http://ir.library.sust.edu:8080/xmlui/handle/123456789/60 Mon, 17 Nov 2025 07:56:50 GMT 2025-11-17T07:56:50Z http://ir.library.sust.edu:8080/xmlui/handle/sust/247 A Study of Recognition and Enumeration for Decomposable Ordered Sets Uddin, Mohammad Salah In this research, we consider mainly two repeatedly studied combinatorial problems in the theory of posets (partially ordered sets). The first one, known as the Recognition Problem, is to recognize those classes of posets that satisfy some common structural properties. Here, we give the recognitions of the most computationally tractable classes of posets, namely the decomposable posets. Well-known classes of the decomposable posets are the classes of P -graphs, P - series, and series-parallel posets. Also, we introduce the notions of the classes of factorable posets and composite posets. Due to many computational aspects of the incidence matrices, they have classical applications in recognizing various classes of posets and graphs. For this, we introduce the notion of poset matrix, an incidence matrix, to represent finite posets. Here, we define the order relation in a square (0,1)-matrix and give an association of this matrix to the posets. We show that every poset matrix can be relabeled to an upper (equivalently, lower) triangular matrix that represents a unique poset up to isomorphism. We introduce the notions of the ordinal sum, ordinal product, and composition of matrices. We establish the algebraic interpretations of the direct sum, ordinal sum, Kronecker product, ordinal product, and composition of matrices in the case of poset matrices. We give the matrix recognitions of the classes of P - graphs, P -series, series-parallel posets, factorable posets, and composite posets by using the poset matrix. Finally, we give a matrix recognition of the class of all decomposable posets that generalizes most of the above results regarding the matrix recognitions of posets. viiThe second problem, known as the Enumeration Problem, is to count the number of pairwise nonisomorphic posets with a certain number of elements be- longing to a particular class of posets. Among several methods for the enumera- tion of posets, here, we consider the exact enumeration method. The algorithmic methods for the enumerations of some classes of decomposable posets considered in the previous researches are of type generate-one and count-one. As a result, the running time of these algorithms grows more rapidly even though the posets are significantly small in size. It is mainly due to the recursions in generating pairwise nonisomorphic posets that make these algorithms highly time-complex. Therefore, it was always a great challenge to give polynomial-time algorithms to make some enumeration process time-efficient. Since the generating methods for the decomposable posets seem to consist of the recursive constructions, algorith- mic methods for the enumerations of such posets were ignored by some authors. Here, we give an exact enumeration method for the unlabeled P -series and series- parallel posets by using the poset matrix. In both cases, we give the enumeration of the unlabeled disconnected posets according to the number of connected direct terms of the posets. In the case of the unlabeled connected series-parallel posets, we give the enumeration of the posets according to the number of ordinal terms that are either the singleton or disconnected posets. For these, we use the results regarding the matrix recognitions of the classes of P -series and series-parallel posets. We also give some algorithms to determine the parameters involved in the enumeration formulae, and finally, compute the number of unlabeled posets. We show that these enumeration algorithms have polynomial-time complexities. Moreover, we implement these enumeration algorithms into the computer and obtain the numbers of unlabeled P -series up to 75 elements and the numbers of unlabeled series-parallel posets up to 33 elements. A thesis for the degree of Doctor of Philosophy in Mathematics : "A Study of Recognition and Enumeration for Decomposable Ordered Sets". Mon, 01 Nov 2021 00:00:00 GMT http://ir.library.sust.edu:8080/xmlui/handle/sust/247 2021-11-01T00:00:00Z http://ir.library.sust.edu:8080/xmlui/handle/sust/244 INVESTIGATION OF NONLINEAR OPTICAL RESPONSES OF BOVINE SERUM ALBUMIN AND SOME AMINO ACIDS USING Z-SCAN TECHNIQUE Tarek, Sarfuddin Ahmed The Z-scan technique is a relatively simple but sensitive technique for studying third-order Nonlinear optical effects in materials. In this research work, we have implemented the continuous wave (CW) closed aperture (CA) Z-scan in conjunction with UV-Visible Spectroscopy for the optical characterization of Bovine serum albumin (BSA) and 13 of its constituent amino acids (AA). The Z-scan and UV-Vis spectroscopy are the two complementary optical techniques used for elucidating the interactions of electromagnetic radiations with studied materials at their molecular levels. Here, CW Z-scan has been employed to study third-order