Edge Detection of Long Bone X-Ray Images using Cubic B-Spline Wavelet
1Nor Ashikin Mohamad Kamal and 2Arsmah Ibrahim
1Pusat Pengajian Sains Komputer
2Pusat Pengajian Matematik
Fakulti Teknologi Maklumat dan Sains Kuantitatif
UiTM Shah Alam
Edge detection is a fundamental step in image analysis. This is because edges characterize object boundaries useful for identification of object in a scene. The importance of edge detection increases as more people seek for automation in image processing systems. Determining bone edges is important because it can provide surgeons with important information for diagnosis, which in turn enables them to give better treatment decision to their patients. Many edge detectors have been developed and presently wavelet transform is one of the popular approaches. This is because wavelet transform has the advantage of detecting edges using different scales. Edges can be represented and detected efficiently through its local maximum. This paper discusses the implementation of Cubic B-Spline wavelet on long bone x-ray images in detecting the edges using the local maxima modulus. Preliminary results show that this method can identify edges very well which can make it applicable to detect bone abnormalities.
Finite Elements Model of Shape Memory Alloy Anti-Symmetric Angle-Ply Composite Beams for Active Shape Control
Nik Mohamad, N.A1, Mohd Ihsan, A.K.A.2 and A. Rasid, Z.3
1,2Department of Mechanical & Material Engineering
Universiti Kebangsaan Malaysia, Bangi
3Department of Mechanical Engineering,
Kolej Sains dan Teknologi, UTMKL, KL
Shape memory alloy (SMA) wires are embedded within laminated composite beams to take advantage of the shape memory effect property of the SMA. Active shape controls of these structures are studied using the finite element method. A non-linear finite element model and its source codes were developed for this purpose. Both Euler-Bernoulli’s and Timoshenko’s beam theories are used. The former theory requires 4 degree of freedom elements while in the later the 6 degree of freedom elements are used. The geometric non-linear model is based on the von Karman non-linear strain. The effect of SMA is captured by adding the geometric stiffness matrix to the typical stiffness matrix of composite plates. The Newton-Raphson method is then used to obtain the transverse deflections of the beams. Two methods of shape controls are considered here: The active property tuning (APT) and the active strain energy tuning (ASET). The values of recovery stresses for the ASET improvement of the SMA are determined from the Brinson’s model. Studies are conducted on the anti-symmetric angle ply SMA laminated composite beams. The effect of several parameters such as the geometric, mechanical and SMA transformation effects on the deflections of the SMA composite beams are studied. It was found that the effect of moment recovery on the beam deflection is significant and with appropriate configurations of SMA composite beams, the deflection of the beams due to external loading can be suppressed.
Convergence Monte Carlo Simulation to the Black-Scholes Formula in Pricing Warrants
Department of Mathematics,
Parahyangan Catholic University,
Jalan Ciumbuleuit 94, Bandung,
40141 West Java,
Warrants are call options issued by firms, which gives the holder the right to buy the underlying asset from the firm by a certain date for a certain price. Many methods for pricing warrants. In this paper, the value of the warrant will be determined by using Black-Scholes formula and Monte Carlo simulation. Monte Carlo methods will be used here are standard Monte Carlo and antithetic variable. Warrant value from Black-Scholes formula and Monte Carlo simulation will be compared each other. Convergence warrant value from Monte Carlo simulation to the Black-Scholes formula will be presented here.
Finite Elements Model of Shape Memory Alloy Anti-Symmetric Angle-Ply Composite Plates for Active Modal Modifications
Z.A. Rasid, S. Sarip & M.Z. Hassan
Universiti Teknologi Malaysia
Shape memory alloy (SMA) wires are embedded within laminated composite plates to take advantage of the shape memory effect property of the SMA. Active modal modifications of laminated composite plates with SMA wires are studied using finite element method. A linear finite element model and its source codes were developed for this purpose. The plate-bending model used in this study was developed based on the first order shear deformation theory (FSDT) and the finite element model used is the serendipity quadrilateral element with 40 degree of freedoms per element. The effect of SMA is captured by adding the geometric stiffness matrix to the typical stiffness matrix of composite plates. With the mass matrix, the typical eigen-value problem is solved where the eigen values represent the natural frequencies of the plates. Two methods of frequency improvement are considered here: The active property tuning (APT) and the active strain energy tuning (ASET). The values of recovery stresses for the ASET improvement of the SMA are determined from the Brinson’s model. Studies are conducted on the anti-symmetric angle ply SMA laminated composite plates. The effect of several parameters such as geometric, mechanical and transformation effects on the natural frequencies and the mode shapes of the SMA composite plates are studied. It was found that the effect of SMA is similar for couples of frequency modes where frequencies of mode I and IV seems to have the greatest effect in the case of simply supported and clamped-clamped boundary conditions.
A Preconditioning Technique for Elliptic Problems in Two Dimensions.
