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Construction and Application of Log-linear Models to Assess Academic Performance
Get PDFLog-Linear Models (LLMs) are important techniques used in categorical data analysis. Though there are some available published work about LLMs, the explanation of model building process and the theoretical background are not adequate. Furthermore, research about the application of the LLM theory and the selection procedure of the best model are handful. Therefore, this manuscript aims to fill that vacuum. At first, the construction of LLM and Hierarchical Log-Linear Models (HLLMs), a branch of LLMs are discussed in connection with both 2×2 and 2×2 ×2 contingency tables. Secondly, an application is presented to analyze the collected data set about the academic performance of elementary students. The manuscript also discusses the criteria to select the best model that fits the collected data
Generalized Differential Transform Method for Solving Some Fractional Integro-Differential Equations
Get PDFIn this paper, we use a generalized form of two-dimensional Differential Transform (2D-DT) to solve a new class of fractional integro-differential equations. We express some useful properties of the new transform as a proposition and prove a convergence theorem. Then we illustrate the method with numerical examples
An Initial Value Technique using Exponentially Fitted Non Standard Finite Difference Method for Singularly Perturbed Differential-Difference Equations
Get PDFIn this paper, an exponentially fitted non standard finite difference method is proposed to solve singularly perturbed differential-difference equations with boundary layer on left and right sides of the interval. In this method, the original second order differential difference equation is replaced by an asymptotically equivalent singularly perturbed problem and in turn the problem is replaced by an asymptotically equivalent first order problem. This initial value problem is solve by using exponential fitting with non standard finite differences. To validate the applicability of the method, several model examples have been solved by taking different values for the delay parameter δ , advanced parameter η and the perturbation parameter ε . Comparison of the results is shown to justify the method. The effect of the small shifts on the boundary layer solutions has been investigated and presented in figures. The convergence of the scheme has also been investigated
Adjoint Appell-Euler and First Kind Appell-Bernoulli Polynomials
Get PDFThe adjunction property, recently introduced for Sheffer polynomial sets, is considered in the case of Appell polynomials. The particular case of adjoint Appell-Euler and Appell-Bernoulli polynomials of the first kind is analyzed
Charge-transfer or excimeric state? Exploring the nature of the excited state in cofacially arrayed polyfluorene derivatives
No full textIt is well known that upon electronic excitation various π-stacked dimers readily exhibit excimer formation, facilitated by a perfect sandwich-like arrangement between the chromophores. However, it is unclear whether such a dimer is also capable of electron transfer upon excitation, if a strong electron-donating group is covalently attached. In this work, we probe the nature of the excited state in a series of cofacially arrayed polyfluorene derivatives with electron-rich aromatic donor attached via a methylene linker. Our studies show that in all cases excimer formation is energetically favorable, and promotion of a charge-transfer state in such systems is possible but requires a free energy for electron transfer far exceeding 1 V. These findings shed light on important design principles for molecular scaffolds capable of stabilizing both excimeric and charge-transfer states upon their excitation
Study of Specially and Temporally Dependent Adsorption Coefficient in Heterogeneous Porous Medium
Get PDFOne-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs
Local Non-Similar Solution of Powell-Eyring Fluid flow over a Vertical Flat Plate
Get PDFOur objective is to obtain the non-similarity solution of non-Newtonian fluid for Powell-Eyring model by a local non-similarity method. Here, free stream velocity is considered in power-law form (=m). The governing equations are transformed using non-similar transformations and derived equations are treated as ordinary differential equations. Non-similar solutions are obtained for different values of power-law index and stream-wise location . Influence of various parameters on velocity and temperature field are presented graphically using MATLAB bvp4c solver
An Efficient Computational Method for Solving a System of FDEs via Fractional Finite Difference Method
Get PDFThis paper aims to provide a numerical method for solving systems of fractional (Caputo sense) differential equations (FDEs). This method is based on the fractional finite difference method (FDM), where we implemented the Grünwald-Letnikov’s approach. This method is computationally very efficient and gives very accurate solutions. In this study, the stability of the obtained numerical scheme is given. The numerical results show that the proposed approach is easy to be implemented and are accurate when applied to system of FDEs. The method introduces promising tool for solving many systems of FDEs. Two examples are given to demonstrate the applicability and the effectiveness of our method
Single reagent treatment and degradation of switchgrass using iron(III)chloride: The effects on hemicellulose, cellulose and lignin
No full textThe possibility of using abundant metal chlorides as a single reagent for pretreatment and degradation of switchgrass biomass was studied. Three metal chlorides: MgCl2, CaCl2 and FeCl3 were tested in the initial phase and FeCl3 at 2% w/w loading was found as the most effective reagent for treatment and hydrolysis of switchgrass in hot compressed water. Therefore, FeCl3 was selected for the detailed study and the heat treatment at 140–160 °C or microwaving for 6–10 min was required to activate the FeCl3 after impregnation of switchgrass. These samples could be hydrolyzed in water at 160 °C, without additional catalyst or reagent to produce reducing sugars. In the hydrolysis experiments, FeCl3 impregnated and micro waved switchgrass produced slightly higher total reducing sugar (TRS) yields of 31.5%; whereas the samples heated at 140 °C after FeCl3 impregnation produced 28.6% TRS yield. In a thermogravimetric analysis study, the decomposition temperature of lignin fraction showed the highest shift (ΔTdecomp ~ - 42 °C) after adding 2% w/w FeCl3 and microwaving for 10 min, indicating that strong interactions between FeCl3 and lignin is likely the primary cause of enhancement in polysaccharide degradation