ICAPS 2023
Permanent URI for this collectionhttp://repository.kln.ac.lk/handle/123456789/26832
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Item A study on mechanical properties of a polymer composite based on areca nut fiber(Faculty of Science, University of Kelaniya Sri Lanka, 2023) Madubhashani, H. A. C.; Senaviratne, V. A.; Pemasiri, B. M. K.Plant-based raw food items such as fruits and vegetables are damaged during storage and transportation due to high temperatures, water vapours, mechanical shocks and vibrations, microorganisms, etc. This study is aimed at developing a packaging material using areca nut fibers and Chemifix as an effective substitute for available packaging materials. The areca nut husks were used to extract the fibers. The fibers were extracted by the retting process, and the extracted fibers were subjected to alkali treatment. The samples were made by combining Chemifix with areca nut fibers in various ratios to obtain 0% wt, 9% wt, 11% wt, 14% wt, 20% wt, 25% wt, and 30% wt fiber content in the prepared composite samples. A pure Chemifix sheet and commercially available cardboard, gypsum, and medium-density fiberboard (MDF) were used as reference materials. The prepared composite samples’ density, thermal conductivity, water absorption, Young’s modulus, tensile strength, and elongation were measured and compared with those of the reference samples. The density and thermal conductivity of the composite samples with 20%, 25%, and 30% areca nut fiber weight percentages ranged from 350 to 700 kg m-3 and 0.2 to 0.3 W m-1 K-1, respectively. The density and thermal conductivity of the reference samples (0% wt) were 1372 kg m-3 and 0.78 W m-1 K-1 respectively. 9% wt and 11% wt fiber containing composite samples showed high resistance to water absorption. The other four composite samples absorbed more water than 100% of the sample mass. However, a low water absorption rate was present in all composite samples than in the commercial samples tested in this study except gypsum board. Young’s modulus and breaking point of samples with 20% wt, 25% wt and 30% wt were in order of 108 N m-2 and 107 N m-2 respectively. The elongation of the samples decreased with the increasing fiber content. The reference sample (0% wt) had an elongation exceeding 100%. This study reveals that the prepared composite samples with a moderate fiber content (20%) show promising properties suitable for the storage and transportation of raw plant products.Item Controlled 𝑲 −frames in quaternionic setting(Faculty of Science, University of Kelaniya Sri Lanka, 2023) Khokulan, M.; Ramakrishnan, R.Quaternion is an extension of complex numbers from the two-dimensional plane to fourdimensional space and forms non-commutative division algebra. A feature of quaternion is that the multiplication of two quaternions is non-commutative, from the non-commutativity the quaternionic Hilbert spaces are defined in two ways such as right quaternionic Hilbert space (𝑉𝐻𝑅) and left quaternionic Hilbert space (𝑉𝐻 𝐿). 𝐾 −frames are more general than ordinary frames in the sense that the lower frame bound only holds for the elements in the range of 𝐾, where 𝐾is a bounded linear operator in 𝑉𝐻 𝐿. Controlled frame is one of the newest generalizations of the frame which has been introduced to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this research, the notion of a controlled 𝐾 −frame is introduced in left quaternionic Hilbert space along the lines of their real and complex counterparts and some of their properties were analysed. Let 𝑉𝐻 𝐿 be a left quaternionic Hilbert space, 𝐾 ∈ 𝐵(𝑉𝐻 𝐿) and 𝐶 ∈ 𝐺𝐿+(𝑉𝐻 𝐿), where 𝐵(𝑉𝐻 𝐿)is the set of all bounded linear operators and 𝐺𝐿+(𝑉𝐻 𝐿) is the set of all positive bounded linear operators in 𝑉𝐻 𝐿 with bounded inverse. A sequence of family 𝛷 = {𝜑𝑘}𝑘∈𝐼 in 𝑉𝐻 𝐿 is called a 𝐶 − controlled 𝐾 − frame for 𝑉𝐻 𝐿 if there exist constants 𝑚, 𝑀 > 0 such that 𝑚‖𝐾†𝜑‖2 ≤ Σ𝑘∈𝐼 ⟨𝜑𝑘⟩⟨𝜑⟩ ≤ 𝑀‖𝜑‖2 , for all 𝜑 ∈ 𝑉𝐻 𝐿. First, we established a result that shows that any 𝐾 − frame is a controlled 𝐾 −frame under certain conditions. Let 𝐾 and 𝐶 be self -adjoint with 𝐶𝐾 = 𝐾𝐶. If 𝛷 = {𝜑𝑘}𝑘∈𝐼 is a 𝐾 − frame for 𝑉𝐻 𝐿 then 𝛷 = {𝜑𝑘}𝑘∈𝐼 is a 𝐶 − controlled 𝐾 − frame for 𝑉𝐻𝐿. Then we derived a necessary and sufficient condition for a sequence to be a controlled 𝐾 − frame and we have shown that every 𝐶 − controlled 𝐾 − frame is a 𝐶−1 − controlled 𝐾 − frame. Suppose that 𝐾 ∈ 𝐵(𝑉𝐻𝐿). A sequence 𝛷 = {𝜑𝑘}𝑘∈𝐼 is a 𝐶 − controlled𝐾 − frame for 𝑉𝐻𝐿 if and only if 𝑅(𝐾) ⊆ 𝑅(𝑇𝐶𝛷), where 𝑅(𝐾) is the range of 𝐾. Suppose that𝐶𝐾 = 𝐾𝐶. If 𝛷 = {𝜑𝑘}𝑘∈𝐼 is a 𝐶 − controlled 𝐾 − frame for 𝑉𝐻𝐿 then 𝛷 = {𝜑𝑘}𝑘∈𝐼 is a 𝐶−1 −controlled 𝐾 − frame for 𝑉𝐻𝐿. Finally, we proved that the sum of two controlled 𝐾 − framesremains a controlled 𝐾 − frame under certain conditions in left quaternionic Hilbert space. Let𝐶𝐾 = 𝐾𝐶. Suppose that 𝛷 = {𝜑𝑘}𝑘∈𝐼 and 𝛹 = {𝜓𝑘}𝑘∈𝐼are 𝐶 − controlled 𝐾 − frames for 𝑉𝐻𝐿 with bounds 𝑚, 𝑀 and 𝑚′, 𝑀′, respectively. If 𝑇𝛷𝑇𝛹 † = 𝐶−1𝐾𝐾†, then {𝜑𝑘 + 𝜓𝑘}𝑘∈𝐼 is also a 𝐶 − controlled 𝐾 − frame for 𝑉𝐻𝐿.