Sarah Flora Samson Juan
Universiti Malaysia Sarawak (UNIMAS)
The finite element method is a powerful tool to numerically solve differential equations derived from diverse physical and engineering problems. When the problem is linear, this method leads to a system of linear equations of relatively large size. The Conjugate Gradient method is used to solve the resulting system of linear equations. This paper investigates the performance of the numerical method when the number of iterations is reduced. To achieve this, a two-level addictive Schwarz preconditioner is introduced, based on the domain decomposition method, in the CG method. The quality of this preconditioner is important as this supports the reliability of the method to converge faster. We validate the effectiveness of the preconditioner CG method for some two dimensional elliptic problems and numerical results show that the number of iterations is reduced and the condition number of the preconditioner matrix from the system is much smaller than the non-preconditioned matrix.
Magnetic Contour Plane As A Historical Framework For Brainstorm
Tahir Ahmad *, Rashdi Shah Ahmad** and Liau Li Yun *
*Department Of Mathematics
** Department Of Physics
Faculty of Science
University of Technology Malaysia,
81310 Skudai, Johor.
Embodied biological agents have histories which usually irreversible and reflected in their structure. Without the historical context, we cannot understand their structure, appearance and behaviour. An epilepsy disorder patient is an agent. This paper describes on how FTTM (Fuzzy Topographic Topological Mapping), which has been developed initially as a mathematical model for solving the inverse neuromagnetic problem, can be viewed as a framework for model of irreversible time for the patient.
Two-Generator Two-groups of Class Two of Order 32 and Their Application in Crystallography
1Norashiqin Mohd Idrus, 2Nor Haniza Sarmin and 3Shahrizal Shamsuddin
1,3Fakulti Sains dan Teknologi
Universiti Pendidikan Sultan Idris
35900 Tanjong Malim
Perak Darul Ridzuan.
2Department of Mathematics,
Faculty of Science,
Universiti Teknologi Malaysia,
Johor Darul Ta’zim.
Group Theory is a beautiful area of mathematics that systematizes and formalizes mathematical study of symmetry. Symmetry concepts have many applications in various scientific disciplines such as in biology and chemistry. In physics, it should be emphasized that group theory is primarily valuable for analyzing the effects of known geometrical symmetry on some systems. In this research, we focus on 2-generator p-groups of nilpotency class two of order 32, where p=2 and 3. Specific groups that are isomorphic to each of the group in this classification will first be determined. By choosing those that are symmetry, their application in crystallography, particularly in infrared and Raman spectra activities, will be explored.
The Graph of Relative Diagram Groups from Relative Diagram Groups
1Sri Gemawati and 2Abd. Ghafur Bin Ahmad
1Department of Mathematics,
Faculty Mathematics and Natural Siences,
Universitas Riau, Pekanbaru, Indonesia.
3School of Mathematical Sciences,
Faculty of Science and Technology,
Universiti Kebangsaan Malaysia,
43600 Bangi, Selangor, Malaysia.
In this paper, we will discuss the construction of relative diagram groups from group that presented by relative monoid presentation and their graphs will be presented. The graphs obtained are related to the word in . Therefore, the number of generator of the diagram group can be determined.
Exterior Squares of Infinite Non-Abelian 2-Generator Groups of Nilpotency Class 2
1Nor Haniza Sarmin, 2Nor Muhainiah Mohd Ali, 3Luise-Charlotte Kappe
1,2Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia,
81310 Skudai, Johor.
Department of Mathematical Sciences,Binghamton University,
Binghamton, New York, 13902-6000 USA.
Let R be the class of infinite non-abelian 2-generator groups of nilpotency class 2. Using their classification and non-abelian tensor squares given by N.H. Sarmin in 2002, we determine the exterior squares of all groups in R.
On Counting the Conjugacy Classes of 2-Generator p-Group of Class 2
1Azhana Ahmad, 2Robert F. Morse, 3Nor Haniza Sarmin, 4Satapah Ahmad
1,3Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia,
81310 Skudai, Johor, Malaysia.
2Department of Electrical Engineering and Computer Science, University of Evansville,
Evansville, IN 47722, USA.
4Department of Chemistry, Faculty of Science, Universiti Teknologi Malaysia,
81310 Skudai, Johor, Malaysia.
In this paper, we present results concerning the number of conjugacy classes and the structure of 2-generator p-groups of class 2. Our results rely on the classification of 2-generator p-groups of class two, p and odd prime number given by M. Bacon and L. –C. Kappe in 1993 and p=2 given by L. –C. Kappe, N. H. Sarmin and M. Visscher in 1999. These groups have four types. For type 1, 2, and 3 groups we obtain a count of the conjugacy classes for a base case from which all other groups within each type are central extensions. We derive a recursive formula to count the number of conjugacy classes of the central extensions using our results for the base cases.
