Annual Research Symposium (ARS)
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Item Providing access to public health information via the institutional repository, Faculty of Medicine: A feasibility study based on medical undergraduates.(University of Kelaniya, 2013) Abeygunasekera, C.M.; Marasinghe, M.P.L.R.Community Medicine Clerkship and Community Attachment programs provide opportunity for medical undergraduates to learn how public health services are provided to the community. Their knowledge on health promotion, disease prevention, healthcare planning and management, demography and understanding epidemiology of diseases in the Sri Lankan context are very important. They are expected to read from diverse information sources to gain this knowledge, in addition to field based learning. As most of the recommended reading materials are considered grey literature sources, students are in a difficulty to access those resources within the library. Students face difficulties in accessing available online materials too, as some of the websites do not provide the information in a user friendly manner. With the understanding of possible barriers to access information, the Medical Library, University of Kelaniya, has developed a repository collection on ‘Public Health Information Resources,’ which are recommended as student reading materials for Community Medicine Clerkship and Attachment programs. This is under its online Institutional Repository (IR), developed using DSpace Software. This repository provides links to access a collection of resources published by different institutes. This is in addition to university libraries, which develop online digital repositories to preserve and distribute the intellectual scholarly information of the parent institute. A questionnaire and the User Guide to access the repository were given to a sample of fifty (50) students from Batch 21, who completed the Clerkship programme. Response rate to the questionnaire was 82% and more than 80% of students who were among the respondents ranked the collection as a useful resource which fulfilled their public health information needs. Barriers to information access were also assessed. Respondents have identified a list of difficulties they had in the past. Based on the feedback received, a resource collection inclusive of students’ suggestions is being planned to be introduced to the next batch of students.Item Information Seeking Habits and Practices of Freshman Medical Students of University of Kelaniya(Faculty of Graduate Studies, University of Kelaniya, Sri Lanka, 2016) Abeygunasekera, C.; Solangaarachchi, I.; Beddage, T.; Hewage, S.Studying information-seeking habits of different groups of students is important as a decision making tool for collection development practices and introducing variety to library services. This study examined the past experiences of information access and usage by freshman medical students prior to their university admission. A survey was conducted on the new batch of MBBS students admitted in 2016 using a self-administered questionnaire distributed at the orientation programme. Of the 155 respondents, majority (65.1%) were female students. They represented eight administrative districts of the country. Highest percentage of students was admitted from the Western Province (52.9%), while 20.6% and 10.3% were from North Western and Central provinces respectively. Students who reportedly visited the library at least on a weekly basis constituted 52.9% of the sample, while the remaining 47.1% did so less frequently. Even though the main information seeking mode was searching the web (99%), a considerable number of students used library books (80%) and personal textbooks (61.9%). Library books were a source of information for 83.7% of females and 75.5% of males, while use of personal text books for this purpose was noted by 62.2% of female and 60.4% of male students. Books lent by colleagues were a source of information for 37.8% of females and 47.2% males. The main purpose of information used by majority of students (84%) was self-study. Seventy-six percent (n=118) of students used information for gaining additional subject knowledge while 68.4% (n=106) used it for entertainment and 50.3% (n=78) for project work. School library is the place for information access for 98.7% of the students, followed by town council libraries (37.4%) and provincial council libraries (16.8%). There was no significant difference between males and females (p = 0.701) or those from the Western Province and other provinces (p = 0.082), when it comes to frequency of library usage. The research finds that even though the main information seeking method of sampled freshman medical students is the internet, a considerable number still rely on libraries and other print based resources.Item The red shifts of pulses of light which are emitted at a point