Abstract: In this paper, we investigate certain spaces of
generalized functions for the Fourier and Fourier type integral
transforms. We discuss convolution theorems and establish certain
spaces of distributions for the considered integrals. The new Fourier
type integral is well-defined, linear, one-to-one and continuous with
respect to certain types of convergences. Many properties and an
inverse problem are also discussed in some details.
Abstract: In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.
Abstract: In this paper, x-ray impact of Taguchi method and design of experiment philosophy to project relationship between various factors leading to output yield strength of rebar is studied. In bar mill of an integrated steel plant, there are two production lines called as line 1 and line 2. The metallic properties e.g. yield strength of finished product of the same material is varying for a particular grade material when rolled simultaneously in both the lines. A study has been carried out to set the process parameters at optimal level for obtaining equal value of yield strength simultaneously for both lines.
Abstract: We study the fracture mechanics of peeling of thin films perfectly bonded to a rigid substrate of any random surface topology using an analytical formulation. A generalized theoretical model has been developed to determine the peel strength of thin elastic films. It is demonstrated that an improvement in the peel strength can be achieved by modifying the surface characteristics of the rigid substrate. Characterization study has been performed to analyze the effect of different parameters on effective peel force from the rigid surface. Different surface profiles such as circular and sinusoidal has been considered to demonstrate the bonding characteristics of film-substrate interface. Condition for the instability in the debonding of the film is analyzed, where the localized self-debonding arises depending upon the film and surface characteristics. This study is towards improved adhesion strength of thin films to rigid substrate using different textured surfaces.
Abstract: Course timetabling problems occur every semester in a university which includes the allocation of resources (subjects, lecturers and students) to a number of fixed rooms and timeslots. The assignment is carried out in a way such that there are no conflicts within rooms, students and lecturers, as well as fulfilling a range of constraints. The constraints consist of rules and policies set up by the universities as well as lecturers’ and students’ preferences of courses to be allocated in specific timeslots. This paper specifically focuses on the preferences of the course timetabling problem in one of the public universities in Malaysia. The demands will be considered into our existing mathematical model to make it more generalized and can be used widely. We have distributed questionnaires to a number of lecturers and students of the university to investigate their demands and preferences for their desired course timetable. We classify the preferences thus converting them to construct one mathematical model that can produce such timetable.
Abstract: The construction of Intensity-Duration-Frequency (IDF) curves is one of the most common and useful tools in order to design hydraulic structures and to provide a mathematical relationship between rainfall characteristics. IDF curves, especially those in Peninsular Malaysia, are often built using moving windows of rainfalls. However, these windows do not represent the actual rainfall events since the duration of rainfalls is usually prefixed. Hence, instead of using moving windows, this study aims to find regionalized distributions for IDF curves of extreme rainfalls based on storm events. Homogeneity test is performed on annual maximum of storm intensities to identify homogeneous regions of storms in Peninsular Malaysia. The L-moment method is then used to regionalized Generalized Extreme Value (GEV) distribution of these annual maximums and subsequently. IDF curves are constructed using the regional distributions. The differences between the IDF curves obtained and IDF curves found using at-site GEV distributions are observed through the computation of the coefficient of variation of root mean square error, mean percentage difference and the coefficient of determination. The small differences implied that the construction of IDF curves could be simplified by finding a general probability distribution of each region. This will also help in constructing IDF curves for sites with no rainfall station.
Abstract: Most of self-tuning fuzzy systems, which are
automatically constructed from learning data, are based on the
steepest descent method (SDM). However, this approach often
requires a large convergence time and gets stuck into a shallow
local minimum. One of its solutions is to use fuzzy rule modules
with a small number of inputs such as DIRMs (Double-Input Rule
Modules) and SIRMs (Single-Input Rule Modules). In this paper,
we consider a (generalized) DIRMs model composed of double
and single-input rule modules. Further, in order to reduce the
redundant modules for the (generalized) DIRMs model, pruning and
generative learning algorithms for the model are suggested. In order
to show the effectiveness of them, numerical simulations for function
approximation, Box-Jenkins and obstacle avoidance problems are
performed.
