Journal of Science Latest Articleshttps://jsc.sljol.info/articles/Latest articles published by Journal of Scienceen-usWed, 05 Oct 2022 09:13:19 -0000Actuarial analysis of claim per payment event: theoretically developing estimation link between quantum mechanics and insurance modelinghttps://jsc.sljol.info/article/10.4038/jsc.v12i2.32In general, business, underwriting firms usually write policy terms by imposing additional deductible conditions in order to mitigate the risk of loss and discourage frivolous claims by modifying the indemnity payable by the underwriter where loss occurs. Under deductible conditions, underwriting firms will only be liable in a loss event where it becomes apparent that the loss has exceeded the deductible defined in the policy terms. The maximum accumulated number of losses retained by the insured applying deductible policy modifications is usually set as part of the terms and conditions of the policy documents. This paper develops an analytical framework for evaluating the effect of structural properties of dirac-delta on insurance risk variables with deductible clauses. The objective is to obtain models for the excess of loss random variable in a payment event. In order to achieve this and create analytically sound theoretical platform of investigating payment distribution functions, the quantum structure of dirac-delta is first examined in respect of probability density function. The import of adopting the dirac-delta function in this paper lies in its elegance to permit alternative technique to obtain analytically useful models for insurance severity beneficial to both the insured and insurer with particular reference to rate relativity deductible clause. We then obtained insurance excess of loss severity and variance for an arbitrary policy under deductible coverage conditions. As part of our contributions, theorems in respect of loss were stated and proved for underwriters to see reasons for their applications and use in policy underwriting decisions. Published on 2021-12-28 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i2.32An alternative method for constructing Hadamard matriceshttps://jsc.sljol.info/article/10.4038/jsc.v12i2.33<p class="Default">Symmetric Hadamard matrices are investigated in this research and an alternative method of construction is introduced. Using the proposed method, we can construct Hadamard matrices of order 2<sup>n+1</sup>(<em>q</em>+1) where <em>q ≡</em> 1 (mod 4) and <em>n ≥</em> 1.</p><p class="Default"> </p>This construction can be used to construct an infinite number of Hadamard matrices. For the present study, we use quadratic non-residues over a finite field. Published on 2021-12-28 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i2.33Phytochemicals and antioxidant properties of the leaves of wild guava varieties grown in Sri Lankahttps://jsc.sljol.info/article/10.4038/jsc.v12i2.34Guava (<em>Psidium guajava </em>Linn.) is well-known throughout the world for its food, nutritional, and medicinal properties. Several guava cultivars/varieties are available in Sri Lanka, which can be classified as common, wild, or introduced. Though common guava has been extensively studied for its phytochemistry and pharmacology, only a few studies on wild varieties has been available so far. Therefore, this study focused on the investigation of phytochemical constituents and antioxidants capacity of two main wild guava varieties grown in Sri Lanka namely, <em>Psidium guajava </em>(cv. Getta-pera) and <em>Psidium guineense </em>(cv. Embul-pera). An Ultrasound-assisted-extraction technique was used to extract plant constituents, and water was used as the solvent. The phytochemicals were qualitatively and quantitatively analyzed using standard methods whereas the antioxidant capacity was determined using the DPPH and FRAP assays. Phytochemical screening revealed that both varieties contain most of the important phytochemicals. Though both showed higher anti-oxidant activity, Embul-pera had the highest in both the FRAP and DPPH assays, with 612.69±0.50 mg Trolox Eq/g and IC50 value of 191.69±0.25 ppm respectively. The highest level of all quantified phytochemicals, particularly polyphenolic content (327.87±0.23 mg GAE/g extract) was found in Embul-pera. As a conclusion, two wild guava varieties considered in the study contain a diverse phytochemical profile and higher antioxidant properties similarity to the common guava. It can be recommended that Getta-pera” and “Embul-pera” are excellent alternatives to be used in functional foods and nutraceuticals preparation and hence to promote the cultivation as economic plants. Published on 2021-12-28 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i2.34An alternative approach for the anti-magic labelling of a wheel graph and a pendant graphhttps://jsc.sljol.info/article/10.4038/jsc.v12i2.35The Anti-magic labelling of a graph <em>G</em> with <em>m</em> edges and vertices, is a bijection from the set of edges to the set of integers {1, …, <em>m</em>} such that all ‘<em>n</em>’ vertex summations are pairwise distinct. The vertex summation is the summation of the labels assigned to edges incident to a vertex. There is a conjecture that all simple connected graphs except <em>K<sub>2</sub></em> are anti-magic. In our research, we found an alternative anti-magic labelling method for a wheel graph and a pendant graph. Wheel graph is a graph that contains a cycle of length <em>n</em> - 1 and for which every graph vertex in the cycle is connected to one other graph vertex known as the “hub”. The edges of a wheel, which connect