Capability of Infinite 2-Generator Groups of Nilpotency Class Two
1Nor Haniza Sarmin, 2Nor Muhainiah Mohd Ali and 3Luise-Charlotte Kappe
1,2Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia
81310 Skudai, Johor, Malaysia.
3Department of Mathematical Sciences, Binghamton University
Binghamton, New York, 13902-6000, USA
A group is called capable if it is a central factor group. R.Baer characterized finitely generated abelian groups which are capable as those groups which have two or more factors of maximal order in their direct decomposition. Using the explicit knowledge of the nonabelian tensor squares of infinite 2-generator groups of nilpotency class two given by N.H. Sarmin in 2002, we characterized the capable ones among those groups.
On the Rosenberger Monster II
Robert Fitzgerald Morse
University of Evansville, Evansville, IN 47722 USA
The largest finite generalized triangle group has order and is called the Rosenberger Monster which we denote by R. The structure of R has been investigated by Rosenberger, Howie, Morse and others both analytically and with computer calculations. In this talk we will report on computing various homological functors for the Rosenberger Monster. This includes computing the Schur Multiplier and the nonabelian tensor square and nonabelian exterior square for R.
Group Theoretical Approach in Determining the Molecular Vibration of the Square Pyramid Molecule
1Rohaidah Hj. Masri, 2Nor’aini Aris, 3Nor Haniza Sarmin & 4Satapah Ahmad
1Department of Mathematics, Faculty of Science, Universiti Pendidikan Sultan Idris
2,3Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia
4Department of Chemistry, Faculty of Science, Universiti Teknologi Malaysia
Group theory provides a systematic approach to describe the symmetry concept in molecular vibrations. An exploitation of this symmetry in polyatomic structure is possible by using group representation theory and the projection operator theory. The underlying group theory, such as the irreducible representations of symmetry group isomorphic to its point group is applied in the specific example of the square pyramid model of AB5 molecule. The work presented in this paper is a preliminary investigation of finding an efficient method of computing and describing molecular vibrations of molecules which exhibit a large number of vibration modes. Here, all the main steps are illustrated with the example of the group of symmetries of a regular polygon, D4. The visualization of vibration modes of AB5 are given in the last part of this paper.
Some Numerical Algorithms for Parallel Multigrid Method on Distributed Parallel Computer Systems
Norma Alias, Tan Sui Chin, Shalela Mohd Mahali
Department of Mathematics,
Faculty of Science,
A highly parallel multigrid-like method for the solution of Partial Differential Equation. This paper, we focuses on three major parallel techniques: domain decomposition, Full Multigrid and preconditioner Multigrid method using F, V, W cycle. Based on some parallel techniques, these methods are straight minimizing the execution time, computational complexity, communication cost, waiting and idle time. The PVM library is implemented in order to exchange the data among processors on a distributer parallel computer systems. The solver algorithms are developed for three-dimensional PDE problem and validated with the available experimental data. Some sequential and parallel performance measurements under consideration are speedup, efficiency, effectiveness, temporal performance, accuracy, convergence and communication cost.
On The Boundedness Of Certain Rough Singular Integral Operators
Hussain M. AI-Qassem
Department of Mathematics and Physics, Qatar University
We establish the boundedness for a class of singular integral operators and a class of related maximal operators when their singular kernels are given by functions in and satisfies a certain integrability condition. Our results shows that the class of operators behaves completely different from the classical class of Calderón-Zygmund operators . Moreover, our results represent an improvement and extension over previously known results.
A Note on the Partial Differential Equations and Convolutions
Adem Kiliçman & Hassan Eltayeb
Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor
A partial differential equation of second order,
and define the matrix
then the PDE is called
Parabolic if the
Hyperbolic if the
Elliptic if the
In this study we consider the
and it was examined that, whether the convolution equation
is invariant under the type PDE where and are solutions of non homogenous than and are also solutions for non homogeneous wave equation where single convolution and double convolution that is defined by
where and are integrable functions, see .
A Study of Two Space Dimensions Generalized Order Partial Differential Equations of the Parabolic Type
1Ithnin Abdul Jalil and 2Rio Hirowati Shariffudin
1Department of Physics, Faculty of Sciences, Universiti of Malaya
2Institute of Mathematical Sciences, Faculty of Science, University of Malaya
50603 Kuala Lumpur, Malaysia.
In this paper we shall study on the methods pertaining to the numerical solution of the generalized order parabolic equation
on a finite rectangular domain , , with , and . We still adopt the shifted Grünwald at all time levels, that is
with as Grünwald weights. The numerical scheme attempted is the Crank-Nicolson method which is implicit in nature. Unlike the classical parabolic equation, the resulting matrix is the lower triangular matrix with non-zero elements on the super diagonal. Normally the tri-diagonal matrix is reduced to bi-diagonal for direct solutions of the tri-diagonal matrix equation. Yet iterative methods are extensively used to solve tri-diagonal matrix. In this paper we report the iterative simulations of the above-mentioned problem. The simulations of even numbers of unknowns are considered.