Abstract: In this work, we propose an algorithm developed under Python language for the modeling of ordinary scalar Bessel beams and their discrete superpositions and subsequent calculation of optical forces exerted over dielectric spherical particles. The mathematical formalism, based on the generalized Lorenz-Mie theory, is implemented in Python for its large number of free mathematical (as SciPy and NumPy), data visualization (Matplotlib and PyJamas) and multiprocessing libraries. We also propose an approach, provided by a synchronized Software as Service (SaaS) in cloud computing, to develop a user interface embedded on a mobile application, thus providing users with the necessary means to easily introduce desired unknowns and parameters and see the graphical outcomes of the simulations right at their mobile devices. Initially proposed as a free Android-based application, such an App enables data post-processing in cloud-based architectures and visualization of results, figures and numerical tables.
Abstract: At present, application of the extension of soft set theory in decision making problems in day to day life is progressing rapidly. The concepts of fuzzy soft set and its properties have been evolved as an area of interest for the researchers. The generalization of the concepts recently got importance and a rapid growth in the research in this area witnessed its vital-ness. In this paper, an application of the concept of generalized fuzzy soft set to make decision in a social problem is presented. Further, this paper also highlights some of the key issues of the related areas.
Abstract: The very well-known stacked sets of numbers referred
to as Pascal’s triangle present the coefficients of the binomial
expansion of the form (x+y)n. This paper presents an approach (the
Staircase Horizontal Vertical, SHV-method) to the generalization of
planar Pascal’s triangle for polynomial expansion of the form
(x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle
is different from other generalizations of Pascal’s triangles given in
the literature. The coefficients of the generalized Pascal’s triangles,
presented in this work, are generated by inspection, using embedded
Pascal’s triangles. The coefficients of I-variables expansion are
generated by horizontally laying out the Pascal’s elements of (I-1)
variables expansion, in a staircase manner, and multiplying them with
the relevant columns of vertically laid out classical Pascal’s elements,
hence avoiding factorial calculations for generating the coefficients
of the polynomial expansion. Furthermore, the classical Pascal’s
triangle has some pattern built into it regarding its odd and even
numbers. Such pattern is known as the Sierpinski’s triangle. In this
study, a presentation of Sierpinski-like patterns of the generalized
Pascal’s triangles is given. Applications related to those coefficients
of the binomial expansion (Pascal’s triangle), or polynomial
expansion (generalized Pascal’s triangles) can be in areas of
combinatorics, and probabilities.
Abstract: Scripts are one of the basic text resources to understand
broadcasting contents. Topic modeling is the method to get the
summary of the broadcasting contents from its scripts. Generally,
scripts represent contents descriptively with directions and speeches,
and provide scene segments that can be seen as semantic units.
Therefore, a script can be topic modeled by treating a scene segment
as a document. Because scene segments consist of speeches mainly,
however, relatively small co-occurrences among words in the scene
segments are observed. This causes inevitably the bad quality of
topics by statistical learning method. To tackle this problem, we
propose a method to improve topic quality with additional word
co-occurrence information obtained using scene similarities. The
main idea of improving topic quality is that the information that
two or more texts are topically related can be useful to learn high
quality of topics. In addition, more accurate topical representations
lead to get information more accurate whether two texts are related
or not. In this paper, we regard two scene segments are related
if their topical similarity is high enough. We also consider that
words are co-occurred if they are in topically related scene segments
together. By iteratively inferring topics and determining semantically
neighborhood scene segments, we draw a topic space represents
broadcasting contents well. In the experiments, we showed the
proposed method generates a higher quality of topics from Korean
drama scripts than the baselines.
