Annual Research Symposium
http://repository.kln.ac.lk/handle/123456789/2460
20200811T20:27:39ZInfluence of Gender on Academic Performance: A Comparative Study between Management and Commerce Undergraduates in the University of Kelaniya, Sri Lanka
http://repository.kln.ac.lk/handle/123456789/7960
Influence of Gender on Academic Performance: A Comparative Study between Management and Commerce Undergraduates in the University of Kelaniya, Sri Lanka
Weerakkody, W.A.S.; Ediriweera, A.N.
Many studies have been carried out on the factors affecting the students' academic
performance in university examinations. Some of these factors have been identified
as attendance of lectures, knowledge of English, income of the parents, perceptions of
learning, attitudes of students and lecturers towards education, teaching aids and method and
environmental factors. In countries such as United Kingdom, Australia, New Zealand and
USA, it has been recorded that, gender has a significant relationship with the examination
performance. Further, these studies have been done for individual subjects. According to
this, it can be identified that there are theoretical explanations in respect of influence of
gender on university students' academic performance. But there is a lack of comparative
studies. Most of them have examined the difference of relationship between gender and
academic performance of several categories of university students in Western countries.
Therefore, it is important to conduct research in nonWestern context. As such, this research
tries to indicate the difference of influence of gender on academic performance of various
student groups in the Sri Lankan university system by selecting Management & Commerce
students who study in the Diversity of Kelaniya.
The objective of the research is to investigate whether there is a significant difference of the
performance of Bachelor of Business Management (Human Resource, Accountancy, and
Marketing) Special Degree Examinations and performance of the Bachelor of Commerce
Special Degree Examinations among the university students with respect to their gender.
Variables are neither manipulated nor controlled for the study. Hence, the study was
conducted in a non contrived setting. The data for this study was collected at a several point
in time. Sample for this study was selected from the students of the above mentioned study
programmes. The survey was carried out using 5 years data related to the period, from
2002/2003 academic year to 2006/2007 academic year. The sample was consisted of 1200
students ( 600 females and 600 males). Stratified random sampling was used to select the
sample. The unit of analysis was at the individual level. For this study, independent sample
ttest was used to compare the academic performance of two ��ender categories. Results
indicated that there is no significant difference between Commerce and Management
students but significant differences could be seen between the academic performance of
the male and female students in this study. Exploratory data analysis indicated that in all
the course units of Management degrees and Commerce degree, female students tend to
perform better at the university examinations than their male counterparts. Hence, the study
found that irrespective of the fact that students are Management or Commerce; female
students have higher academic performance than the male students.
20080101T00:00:00ZAn Assessment of the Influence of Fundamental Factors on Share Prices in Sri Lanka
http://repository.kln.ac.lk/handle/123456789/7936
An Assessment of the Influence of Fundamental Factors on Share Prices in Sri Lanka
Fernando, G.W.J.S.
This study analyses certain fundamental factors which are determinants of equity share
prices in Sri Lanka. These factors are earning, growth, leverage, risk and company size.
The literature review of the study have identified various aspects of equity share valuation.
The theoretical and empirical studies have been used to formulate the foundation for the
study. To assess above mentioned fundamental factors on share prices, multiple regression
analyze was used with a log linear model as a cross section analyses related to the period
19932001. The sample for the study was selected from companies registered and listed in
the Colombo Stock Exchange. The sample consisted of 40 companies from a group of239
companies in all industries.
Result show that dividends appear to be a powerful influence in determining share prices
than growth and retained earnings. Business risk and financial risk cannot be assessed
because they are redundant variables. Company size is having a considerable influence on
share prices and, accordingly large companies enj oy higher values for shares.
On the basis of findings the following observation was made about the stock market in Sri
Lanka.
"The determinants of valuation of the share prices are not very clear. It goes mainly by
considering dividend and company size factors which are readily measurable. However,
factors like growth and risk cannot be measured with more certainty"
20080101T00:00:00ZStructure of primitive Pythagorean triples and the proof of a Fermat's theorem
http://repository.kln.ac.lk/handle/123456789/7932
Structure of primitive Pythagorean triples and the proof of a Fermat's theorem
Jayasinghe, W.J.M.L.P.; Piyadasa, R.A.D.