nonlinear refraction in terms of nonlinear optical (NLO) phase shifts (𝛥𝛷0) at 655 nm incident wavelength and at an optical power range of 74 mW to 106 mW, whereas the UV-Visible spectroscopy has been done in the 190 nm to 700 nm wavelengths to find the absorption by the molecules within this spectrum. The main objective of this study was to investigate variations in (𝛥𝛷0) of the amino acids with irradiances and at the same time investigate, whether there exists a relationship between the (𝛥𝛷0) of the Amino acids and that of BSA. To do that we have introduced a parameter called ‘Molar Phase shift Per unit power’ (𝜁𝑀) that is akin to the molar extinction coefficient (𝜀𝑚) used in the comparative study of UV- Visible absorbance. Also, these results are compared with a model that we have proposed herein. As a precursor to our experimental study, we have done an extensive review of the Z-scan covering the basics of the experimental method and its applications in the field of materials characterization, particularly in biomaterials research. The literature review provides a comprehensive overview of the CW Z-scan and the associated thermo-optic interaction affecting the refractive properties of materials. Additionally, our review work covers the historical background of research on amino acids, as well as nonlinear optical study using Z- scan technique. It has been observed that the amino acids with conjugated double bonds serve as active elements in both linear and nonlinear optical interactions. The materials and methods section describes instruments, materials, and step-by-step procedures followed in the preparation and handling of samples for UV-Visible spectroscopy and Z-scan experiments followed by the details of each experimental setup and instrumentation. ii The UV-Visible spectroscopy results for BSA and the amino acids have agreed well with previously published results. However, some previously unpublished details of methionine and lysine have been made. Furthermore, we have introduced revised model relating the molar extinction coefficient of BSA at 278 nm to the coefficients associated with constituent amino acids. This modification has resulted in significantly improved outcomes compared to previously reported values. Z-scans results of the samples have been compared in terms of their molar phase shifts per unit power (𝜁𝑀). It has been established that the nonlinear refraction in the CW regime is caused by multiphoton absorption. The data analysis and interpretation of results are presented, along with comparisons with previous studies and theoretical predictions. At the end of the analysis, we suggest extending this work to include other materials, wavelengths, and the time domain in the femtosecond regime to validate the observations made in this study. In summary, this doctoral thesis provides a comprehensive examination of the third-order nonlinear response exhibited by proteins and amino acids in the CW regime at 665 nm, which falls under the domain of optical spectroscopy. The findings of this study may contribute significantly to the advancements in the field of nonlinear optical spectroscopy. the degree of Doctor of Philosophy In Physics "INVESTIGATION OF NONLINEAR OPTICAL RESPONSES OF BOVINE SERUM ALBUMIN AND SOME AMINO ACIDS USING Z-SCAN TECHNIQUE." Sat, 01 Jul 2023 00:00:00 GMT http://ir.library.sust.edu:8080/xmlui/handle/sust/244 2023-07-01T00:00:00Z http://ir.library.sust.edu:8080/xmlui/handle/sust/237 Development of appropriate structured mathematical models for fish population dynamics along with efficient numerical schemes for the solutions of the developed and other models of engineering problems Ahamad, Razwan This thesis is mainly concentrated to obtain numerical solutions of real world problems encountered in continuum mechanics and other branches of sciences like development, management and production oriented agricultural sectors. Appropriate mathematical models are well established for all continuum mechanics problems and hence in such instances a faster algorithm or a technique is the only requirement for obtaining numerical solutions. On the other hand, though the dynamic model approach is a widely applied technique to a number of environmental management and sustainability issues like fisheries management problems still needed to be developed. Therefore, primarily the thesis intends to develop appropriate mathematical models for such real problems and then stresses to obtain their numerical solutions. More specifically, we intended firstly to develop appropriate mathematical model in order to calculate fish population. As an outcome, we finally present the model by a system of hyperbolic partial differential equations with linear and nonlinear boundary conditions for the calculation of fish population. Secondly, an appropriate model for mathematical estimation of fish production performances is developed for the calculation of fish sizes in different time span depending on initial sizes. Then, as an important integral