to the hub are called “spokes”. Pendant graph is a corona of the form <em>C<sub>n</sub></em>ʘ<em>K</em><sub>1</sub> where <em>n</em> ≥ 3. We label both wheel graph and pendant graph using the concept of the anti-magic labelling method of the path graph <em>P<sub>n</sub></em><sub>-1</sub>. For wheel graph, we removed the middle vertex of the wheel graph and created a path graph using the vertices in the outer cycle of the wheel graph. Then the spokes of the wheel graph are represented by adding one edge to each vertex. For Pendant graph, we created a path graph using the cycle of the pendant graph and connect the pendant vertices to every vertex of the path graph. In both cases, we label all the edges using the concept of the anti-magic labelling of path graph P<em><sub>n</sub></em><sub>-1</sub>. Finally, we calculated the vertex sum for each vertex and proved that every vertex sums are distinct and in the wheel graph, middle vertex takes the highest value. Published on 2021-12-28 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i2.35Anti-magic like labelling of marigold graphhttps://jsc.sljol.info/article/10.4038/jsc.v12i2.36In this paper, we present a new family of graphs called Marigold graphs and introduce a new labelling method similar to the anti-magic labelling. The Marigold graph is generated from any number of copies of fully binary trees which are going through concentric circles. All copies of trees are connected to a middle vertex and the height of the Marigold graph is increasing with <em>n</em> concentric circles. One copy is considered as one petal in the marigold graph. A Marigold graph with copies (petals) and height (number of concentric circles) <em>k</em> is <em>M <sup>n</sup><sub>k</sub></em> denoted by . The labelling method is defined as follows: A graph with ‘<em>m</em>’ edges and ‘<em>n</em>’ vertices is labelled as an injection from the set of edges to the integers {1, …, <em>x</em>} such that all ‘<em>n</em>’ vertex sums are pairwise distinct, where the vertex sum is the sum of labels of all edges incident with that vertex. In our work, for edge labelling, we consider the petals one by one and denote the <em>r</em><sup>th</sup> edge at <em>k</em><sup>th</sup> level as <em>e<sup>k</sup><sub>r</sub></em> , and define a function to label edges of the first petal. Then define the new labelling method for other petals, such that for <em>n</em><sup>th</sup> petal, edge labelling is starting with <em>J<sub>n</sub></em><sub>–1 </sub>+ 1 (where <em>J<sub>n</sub></em><sub>–1 </sub>is the summation of all edge values in (<em>n</em> –1)<sup>th</sup> petal, ∑<em><sup>i</sup></em><sup>=1</sup><em><sub>m</sub></em> (<em>n</em>–1, <em>i</em>) = <em>J<sub>n</sub></em><sub>–1 </sub>and continue the labelling as a monotonically increasing sequence. We discuss some illustrative examples that might be used for studying the Anti-magic like labelling of Marigold graphs. Published on 2021-12-28 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i2.36A monthly evaluation of microbiological and chemical quality of bottled drinking waterhttps://jsc.sljol.info/article/10.4038/jsc.v12i2.37Use of bottled water has flourished in Sri Lanka, owing to its high demand, however, the quality of commercially available bottled drinking water is questionable. The objective of the current study was to assess the monthly variation of microbiological and chemical quality of bottled water. Three brands were selected, twenty-four bottles of each brand were collected for analysis. Microbiological and chemical analysis were carried out monthly. Though the shelf life of bottled drinking water is one year, the experiment was terminated in eight months as bacterial counts showed a steady decline with time as follows. The results indicated that Total Coliform [TC], Fecal Coliform [FC] and Heterotrophic Plate Count [HPC] bacteria decreased throughout the shelf life. There were significant differences in TC (P<0.05) and FC (P<0.01) between microorganisms initially present and after eight months of storage. Even though SLSI permitted levels for presumptive TC is less than zero cfu per 100ml, the average count of TC was 139 cfu per 100 ml at the end of the first month. According to national and international standards, the FC count should be zero per 100 ml for drinking water. However, at the first month some bottled water samples exceeded this limit for presumptive FC, with an average count of 32.5 cfu per 100 ml. For HPC bacteria, only one brand exceeded the WHO guidelines (50 cfu/ml). No algal species were detected. Fungal colonies showed a reduction in number over an eight-month duration. <em>Penicillium </em>sp. and <em>Aspergillus </em>sp. were dominant. Chemical parameters were within the permitted levels, except hardness in water samples. The result of this study reveals that the bottled water industry needs to be monitored closely and continuously by relevant authorities, intending to provide safe bottled water to the public. Published on 2021-12-28 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i2.37Assessment of microbiological and chemical quality of springwater in Riverston of Knuckles mountain range in Sri Lankahttps://jsc.sljol.info/article/10.4038/jsc.v12i2.38Safe and readily available water is important for public health, whether it is used for drinking, domestic use, food production or recreational purposes. The main objectives of this study were to assess the microbiological and chemical quality of spring water in Riverston, situated in the Knuckles Mountain range, Sri Lanka and to identify bacteria isolated from