In a short survey of survey of primitive Pythagorean triples (x,y,z) 0 < x < y < z
, we have found that one of x, y, z is divisible by 5 and z is not divisible by 3, there
are Pythagorean triples whose corresponding element are equal , but there cannot be two
Pythagorean triples such that (x10 y��" z1 ), (x1, zP z
2
) , where z1 and z
2
hypotenuses of the
corresponding Pythagorean triples. This is due to a Fermat's theorem [1] that the area of a
Pythagorean triangle cannot be a perfect square of an integer, which can directly be used
to prove Fermat's last theorem for n = 4. Therefore the preceding theorem is proved using
elementary mathematics, which is the one of the main objectives of this contribution. All
results in this contribution are summarized as a theorem.
Theorem
If (x, y, z) is a primitive Pythagorean triangle, where z is the hypotenuse, then z is never
divisible by 3, andJ? = O(mod3) , xyz = O(mod5) ,and there are Pythagorean triangles
whose corresponding one side is the same. But there are no two Pythagorean triangles such
that (x1,y"z1) , (x"z"z
2
) ), where z"z
2
are hypotenuses.
Proof of the theorem
Pythagoras' equation can be written as
z2 =y2+x2 ,(x,y)= 1 (1)
and if z = O(mod 3) ,then since J? is not divisible by 3, z2= y2 1+ x2 1+ 2 .Now,
it follows at once from Fermat's little theorem that z cannot be divisible by 3. If
xyz is not divisible by 5, squaring (1), one obtains z4 = y4 + x4 + 2x2 y2 and hence
z4 1 = y4 1+ x 4 1+ 2(x2 y2 ± 1)+ t, where t = 1 or 3. Therefore xyz = O(mod5). It
is easy to obtain two Pythagorean triples whose corresponding two elements are equal,
from the pairwise disjoint sets which have recently been obtained in Ref.2. For example
3652 =3642 +2 2 3652 =3642 +2 2 3652 =3572 +�� 2 .Now, assume that there exists ' '
two primitive Pythagorean triples of the form
a
z = bz + cz
dz =az +cz
(1)
(2)
It is clear that a is odd and c = O(mod 3) .F rom these two equations, one obtains immediately
d2  b2 = 2c2, d2 + b2 = 2a2, and therefore
d4 b4 = 4c2a2 = w�� (3)
It has been proved by Fermat, after obtaining the representation of the primitive Pythagorean
triples as x = 2rs,y = r2 s2 ,z = r2 + s2, where 0 < s < r and r,s are of opposite parity,
that (3) has no non trivial integral solution for d,b, w.To prove the same in an easy
manner consider the equation d2 + b2 = 2a2 in the form d2 a2 = a2 b2 and writing it
as ( d a)( d + a) = (a b)( a +b) use the technique used in Ref.3 to obtain the parametric
solution for d andb If d a= a b., then d + b = 2a , from we deduce db= a2 .This
never holds since (d,a)= 1 = ( b,a) by (1) and (2).1f (d a)!!=( a b) , where (u, v) =1 ,
V
then V ( d + a)= (a +b) . From these two relations, one derives the simultaneous
u
equations
vd ub = a( u v)
ud+vb=a(u+v)
(4a)
(4b)
From ( 4a),( 4b ),it is easy to deduce the relations that we need to prove the theorem as
(v2 + u2 )d = [2uv + u2 v2 ]a, (v2 + u2 )b = [2uv (u2 v2 )]a,
(v2 +u2)(d+b))=4uva, v2 +u2 =2a, assuming that uand v are odd.
Hence d b=(u2 v2),(d+b)=2uv. Therefore d2 b2 =2(u2 v2)uv=2c2 and
hence u, v are perfect squares and we can find two integers g,h such that.
g4 h4 = w21 < w�� .Now, proof of the last part of the theorem follows from the method of
infinite descends of Fermat. Even if u and v are of opposite parity proof of the theorem
can be done in the same way.
To complete the proof of a Fermat's theorem that g4 h4 = w�� is not satisfied by any
nontrivial integers, we write (g2 + h2 )(g2 h2) = w�� , where g,h are of opposite parity,
to obtain g2 + h2 = x2, g2 h2 = y2 and x4 y4 = 4g2 h2 = z�� , where x and y are odd
and eoprime. But, in the case of the main theorem, we have shown that this is not
satisfied by any nontrivial odd x, y and even z0 numbers . This completes the proof of the
Fermat's theorem we mentioned above.