on the surface of a sphere and at a point inside of the sphere comprising electrically counterpoised dust with constant uniform density as observed by an observer in a large distance away in the exterior region(University of Kelaniya, 2013) Wimaladharma, N.A.S.N.; de Silva, N.; Hewageegana, P.S.A sphere, comprising a special kind of matter, with electrically counterpoised dust in which all the elastic forces have been cancelled out has been considered. A static spherically symmetric solution to Einstein’s field equations has been found using a new set of boundary conditions. In introducing these new boundary conditions, we assume that the radial coordinates in and out of the sphere need not be the same and we are guided by the notion of what may be called proper distances and proper times of two observers on either side of the sphere .In these new boundary conditions we replace ordinary partial derivatives by generalized partial derivatives in curvilinear coordinates. Then the solution takes the form 2 2 2 2 2 2 2 2 1 dr r d l r c dt l r ds 0 r a 2 2 2 2 2 2 2 2 2 2 1 1 1 dR R d R A c dT R A ds R A where l a l a A 2 2 , l r is the solution of the Lane-Emden equation y r lx dx dy x dx d x , 1 2 3 2 , l is a constant of dimension length , a is the coordinate radius of the sphere. In our approach r a in the matter-filled region corresponds to R Ain the region without matter, outside the sphere. The red shift of a pulse of light emitted at a point on the surface of the sphere as observed by an observer who is at a large distance in the exterior region of the sphere is calculated. This valueequals to l a l a l a l a when the observer is at infinity. The comparison of this value with the value for the red shift obtained using the metric derived using the standard (Lichernowicz) boundary conditions which says that the metric coefficients and their partial derivatives are continuous across the boundary of the sphere when the observer is at infinity is also done. It is shown that the values obtained for the red shifts are the same irrespective of the boundary conditions used. The red shift of a pulse of light emitted at a point inside of the surface of the sphere as observed by an observer who is at a large distance in the exterior region of the sphere is also calculated and it is shown that the value obtained is different from the value obtained using the metric derived using standard (Lichernowicz) boundary conditions.Item The velocity of a particle relative to an observer instantaneously at rest coinciding with the point through which the particle passes in a spherical distribution of matter comprising electrically counterpoised dust with constant uniform density(University of Kelaniya, 2013) Wimaladharma, N.A.S.N.; de Silva, N.; Hewageegana, P.S.A sphere comprising a special kind of matter, electrically counterpoised dust in which all the elastic forces have been cancelled out, has been considered. A static spherically symmetric solution to Einstein’s field equations has been found using a new set of boundary conditions. In introducing these new boundary conditions, we assume that the radial coordinates in and out of the sphere need not be the same and we are guided by the notion of what may be called proper distances and proper times of two observers on either side of the sphere. In these new boundary conditions we replace ordinary partial derivatives by generalized partial derivatives in curvilinear coordinates. Then the solution takes the form 2 2 2 2 2 2 2 2 1 dr r d l r c dt l r ds 0 r a 2 2 2 2 2 2 2 2 2 2 1 1 1 dR R d R A c dT R A ds R A where l a l a A 2 2 , l r is the solution of the Lane-Emden equation y r lx dx dy x dx d x , 1 2 3 2 , l is a constant of dimension length , a is the coordinate radius of the sphere . In our approach r a in the matter-filled region corresponds to R A in the region without matter, outside the sphere.The velocity of a particle relative to an observer instantaneously at rest coinciding with the point through which the particle passes has been calculated for this metric. Using these values, a minimum value for a measure of energy with which the particle has to be projected at the center of the sphere, to reach infinity has been calculated to be l a l a l a c where c is the velocity of the light. A minimum value for a measure of energy with which the particle has to be projected at the center of the sphere, to reach infinity has also been calculated for metric derived using standard (Lichernowicz) boundary conditions which says that the metric coefficients and their partial derivatives are continuous across the boundary of the sphere. It is shown that we have the same value irrespective of boundary conditions used. Also a minimum value for a measure of energy with which the particle has to be projected at the center of the sphere, to reach the exterior region of the sphere has been calculated to be l a