Science
http://repository.kln.ac.lk/handle/123456789/1
2017-07-28T16:57:49ZAnalysis of a stochastic predator-prey model
http://repository.kln.ac.lk/handle/123456789/207
Analysis of a stochastic predator-prey model
Prasadini, K.D.S.; Mallawa Arachchi, D.K.
In biological systems Lotka-Volterra predator-prey model describes the population
dynamics of two interacting species of predators and its preys. Classical predatorprey
model is a primitive deterministic model governed by the two differential
equations, namely,
���� = (������ − ��������) ���� and ���� = (�������� − ������) ����
where �� and �� denote prey and predator respectively, and ����, ����, ���� and ���� are
parameters.
This model can be improved by introducing stochasticity that accounts for the
random fluctuations of a realistic predator-prey dynamical system. In this research
work, we use Stochastic Differential Equation (SDE) approach. There are various
ways, based on various assumptions, to incorporate SDE. One common approach is
to use equations of the following form:
���� = (������ − ��������) ���� + ��(���� + ����)�� ������
���� = (�������� − ������) ���� + ��(���� + ����)�� ������
These types of Stochastic Differential Equations (SDE) can be simulated in Matlab
using numerical methods such as Euler-Maruyama method. Phase planes of the
deterministic and stochastic models are carried out to demonstrate the behavior of
this modified model.
Our initial goal is to compare different stochastic models with the original
deterministic model through simulations. The deterministic model has a positive
equilibrium which is globally stable for positive values of the parameters.
Nevertheless, in the stochastic model, the predator and prey populations may tend to
extinction. Extinction percentages of predator or prey population are summarized
and analyzed through this research work.
2016-01-01T00:00:00ZThe chromatic number of prime graph of a noncommutative ring Mn×n(Z2)
http://repository.kln.ac.lk/handle/123456789/206
The chromatic number of prime graph of a noncommutative ring Mn×n(Z2)
Kolombage, K.A.D.D.B.V.; Wijesiri, G.S.
Graph theory is a significant area of Mathematics as its outstanding applications in
many fields such as biochemistry, electrical engineering, computer science and
operational research. Besides Graph theory, Ring theory is an abstract area in
Mathematics. A ring consists of a set equipped with two binary operations that
generalize the arithmetic operations of addition (+) and multiplication(∗). Theorems
obtained as a result of abstract study of rings can be applied to solve problems arising
in number theory, geometry and many other fields.
The study of rings with the help of graphs began when a graph of a commutative ring
was defined by I. Beck in 1988. Then a new bridge was formed between graph theory
and the algebraic concept “ring” noted as prime graph of a ring ��, denoted by ����(��)
by B. Satyanarayana, K. Shyam Prasad, and D.Nagaraju in 2010. Later on with the
help of existing concepts, K. Patra and S. Kalita investigated the chromatic number
of prime graph, ������(ℤ��) of ring ℤ�� for different values of ��.
Prime graph of a ring �� is a graph whose vertices are all elements of the ring and any
two vertices ��, �� of the vertex set are adjacent if and only if �� ∗ �� = 0 or �� ∗ �� = 0
and �� ≠ ��
In this paper, we investigate the chromatic number of prime graph of some noncommutative
rings ����×��(ℤ��) for different values of n. The chromatic number of
prime graph of some commutative rings are formed on the recognition of the
conjecture that chromatic number, ��(��) and clique number are the same. But for
non-commutative rings this is not always the case. Hence, in order to find the
chromatic number of prime graph of a non-commutative ring, ����×��(ℤ��), we have
looked into MATLAB for a tactical solution.
2016-01-01T00:00:00ZHomogenization of Daily Temperature Data
http://repository.kln.ac.lk/handle/123456789/135
Homogenization of Daily Temperature Data
Hewaarachchi, A.P.; Li, Yingbo; Lund, Robert; Rennie, Jared
This paper develops a method for homogenizing daily temperature series. While daily temperatures are
statistically more complex than annual or monthly temperatures, techniques and computational methods
have been accumulating that can now model and analyze all salient statistical characteristics of daily temperature
series. The goal here is to combine these techniques in an efficient manner for multiple changepoint
identification in daily series; computational speed is critical as a century of daily data has over 36 500 data
points. The method developed here takes into account 1) metadata, 2) reference series, 3) seasonal cycles, and
4) autocorrelation. Autocorrelation is especially important: ignoring it can degrade changepoint techniques,
and sample autocorrelations of day-to-day temperature anomalies are often as large as 0.7. While daily homogenization
is not conducted as commonly as monthly or annual homogenization, daily analyses provide
greater detection precision as they are roughly 30 times as long as monthly records. For example, it is relatively
easy to detect two changepoints less than two years apart with daily data, but virtually impossible to flag
these in corresponding annually averaged data. The developed methods are shown to work in simulation
studies and applied in the analysis of 46 years of daily temperatures from South Haven, Michigan.
2017-01-01T00:00:00ZPhenolic extracts of coconut oil cake: a potential alternative for synthetic antioxidants
http://repository.kln.ac.lk/handle/123456789/134
Phenolic extracts of coconut oil cake: a potential alternative for synthetic antioxidants
Seneviratne, K.N.; Prasadani, W.C.; Jayawardena, B.
Limitations of natural antioxidants include relatively low antioxidant activity, narrow range of food systems where the antioxidants are effective and limited thermal stability compared to synthetic antioxidants. In the present study, the phenolic extract of coconut oil cake (COCE) was tested for antioxidant activity-related food stabilization. Heat stabilities of COCE and synthetic antioxidants were determined by measuring the induction time of sunflower oil enriched with heat-treated antioxidants. In the β-carotene-linoleate emulsion used for testing antioxidant activity, COCE can retain 96 ± 2% of initial colour intensity while BHT can retain 89 ± 2% of initial colour intensity at 60 μg mL–1 concentration after two hours. TBARS contents (MDA equivalents / kg of meat) in COCE-treated and control pork samples after 14 days was 2.80 ± 0.57 and 22.55 ± 2.30 respectively. Heat stability varies in the order butylated hydroxytoluene (BHT) < (butylated hydroxyanisole (BHA) < COCE < tertiary butylhydroxyquinone (TBHQ). The results of these experiments suggest that COCE is a versatile and thermally stable natural antioxidant mixture effective in stabilizing many food systems.
2016-01-01T00:00:00Z