spring water. Water samples were collected from ten springs from different locations. Microbiological and chemical analysis were carried out according to standard protocols. Isolated bacteria were identified using biochemical tests and API identification system. According to the results, Total coliforms (TC) (ranged from 0-27 per 100 ml) and Fecal coliforms (FC) (ranged from 38-326 per 100 ml) bacteria were detected in all water samples tested, and the detected numbers exceeded permitted levels for drinking water. There are four TC species, <em>viz; Escherichia vulneris, Serratia marcescens</em>, <em>Serratia liquefaciens </em>and <em>Proteus mirabilis </em>and one FC species, <em>viz; Escherichia coli </em>(dominant species), were identified during the study. All chemical parameters tested were within the permitted levels. This study reveals that spring water in Riverston, Knuckles Mountain Range is not a safe drinking water source. Hence, it is important to take necessary precautions, especially as spring waters from these areas are consumed by many and is the main source water for the bottling industry in Sri Lanka. Published on 2021-12-28 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i2.38Properties of adjacency matrix of a graph and it's constructionhttps://jsc.sljol.info/article/10.4038/jsc.v12i1.29<p>This research paper studies about the adjacency matrix of a graph, as it is a fundamental matrix associated with any graph. This study about the properties of adjacency matrix and associated theorems is inevitable since the graph is stored in a computer in terms of its adjacency matrix.</p> Published on 2021-08-05 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i1.29Prime labeling of special graphshttps://jsc.sljol.info/article/10.4038/jsc.v12i1.30Prime labeling is the most interesting category of graph labeling with various applications. A graph <em>G= (V(G), E(G))</em> with |<em>v(G)</em>| vertices are said to have prime labeling if its vertices are labeled with distinct positive integers 1,2,3,……,|<em>v</em>| such that for each edge <em>uv </em><em>e E(G)</em> the labels assigned to <em>u</em> and <em>v</em> are relatively prime, where <em>V(G)</em> and <em>E(G) </em>are vertex set and edge set of <em>G</em>, respectively. Therefore, the graph <em>G</em> has a prime labeling whenever any of two adjacent vertices can be labeled as two relative prime numbers and is called a prime graph. In our work, we focus on the prime labeling method for newly constructed graphs obtained by replacing each edge of a star graph <em>K</em><sub>1<em>,n</em> </sub>by a complete tripartite graph <em>K</em><sub>1<em>,m,</em>1</sub> for <em>m</em> = 2,3,4, and 5, which are prime graphs. In addition to that, investigate another type of simple undirected finite graphs generalized by using circular ladder graphs. These new graphs obtained by attaching <em>K</em><sub>1,2 </sub>at each external vertex of the circular ladder graph <em>CL<sub>n</sub></em> and proved that the constructed graphs are prime graphs when <em>n </em>≥ 3 and <em>n </em><em>≠</em> 1 (<em>mod3</em>) . Finally, focus on another particular type of simple undirected finite graph called a scorpion graph, denoted by <em>S</em>(2<em>p</em>,2<em>q</em>,<em>r</em>) . The Scorpion graph gets its name from shape, which resembles a scorpion, having 2<em>p</em> + 2<em>q</em> + <em>r</em> vertices <em>p</em> ≥ 1, <em>q </em>≥ 2, <em>r</em> ≥ 2)are placed in the head, body, and tail respectively. To prove that the scorpion graph has prime labeling, we used two results that have already been proved for ladder graphs. Published on 2021-08-05 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i1.30The effect of natural substances on the radicle development of certain plant seeds during the early germination stagehttps://jsc.sljol.info/article/10.4038/jsc.v12i1.31Successful seed germination is crucial in many plants. Natural substances and chemicals have been used as growth enhancement tools. In the meantime, natural substances are considered environmentally friendly and cost-effective. Hence, the present study was focused on the effects of natural substances such as red rice, white rice washed water, orange coconut, green coconut, and matured coconut water on radicle development of black gram, pumpkin, rice, and maize. Twenty-five healthy sterilized seeds (85%germination rate) of the above plants were pre-soaked in 30 ml of the natural suspension for 24 hours separately at room temperature and repeated twice. Then seeds were transferred to the sterilized petri dish with moistened filter paper and mean values of length of the radicle were measured. Data were subjected to one-way analysis of variance (ANOVA) (P<0.05) followed by Tukey test. Natural substances have not affected radicle development of the tested seeds, except pumpkin, and maize after 24hours whereas in the control radicle length of these two species was 5.48 and 0.68mm, respectively. However, interestingly after 48hours, radicle formation of most tested seeds was highly accelerated by red rice and white rice washed water, except for black gram. Hence, orange coconut, green coconut, and matured coconut water have showed an inhibitory effect on root length development, except for maize at 48 hours. On the other hand, among the selected natural substances red rice and white rice washed water revealed better effects on radicle development. So, they can be used as an environmentally friendly method to stimulate the radicle development. Published on 2021-08-05 00:00:00https://jsc.sljol.info/article/10.4038/jsc.v12i1.31