c . The comparison of this value with the value obtained for the metric derived using standard (Lichernowicz) boundary conditions is also done and it is shown that these two values are the same irrespective of the boundary conditions used.Item Thetanulls of cyclic curves of genus 4(University of Kelaniya, 2013) Wijesiri, G.S.Let be an irreducible smooth projective cyclic curve of genus defined over the complex field . These are by definition compact Riemann surfaces of genus (unless we allow singular points) admitting an automorphism such that and generates a normal subgroup of the automorphism group of When the curve is hyperelliptic, then the curve has extra automorphisms, in particular is not the hyperelliptic involution. The condition implies to having an equation for the curve, where is an affine coordinate on and has order . The branch points of together with the signature of the cover provide algebraic coordinates for the curve in moduli. Choosing a symplectic homology basis for a given curve of genus such that the intersection products and where is the Kronecker delta and a basis for the space of holomorphic 1- forms such that we can define the period matrix of It can be shown that is an element of the Siegel upper-half space . For any and any the Riemann’s theta function is defined as Any point where is the Jacobian of the curve can be written uniquely as , where For any the theta function with rational characteristics is defined as When the entries of column vectors are from the set , then the corresponding theta functions with rational characteristics are known as theta characteristics. A scalar obtained by evaluating a theta characteristics at is called a thetanull. The problem of expressing branch points in terms of transcendentals (period matrix, thetanulls, etc.,) is classical. This is an old problem that goes back to Riemann, Jacobi, Picard and Rosenhein. We do not aim here at a complete account of the classical or contemporary work on these problems. We determine the curves of genus 4 in terms of thetanulls and further study relations among the classical thetanulls of cyclic curves (of genus 4) with an automorphisms. In our work we use formulas for small genus curves introduced by Rosenhein, Thomae’s formulas for hyperelliptic curves, some recent results of Hurwitz space theory, and symbolic manipulation. Inverting the period map has an application in fast genus two curves arithmetic incryptography. We determine similar formulas for genus 4 hyperelliptic curves as the one used in cryptography using genus 2 algebraic curves.Item Derivation and application of a Stochastic Differential Equation (SDE) Model for cricket(University of Kelaniya, 2013) Weerasinghe, W.M.H.N.; Mallawa Arachchi, D.K.Stochastic Differential Equations (SDE) can be used to model many dynamical systems in place of the Markov chain approach. In this research, the SDE model that accounts for the score of a limited over cricket match is formulated based on the assumption that the runs scored and the number of wickets fallen within a single delivery follow a stochastic process. The peculiarity of this model is that a discrete process is modeled by a continuous-time continuous-space stochastic process, which is called a SDE model. Numerical simulations are performed using Euler-Maruyama method. Parameter estimation is carried out using the data available online for teams and individual players. Parameters were estimated for the players in the Indian and Sri Lanka teams considering ten ODI and fifteen T20 matches played between 2009 and 2012. Simulated results give evidence to the validity of the model. Some statistical tests were used to investigate the significance of the results. The model may be used for forecasting purposes. It can also be used to find a suitable batting order that optimizes the total score. The model can also be improved by taking into consideration the other factors that affect the scoring of an innings. For example, the pitch, weather condition and home-ground advantage can be taken into considerationItem Modeling inflation in Sri Lanka using time series and econometric approaches(University of Kelaniya, 2013) Udani, S.A.L.M.; Jayasundara, D.D.M.Inflation is the most important macro economic variable often used to measure the economic growth of a country. It is the rise of the general level of prices of goods and services in an economy over a period of time. In Sri Lanka, it is expressed as the percentage change of the Colombo Consumer Price Index (CCPI). Modeling can be done either using time series approach or econometric approach. Time series approach predicts inflation through modeling the past annual inflation figures only; while econometric approach considers the impact of other economic factors on annual inflation rates. In time series approach an ARIMA(1,1,1) model was fitted to the annual inflation rates of 1953 to 2001 