Abstract: The modelling of physical phenomena, such as the
earth’s free oscillations, the vibration of strings, the interaction of
atomic particles, or the steady state flow in a bar give rise to Sturm-
Liouville (SL) eigenvalue problems. The boundary applications of
some systems like the convection-diffusion equation, electromagnetic
and heat transfer problems requires the combination of Dirichlet and
Neumann boundary conditions. Hence, the incorporation of Robin
boundary condition in the analyses of Sturm-Liouville problem. This
paper deals with the computation of the eigenvalues and
eigenfunction of generalized Sturm-Liouville problems with Robin
boundary condition using the finite element method. Numerical
solution of classical Sturm–Liouville problem is presented. The
results show an agreement with the exact solution. High results
precision is achieved with higher number of elements.
Abstract: The Com-Poisson (CMP) model is one of the most
popular discrete generalized linear models (GLMS) that handles
both equi-, over- and under-dispersed data. In longitudinal context,
an integer-valued autoregressive (INAR(1)) process that incorporates
covariate specification has been developed to model longitudinal
CMP counts. However, the joint likelihood CMP function is
difficult to specify and thus restricts the likelihood-based estimating
methodology. The joint generalized quasi-likelihood approach
(GQL-I) was instead considered but is rather computationally
intensive and may not even estimate the regression effects due
to a complex and frequently ill-conditioned covariance structure.
This paper proposes a new GQL approach for estimating the
regression parameters (GQL-III) that is based on a single score vector
representation. The performance of GQL-III is compared with GQL-I
and separate marginal GQLs (GQL-II) through some simulation
experiments and is proved to yield equally efficient estimates as
GQL-I and is far more computationally stable.
Abstract: Fading noise degrades the performance of cellular
communication, most notably in femto- and pico-cells in 3G and 4G
systems. When the wireless channel consists of a small number of
scattering paths, the statistics of fading noise is not analytically
tractable and poses a serious challenge to developing closed
canonical forms that can be analysed and used in the design of
efficient and optimal receivers. In this context, noise is multiplicative
and is referred to as stochastically local fading. In many analytical
investigation of multiplicative noise, the exponential or Gamma
statistics are invoked. More recent advances by the author of this
paper utilized a Poisson modulated-weighted generalized Laguerre
polynomials with controlling parameters and uncorrelated noise
assumptions. In this paper, we investigate the statistics of multidiversity
stochastically local area fading channel when the channel
consists of randomly distributed Rayleigh and Rician scattering
centers with a coherent Nakagami-distributed line of sight component
and an underlying doubly stochastic Poisson process driven by a
lognormal intensity. These combined statistics form a unifying triply
stochastic filtered marked Poisson point process model.
Abstract: We consider the problem of stabilization of an unstable
heat equation in a 2-D, 3-D and generally n-D domain by deriving a
generalized backstepping boundary control design methodology. To
stabilize the systems, we design boundary backstepping controllers
inspired by the 1-D unstable heat equation stabilization procedure.
We assume that one side of the boundary is hinged and the other
side is controlled for each direction of the domain. Thus, controllers
act on two boundaries for 2-D domain, three boundaries for 3-D
domain and ”n” boundaries for n-D domain. The main idea of the
design is to derive ”n” controllers for each of the dimensions by
using ”n” kernel functions. Thus, we obtain ”n” controllers for the
”n” dimensional case. We use a transformation to change the system
into an exponentially stable ”n” dimensional heat equation. The
transformation used in this paper is a generalized Volterra/Fredholm
type with ”n” kernel functions for n-D domain instead of the one
kernel function of 1-D design.
Abstract: In the present study we have investigated axial
buckling characteristics of nanocomposite beams reinforced by
single-walled carbon nanotubes (SWCNTs). Various types of beam
theories including Euler-Bernoulli beam theory, Timoshenko beam
theory and Reddy beam theory were used to analyze the buckling
behavior of carbon nanotube-reinforced composite beams.
Generalized differential quadrature (GDQ) method was utilized to
discretize the governing differential equations along with four
commonly used boundary conditions. The material properties of the
nanocomposite beams were obtained using molecular dynamic (MD)
simulation corresponding to both short-(10,10) SWCNT and long-
(10,10) SWCNT composites which were embedded by amorphous
polyethylene matrix. Then the results obtained directly from MD
simulations were matched with those calculated by the mixture rule
to extract appropriate values of carbon nanotube efficiency
parameters accounting for the scale-dependent material properties.