20080101T00:00:00ZExact formula for the sum of the squares of spherical Bessel and Neumann function of the same order
http://repository.kln.ac.lk/handle/123456789/7931
Exact formula for the sum of the squares of spherical Bessel and Neumann function of the same order
Jayasinghe, W.J.M.L.P.; Piyadasa, R.A.D.
The sum of the squares of the spherical Bessel and Neumann function of the same order
(SSSBN)is the square of the modulus of the Hankel function when the argument of all
function are real, and is very important in theoretical physics. However, there is no
exact formula for SSSBN.Corresponding formula, which has been derived by
G.N.Watson[l] is an approximate formula[!], [2] valid for Re(z) > 0 ,and it can be
eo (2 k l)!! r(v + k + !) written as J ,; (z) + N; (z) �� 2 L
(
2 ) and the error term RP satisfies
JrZ k=O 2k z 2k k! f V k + !_ 2
IR I
cosvJr p! I (R(v) ,p) I 2 2P • h ?p < sm  t
P cosR(vJr) (2p)!
p1
where
cosh2vt
= �� m! (v,m)
2m sinh2m t+ R
cosht �� (2m)! P
m=O
Upper bound of RP in the important case when v = n + !_ , is undefined since
2
r(n+l+ m cos R(vJr) =cos VJZ' = 0 ,where R stands for the real part and m!(v, m)= )
r (n +lm )
The same formula has been derived [l]by the method called Barne's method but the
error tern is very difficult to calculate. In this contribution, we will show that an exact
formula exists for SSSBN when the order of the Bessel and the Neumann function is
1 . . 2 () 2 () 2 L
n (2kl) !r (n+ k+ l) n +  ,and It can be wntten as J 1 z + N 1 z =  k 2k ( ) • 2 n+ n+ JrZ 2 z k' r n  k + 1
Proof of the formula
2 2 k=O '
In order to show that the above formula is exact, one has to establish the identity,
cosh(2n+ l)t
= I r (n+l+m) 2 2111sinh2111t (1)
. cosht m��of(n+ 1m) 2m!
It is an easy task to show that the equation (1) holds for n= 0 and n= 1. Now, assume
that the equation ( 1) is true for n �� p. It can be easily shown that
cosh(2 p + 3)t = 4 cosh(2 p + 1)t. sinh 2 t + 2 cosh(2 p + 1) cosh(2 p I)t (2)
and hence the following formula holds.
cosh(2 p + 3)t " r(p +I+ m) 2 2111+2 sinh 2111+2 t " r(p +I +m) 2 2111 sinh 2111 t pI r(p +m) 2 2111 sinh 2111 t
_ ::_:_ = :L + 2 :L  :L 7
7



cosh t lll=o r(p + I m) 2m! lll=o r(p + I m) 2m! lll=o r(p m) 2m!
=l+L...J +LJ +LJ m=l r(pm+2) (2m2). m=l r(p+lm) 2m! m=l r(pm+l) (2m1)
+P
2r(2p + 1) )22P sinh2P t r(2p) 22P sinh2p t 22(p+l) sinh2(p+l) t
where p = + (p v +r(2p+1)
2p! r(2) 2 1} 2p!
It can be shown that
Q = I22m sinh2m t
(p +m+ 1). and P = (2p + 1)22P sinh 2P t + 22(p+I) sinh 2(p+t) t
m=l (pm+ 1) !(2m) !
Hence ,
cosh(2p + 3)t = f r(p +m+ 2)2m sinh2m t
COSht v=O r(p + 2m) 2(m)!
Since (1) is now true for n �� p + 1 , by the mathematical induction , the equation (1) is
true for all n .By Nicholson's formula[1],
Jv2(z)+Nv2(z)= :2 J K0(2zsinht)cosh 2wd t (3)
0
where K0 (z) = �� Jezcosht dt is the modified Bessel function of the second kind of the
00
zero order. Substituting for cosh(2v.t) from (1) and using
we obtain
n (2k1J!r(v+k+J) J 12(z)+ N /(z)= 2 �� 2
n+2 n+2 71Z L..J k 2k ( 1 ) k=O 2 Z k!r V k + 2
from which the square of the modulus of the Hankel function follows immediately.
20080101T00:00:00Z