using MINITAB since it is the best model to forecast future inflation rates. The fitted values and the actual figures were approximately similar and the actual values were within the upper limits and lower limits. Econometric approach was conducted by fitting a cointegration equation and vector error correction model (VECM) for the annual inflation rates of 1977 to 2004 using EViews. Since the data series were cointegrated, the ordinary least square (OLS) model was inappropriate. The cointegration equation revealed long run relationship of inflation. Money supply and exchange rate played a significant role of the long run relationship. A vector error correction model implied a short run relationship of inflation. The R-squared value of VECM model showed that real gross domestic product, money supply and exchange rate explain 86.83% of the variance of inflation. It implied that the impact of percentage changes at past years of money supply, exchange rate and real gross domestic product affected the current level of inflation, highly. Both exchange rate and money supply have significant impacts on long run and short run relationships of inflation.Item Roots of a cubic and simple proof of Fermat’s last theorem for n=3(University of Kelaniya, 2013) Ubeynarayana, C.U.; Piyadasa, R.A.D.; Munasinghe, J.; Ekanayake, E.M.P.Introduction: Fermat’s last theorem (FLT) which was written in 1637, became public in 1670, without proof. It has not only evoked the interest of mathematicians but baffled many for over three hundred and fifty years [1],[2]. It is well known that FLT despite its rather simple statement had been difficult to prove even for the small prime exponent .The main objective of this paper is to provide simple proof of the theorem for this special exponent using the Method of Taragalia and Cardom of solving a cubic which is much older than Fermat’s last theorem. Proof of Fermat’s last theorem for n=3 Fermat’s last theorem for 3 n can be stated as that the equation , ( , ) 1 3 3 3 z y x x y (1.1) is not satisfied by non-trivial integer triples x, y, z . Assume that the equation is satisfied by non-trivial integer triples x, y, z . If let x 3m1, y 3k 1, z 3s 1, then we have (2,0, 2)(mod3 ) 3 3 2 y x However 1(mod3 ) 3 2 z , therefore our assumption is wrong and we conclude that xyz 0(mod3) . Since we consider the equation (1.1) for positive and negative integer values, without loss of generality, we can assume that y 0(mod3) ,and let 0(mod3 ) m y . Then 3 1 3 3 3 z x 3 u , z y h , x y g m due to Barlow relations, where are respectively the factors of . Now, 3 2( ) 3 3 1 3 3 g u h x y z m (1.2) Since x y z x (z y) (x y) z y (z x) , x y z 0(3 ugh)It can be shown that [1], 3 3 3 3 3 x y z 3(x y)(z x)(z y) 3 h u g m (1.3) and therefore 3 2 3 0 3 3 3 1 3 g h u ugh m m (1.4) This necessary condition must be satisfied by the integer parameters , of respectively. We will first fix the parameters of and show that (1.4) is not satisfied by integer for any integer using the Method of Tartagalia and Cardoon[4] of finding a roots of a cubic. The equation (1.4) is of the form 3 0 3 3 3 g vwg v w (1.5) where 3 3 3 1 3 3 v w 3 u h m , uh vw m 1 3. 2 , and its roots can be written as 2 , w v w v and +w (1.6) with the cube root of unity. Now 3 3 , w v are the roots of the equation 0 2 3 H Gt t (1.7) where (3 ) 3 1 3 3 G u h m , . 3. 2 1uh H m Moreover real and distinct and this equation has only one real root, namely, g v w, since the discriminant of (1.5) is ,where ( 4 ) 2 3 G H is the discriminant of (1.7),and it is negative. Therefore, it has only one real root [4]. Note that 2 3 6 2 6 3 3 3 3 6 3 1 3 3 2 3 3 3 3 (G 4H ) 3 u 14.3 u h h (3 u h ) 4.3 u h m m m m which is positive when uh 0. On the other hand . 3 1 3 3 3 3 3 3 (3 u h ) 32.3 u h m m which is positive when If 1 2 1 2 1 1 1 1 v w ,v w ,v w (1.8) is another representation of the roots, we must have 2 2 1 1 1 1 v w v w,v w v w , v w v w 2 1 2 1 or v w v w v w v w 2 2 1 1 1 1 , , 2 1 2 1 v w v w In other words , ( ) ( ) 1 1 1 1 v v w w v v w w or ( ) ( ), 1 1 v w v w ( ) ( ) 1 1 v w v w This means that v v w w 1 1 , or , . 1 1 v w w v Therefore, roots must be unique. In particular, we must have a unique real root. From (1.4), it follows that the real root can be expressed in the form g h j m 1 3 or g j h m 1 3 where j is an integer satisfying (3, j) 1. This is due to the fact that ( )[( ) 3 ] 0(mod3 ). 