an analysis of p-Harmonic
Stability Inequality when a p-energy minimizing map is not constant.
Therefore, the possibility of a non-constant p-energy minimizing
map has been ruled out and the constant property for a p-energy
minimizing map has been obtained. Our research finding is to explore
the constant property for a p-stable map from a Euclidean space into
a closed half-ellipsoid in a certain range of p. The certain range of
p is determined by the dimension values of a Euclidean space (the
domain) and an ellipsoid (the target space). The certain range of p
is also bounded by the curvature values on an ellipsoid (that is, the
ratio of the longest axis to the shortest axis). Regarding Liouville-type
results for a p-stable map, our research finding on an ellipsoid is a
generalization of mathematicians’ results on a sphere. Our result is
also an extension of mathematicians’ Liouville-type results from a
special ellipsoid with only one parameter to any ellipsoid with (n+1)
parameters in the general setting.
Abstract: The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.
Abstract: Classification is an important data mining technique
and could be used as data filtering in artificial intelligence. The
broad application of classification for all kind of data leads to be
used in nearly every field of our modern life. Classification helps us
to put together different items according to the feature items decided
as interesting and useful. In this paper, we compare two
classification methods Naïve Bayes and ADTree use to detect spam
e-mail. This choice is motivated by the fact that Naive Bayes
algorithm is based on probability calculus while ADTree algorithm is
based on decision tree. The parameter settings of the above
classifiers use the maximization of true positive rate and
minimization of false positive rate. The experiment results present
classification accuracy and cost analysis in view of optimal classifier
choice for Spam Detection. It is point out the number of attributes to
obtain a tradeoff between number of them and the classification
accuracy.
Abstract: Methodology is suggested to design a linear rectangular microstrip array antenna based on Yagi antenna theory. The antenna with different directors' lengths as parasitic elements were designed, simulated, and analyzed using HFSS. The calculus and results illustrate the effectiveness of using specific parasitic elements to improve the directivity and gain for microstrip array antenna. The results have shown that the suggested methodology has the potential to be applied for improving the antenna performance. Maximum radiation intensity (Umax) of the order of 0.47w/st was recorded, directivity of 6.58dB, and gain better than 6.07dB are readily achievable for the antenna that working.
Abstract: The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.
Abstract: This work presents a new type of the affine projection
(AP) algorithms which incorporate the sparsity condition of a
system. To exploit the sparsity of the system, a weighted l1-norm
regularization is imposed on the cost function of the AP algorithm.
Minimizing the cost function with a subgradient calculus and
choosing two distinct weighting for l1-norm, two stochastic gradient
based sparsity regularized AP (SR-AP) algorithms are developed.
Experimental results exhibit that the SR-AP algorithms outperform
the typical AP counterparts for identifying sparse systems.
Abstract: Information security plays a major role in uplifting the standard of secured communications via global media. In this paper, we have suggested a technique of encryption followed by insertion before transmission. Here, we have implemented two different concepts to carry out the above-specified tasks. We have used a two-point crossover technique of the genetic algorithm to facilitate the encryption process. For each of the uniquely identified rows of pixels, different mathematical methodologies are applied for several conditions checking, in order to figure out all the parent pixels on which we perform the crossover operation. This is done by selecting two crossover points within the pixels thereby producing the newly encrypted child pixels, and hence the encrypted cover image. In the next lap, the first and second order derivative operators are evaluated to increase the security and robustness. The last lap further ensures reapplication of the crossover procedure to form the final stego-image. The complexity of this system as a whole is huge, thereby dissuading the third party interferences. Also, the embedding capacity is very high. Therefore, a larger amount of secret image information can be hidden. The imperceptible vision of the obtained stego-image clearly proves the proficiency of this approach.
Abstract: Technology, multimedia in Open Educational
Resources, can contribute positively to student performance in an
online instructional environment. Student performance data of past
four years were obtained from an online course entitled Applied
Calculus (MA139). This paper examined the data to determine
whether multimedia (independent variable) had any impact on
student performance (dependent variable) in online math learning,
and how students felt about the value of the technology. Two groups
of student data were analyzed, group 1 (control) from the online
applied calculus course that did not use multimedia instructional
materials, and group 2 (treatment) of the same online applied calculus
course that used multimedia instructional materials. For the MA139
class, results indicate a statistically significant difference (p = .001)
between the two groups, where group 1 had a final score mean of
56.36 (out of 100), group 2 of 70.68. Additionally, student
testimonials were discussed in which students shared their experience
in learning applied calculus online with multimedia instructional
materials.
Abstract: This study discovers a novel framework of individual
level technology adoption known as I-P (Individual- Privacy) towards
health information application in Smart National Identity Card. Many
countries introduced smart national identity card (SNIC) with various
applications such as health information application embedded inside
it. However, the degree to which citizens accept and use some of the
embedded applications in smart national identity remains unknown to
many governments and application providers as well. Moreover, the
factors of trust, perceived risk, Privacy concern and perceived
credibility need to be incorporated into more comprehensive models
such as extended Unified Theory of Acceptance and Use of
Technology known as UTAUT2. UTAUT2 is a mainly widespread
and leading theory up to now. This research identifies factors
affecting the citizens’ behavioural intention to use health information
application embedded in SNIC and extends better understanding on
the relevant factors that the government and the application providers
would need to consider in predicting citizens’ new technology
acceptance in the future. We propose a conceptual framework by
combining the UTAUT2 and Privacy Calculus Model constructs and
also adding perceived credibility as a new variable. The proposed
framework may provide assistance to any government planning,
decision, and policy makers involving e-government projects.
Empirical study may be conducted in the future to provide proof and
empirically validate this I-P framework.
Abstract: The paper describes the experiments and the kinetic
parameters calculus of the gasoil hydrofining. They are presented
experimental results of gasoil hidrofining using Mo and promoted
with Ni on aluminum support catalyst. The authors have adapted a
kinetic model gasoil hydrofining. Using this proposed kinetic model
and the experimental data they have calculated the parameters of the
model. The numerical calculus is based on minimizing the difference
between the experimental sulf concentration and kinetic model
estimation.
Abstract: In this paper, fractional order feedback control of a ball
beam model is investigated. The ball beam model is a particular
example of the double Integrator system having strongly nonlinear
characteristics and unstable dynamics which make the control of
such system a challenging task. Most of the work in fractional order
control systems are in theoretical nature and controller design and its
implementation in practice is very small. In this work, a successful
attempt has been made to design a fractional order PIλDμcontroller
for a benchmark laboratory ball and beam model. Better performance
can be achieved using a fractional order PID controller and it is
demonstrated through simulations results with a comparison to the
classic PID controller.