The selected numerical results were presented to indicate the
influences of nanotube volume fractions and end supports on the
critical axial buckling loads of nanocomposite beams relevant to
long- and short-nanotube composites.
Abstract: This paper studies a mathematical model based on the
integral equations for dynamic analyzes numerical investigations of a
non-uniform or multi-material composite beam. The beam is
subjected to a sub-tangential follower force and elastic foundation.
The boundary conditions are represented by generalized
parameterized fixations by the linear and rotary springs. A
mathematical formula based on Euler-Bernoulli beam theory is
presented for beams with variable cross-sections. The non-uniform
section introduces non-uniformity in the rigidity and inertia of beams
and consequently, more complicated equilibrium who governs the
equation. Using the boundary element method and radial basis
functions, the equation of motion is reduced to an algebro-differential
system related to internal and boundary unknowns. A generalized
formula for the deflection, the slope, the moment and the shear force
are presented. The free vibration of non-uniform loaded beams is
formulated in a compact matrix form and all needed matrices are
explicitly given. The dynamic stability analysis of slender beam is
illustrated numerically based on the coalescence criterion. A realistic
case related to an industrial chimney is investigated.
Abstract: Predicting earnings management is vital for the capital
market participants, financial analysts and managers. The aim of this
research is attempting to respond to this query: Is there a significant
difference between the regression model and neural networks’
models in predicting earnings management, and which one leads to a
superior prediction of it? In approaching this question, a Linear
Regression (LR) model was compared with two neural networks
including Multi-Layer Perceptron (MLP), and Generalized
Regression Neural Network (GRNN). The population of this study
includes 94 listed companies in Tehran Stock Exchange (TSE)
market from 2003 to 2011. After the results of all models were
acquired, ANOVA was exerted to test the hypotheses. In general, the
summary of statistical results showed that the precision of GRNN did
not exhibit a significant difference in comparison with MLP. In
addition, the mean square error of the MLP and GRNN showed a
significant difference with the multi variable LR model. These
findings support the notion of nonlinear behavior of the earnings
management. Therefore, it is more appropriate for capital market
participants to analyze earnings management based upon neural
networks techniques, and not to adopt linear regression models.
Abstract: In this paper, we present a quantum statistical
mechanical formulation from our recently analytical expressions for
partial-wave transition matrix of a three-particle system. We report
the quantum reactive cross sections for three-body scattering
processes 1+(2,3)→1+(2,3) as well as recombination
1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The
analytical expressions of three-particle transition matrices and their
corresponding cross-sections were obtained from the threedimensional
Faddeev equations subjected to the rank-two non-local
separable potentials of the generalized Yamaguchi form. The
equilibrium quantum statistical mechanical properties such partition
function and equation of state as well as non-equilibrium quantum
statistical properties such as transport cross-sections and their
corresponding transport collision integrals were formulated
analytically. This leads to obtain the transport properties, such as
viscosity and diffusion coefficient of a moderate dense gas.
Abstract: In this paper, temperature extremes are forecast by
employing the block maxima method of the Generalized extreme
value(GEV) distribution to analyse temperature data from the
Cameroon Development Corporation (C.D.C). By considering two sets
of data (Raw data and simulated data) and two (stationary and
non-stationary) models of the GEV distribution, return levels analysis
is carried out and it was found that in the stationary model, the
return values are constant over time with the raw data while in the
simulated data, the return values show an increasing trend but with
an upper bound. In the non-stationary model, the return levels of
both the raw data and simulated data show an increasing trend but
with an upper bound. This clearly shows that temperatures in the
tropics even-though show a sign of increasing in the future, there
is a maximum temperature at which there is no exceedence. The
results of this paper are very vital in Agricultural and Environmental
research.