3 3 2 m g h g h g h gh It is now clear that 3 h satisfies the equation 0 2 3 t Gt H , This means that (3 ) 8.3 0 6 3 1 3 3 3 3 3 3 3 h u h h u h m m implying that 0 u or , 0 h that is y 0 or x 0 in Fermat’s equation. Hence there is no non-trivial integral triple satisfying the Fermat equation (1.1). We have shown that Fermat’s Last Theorem for 3 n can be proved without depending on the method of infinite descent or complex analysis. The proof given above is short and simple, and simpler than proving [3] the theorem using the method of infinite descent.Item A Virtual Dressing System(University of Kelaniya, 2013) Rajasinghe, R.M.C.N.A.; Wijegunasekara, M.C.Virtual dressing rooms are a relatively new concept, which is slowly becoming a trend on various fashion websites. The virtual dressing room allows a customer who is at home, to virtually try on dresses, and other fashions online. This allows the consumer to gauge, if the style and the fit are an appropriate match before adding it to the virtual shopping cart of a webstore. Customers are nervous about purchasing garments electronically, because they are unsure of what size to order, and how the clothes will look on them. Merchants are nervous about the high volume of apparel returns. For a merchant, the handling of an apparel return can cost up to four times what it costs to process the initial sale of the garment. Industry analysts have estimated that apparel returns for electronic merchants range from about 10% for very basic items to between 35% to 40% for high end clothing. The single biggest reason for returns of apparel purchased electronically is poor fit. The objective of this research is to address the above stated issues. Firstly, to improve the ability to make the right buy, with better opportunities to experiment with the dress style. These are the competitive advantages. Secondly, to reduce the buying risk, time, effort, discomfort, queues at shops, and the proportion of returned items. To address these issues, the technology of image processing, template matching (which is for finding small parts of the image) and thresholding, the simplest method of image segmentation was used. NET was the main framework for this application and C# and C++ are used as the language for the development. The OpenCv libraries were also used for this application. Main functions implemented in this system can be catogorized as follows: 1. Loading the video stream to the form 2. Embedding textile images 3. Facilitating the user to move the textile image that was embedded to the video according to requirements. Any user who is new to the system must select the given item and background. Selected values are written in a text file. These text file values are read by logic files and it would load the appropriate images into the forms. The function cvtColor() in OpenCv converts the input image from one color space to another. In the case of transformation to-from RGB color space the ordering of the channels is specified explicitly (RGB or BGR). In case of non-linear, the input RGB image is normalized to the proper value range in order to get the correct results. Image is scaled before a transformation. Transformations are done within the RGB space by adding or removing an alpha channel, reversing the channel order, conversion to-from 16-bit RGB color (R5:G6:B5 or R5:G5:B5), conversion to-from grayscale and the conversion from a RGB image to gray color. The 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit in a range in between 0 to 1 and the values are then converted to the destination data type. The system is functioned by a threshold color and all the detecting functions are working according to these threshold colors. The OpenCv threshold method is used for the above. The Bayer pattern used in CCD and CMOS cameras allows color pictures from a single plane where R, G and B pixels (sensors of a particular component) are interleaved. The output RGB components of a pixel are interpolated from 1, 2 or 4 neighbors of the pixel with the same color. The implemented system can be used to overcome the identified problems of this study. The system was a real success with the illumination conditions that were used to test the system.Item Roach type of graphs and the characteristics of their partitioning(University of Kelaniya, 2013) Perera, K.K.K.R.The goal of the graph partitioning problem is to find groups such that entities within the same group are similar and different groups are dissimilar. Spectral clustering methods use eigenvalues and eigenvectors of matrices associated with graphs and are widely used in graph-partitioning problems. In this presentation, results concerning spectral clustering properties of roach type of graphs ( and are the number of vertices in the upper and lower paths of the graph) will be presented. The concrete formula for the minimum normalized cut of has already been presented, (Perera & Mizoguchi, 2013). The normalized cut is used to minimize the disassociation between partitions of graphs and maximize the association within partitions. Here we find the characteristic polynomials for the normalized Laplacian matrix of weighted path and roach type of graphs using Chebyshev polynomials and properties of tridiagonal matrices. Subsequently, we find conditions for and , based on which spectral methods perform poorly compared with the minimum normalized cut.