component, computer codes in FORTRAN that employs Finite Volume Method are developed for obtaining numerical solutions of such models. Afterward, other codes in MATLAB are developed for analyzing and graphical presentation of computed data. Substantiation of the outcomes of the developed models is then established by comparing the computed results with the experimental data. The versatility and popularity of Finite Element Method (FEM) is well known. The main and important time consuming step in FEM is the formation of all element matrices. Generally, all the elements in global space are transformed into respective contiguous elements in local space by use of isoparametric/ Abstract   subparametric/ superparametric transformation. For such transformations only all the components of element matrices become integrals of rational functions for the popular quadrilateral as well as for the curved triangular finite elements. The Gaussian quadrature schemes, used in most cases for its simplicity cannot evaluate such rational integrals as it can evaluate the integrals of polynomials of degree/ order (2n-1) with n Gaussian points. For the desired accuracy of the evaluations, more and more Gaussian points are used and eventually that increases the computing time. Therefore, it is an important task to make a proper balance between the accuracy and efficiency of evaluations of numerous rational integrals. So, the thesis concentrates to develop the faster technique by reducing steps of various stages of usual FEM solution procedure for obtaining numerical solutions of numerous boundary value problems governed by hyperbolic, elliptic partial differential equations. For doing so, it stresses to present faster closed form formulae needed to form exactly all types of element matrices for solving such two dimensional boundary value problems encountered in the realm of science and engineering. Since, the faces of finite volume are finite elements so all the formulae are applicable in both FEM, FVM methods. Computer codes compatible with the formulations are also developed accordingly. The efficiency and accuracy of the technique is then demonstrated through application of the formulae in order to obtain the solutions of test problems. Thus, in brief the Thesis includes: (1) appropriate mathematical model for the calculation of fish population, (2) appropriate mathematical model for the calculation of fish population performances (size of fishes), (3) computer codes employing suitable numerical methods (FVM) for obtaining best approximations of solutions of the developed models, and (4) computer codes based on the developed technique for exact computing all the element matrices efficiently in order to solve numerous two dimensional boundary value problems. All the relevant concepts, mathematical tools, devised; modified; improved algorithms, other related topics and the gradual development of the Thesis work are elaborately described in 7 (seven) chapters. A thesis submitted for the degree of Doctor of Philosophy: "Development of appropriate structured mathematical models for fish population dynamics along with efficient numerical schemes for the solutions of the developed and other models of engineering problems". Wed, 01 Nov 2017 00:00:00 GMT http://ir.library.sust.edu:8080/xmlui/handle/sust/237 2017-11-01T00:00:00Z http://ir.library.sust.edu:8080/xmlui/handle/sust/235 Trends and Pattern of Population Aging: Potential Socio- Demographic Consequences in Bangladesh Hossain, Mohammad Kamal Hossain The rapid aging of the global population presents unprecedented challenges, particularly in developing countries like Bangladesh, which is experiencing significant demographic transition.This research paper examines the implications of population aging in Bangladesh, focusing on the trends, patterns, and socio-economic impacts of this demographic shift.Utilizing primary data from Sylhet district and secondary data from the Bangladesh Bureau of Statistics, the study aims to analyze the evolving age-sex structure, assess the needs of the elderly, and measure aging inequality compared to selected Asian countries.The findings reveal that the elderly population is on the rise, with projections indicating that by 2050, it will comprise 20% of the total population.The study highlights the prevalence of geriatric depression and frailty among the elderly, identifying key risk factors and socio-demographic disparities.As the demographic dividend is realized, the implications for economic productivity and the potential burden of an aging population are examined.The research underscores the urgent need for comprehensive policy responses to address the challenges posed by population aging in Bangladesh, emphasizing the importance of understanding the health status and socio-economic conditions of the elderly. “Trends and Pattern of Population Aging: Potential Socio-Demographic Consequences in Bangladesh” Tue, 01 Jun 2021 00:00:00 GMT http://ir.library.sust.edu:8080/xmlui/handle/sust/235 2021-06-01T00:00:00Z