A new operational matrix based on Bernoulli polynomials

In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized to transform the differential equation to a matrix equation which corresponds to a system of algebraic equations with unknown Bernoulli coefficients. This method can be used for many problems such as differential equations, integral equations and so on. Numerical examples show the method is computationally simple and also illustrate the efficiency and accuracy of the method

On α\alpha-adjacency energy of graphs and Zagreb index

Let $A(G)$ be the adjacency matrix and $D(G)$ be the diagonal matrix of the vertex degrees of a simple connected graph $G$. Nikiforov defined the matrix $A_{\alpha}(G)$ of the convex combinations of $D(G)$ and $A(G)$ as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$, for $0\leq \alpha\leq 1$. If $\rho_{1}\geq \rho_{2}\geq \dots \geq \rho_{n}$ are the eigenvalues of $A_{\alpha}(G)$ (which we call $\alpha$-adjacency eigenvalues of $G$), the $\alpha$-adjacency energy of $G$ is defined as $E^{A_{\alpha}}(G)=\sum_{i=1}^{n}\left|\rho_i-\frac{2\alpha m}{n}\right|$, where $n$ is the order and $m$ is the size of $G$. We obtain the upper and lower bounds for $E^{A_{\alpha}}(G)$ in terms of order $n$, size $m$ and Zagreb index $Zg(G)$ associated to the structure of $G$. Further, we characterize the extremal graphs attaining these bounds.Comment: 17 page

The Effect of Political Instability and Institutional Weakness on Administrative Corruption

Although there is valuable literature on areas of corruption, such as political and corporate corruption, a limited number of papers have examined the determinants of administrative corruption. To the best of our knowledge, the multivariate impacts of political instability and institutional weakness on administrative corruption, and the interplay between these constructs, have not been examined using the partial least squares structural equation modeling method. The current study attempts to fill this gap by proposing and testing a model. We test a sample of 677 responses that reflect the perspective of the general public in Basra, Iraq. Findings reveal that the political instability and institutional weakness of public organizations positively impact administrative corruption, while political instability leads to institutional weakness. Institutional weakness mediates the effect of political instability on administrative corruption. Therefore, political instability is a crucial factor causing corruption since it has both direct and indirect effects on administrative corruption. The theoretical contributions, managerial implications, limitations, and recommendations for further research are provided

The effect of culture and organisational culture on administrative corruption

Copyright © 2019 Inderscience Enterprises Ltd. There is extensive literature on corruption, such as political and corporate corruption, some of which examines factors influencing administrative corruption. However, to the best of our knowledge, the multivariate influences of culture and organisational culture on administrative corruption have not been tested using an integrative approach. This paper attempts to fill the gap by building and testing a comprehensive model. We test a sample of 677 responses that reflect the prospective view of the public in Basra, Iraq, using the partial least squares structural equation modelling (PLS-SEM) approach. Our study finds that corrupt culture and weak organisational culture have direct effects on administrative corruption, while corrupt culture leads to weak organisational culture. The latter mediates the impact of corrupt culture on administrative corruption. The higher level of social class, the lower the impact of corrupt culture on administrative corruption

Građa i optička svojstva tankih polikristaliničnih slojeva CuGaxIn1−xSe2

Structural and optical properties of CuGaxIn1−xSe2 (0 ≤ x ≤ 0.75) polycrystalline thin films deposited by vacuum evaporation were studied as a function of composition. The optical absorption spectra of CuGaxIn1−xSe2 thin films (x /=0) show four energy gaps (Eg1 , Eg2 , Eg3 and Eg4 ) which are attributed to the fundamental edge, band splitting by crystal-field and spin-orbit splitting, and to transitions originating from copper 3d levels, respectively. The primary transition energies exhibit bowing behaviour expressed by the relationship Eg1 (x) = 1.011 + 0.448x + 0.186x 2 . The second and third transition energies are higher than the primary transition energies by 0.10–0.11 eV and 0.18–0.185 eV, respectively. The effect of thermal treatment on the values of energy gaps is discussed in terms of the structure of the films. The primary transition energies of annealed CuGaxIn1−xSe2 can be fitted by the parabolic form Eg1 (x) = 1.04 + 0.46x + 0.22x 2 .Proučavali smo strukturna i optička svojstva tankih polikristaliničnih slojeva CuGaxIn1−xSe2, isparenih u vakuumu, u ovisnosti o sastavu (0 ≤ x ≤ 0.75). Optički apsorpcijski spektri tankih slojeva CuGaxIn1−xSe2, (x /=0), pokazuju četiri energijska procijepa (Eg1 , Eg2 , Eg3 i Eg4 ) koji se pridjeljuju osnovnom rubu, cijepanju vrpci kristalnim poljem i cijepanju spin-staza, odnosno prijelazima iz 3d stanja bakra. Prvotni prijelazi pokazuju kvadratnu ovisnost koju izražavamo relacijom Eg1 (x) = 1.011 + 0.448x + 0.186x 2 . Druga i treća prijelazna energija su (0.10 − 0.11 eV) odnosno (0.18 − 0.185 eV) više od primarne prijelazne energije. Pomoću građe slojeva objašnjavamo učinak toplinske obrade na vrijednosti energijskih procijepa. Prvotne prijelazne energije opuštenog CuGaxIn1−xSe2 mogu se predstaviti kvadratnim izrazom Eg1 (x) = 1.04 + 0.46x + 0.22x 2

Građa i optička svojstva tankih polikristaliničnih slojeva CuGaxIn1−xSe2

Structural and optical properties of CuGaxIn1−xSe2 (0 ≤ x ≤ 0.75) polycrystalline thin films deposited by vacuum evaporation were studied as a function of composition. The optical absorption spectra of CuGaxIn1−xSe2 thin films (x /=0) show four energy gaps (Eg1 , Eg2 , Eg3 and Eg4 ) which are attributed to the fundamental edge, band splitting by crystal-field and spin-orbit splitting, and to transitions originating from copper 3d levels, respectively. The primary transition energies exhibit bowing behaviour expressed by the relationship Eg1 (x) = 1.011 + 0.448x + 0.186x 2 . The second and third transition energies are higher than the primary transition energies by 0.10–0.11 eV and 0.18–0.185 eV, respectively. The effect of thermal treatment on the values of energy gaps is discussed in terms of the structure of the films. The primary transition energies of annealed CuGaxIn1−xSe2 can be fitted by the parabolic form Eg1 (x) = 1.04 + 0.46x + 0.22x 2 .Proučavali smo strukturna i optička svojstva tankih polikristaliničnih slojeva CuGaxIn1−xSe2, isparenih u vakuumu, u ovisnosti o sastavu (0 ≤ x ≤ 0.75). Optički apsorpcijski spektri tankih slojeva CuGaxIn1−xSe2, (x /=0), pokazuju četiri energijska procijepa (Eg1 , Eg2 , Eg3 i Eg4 ) koji se pridjeljuju osnovnom rubu, cijepanju vrpci kristalnim poljem i cijepanju spin-staza, odnosno prijelazima iz 3d stanja bakra. Prvotni prijelazi pokazuju kvadratnu ovisnost koju izražavamo relacijom Eg1 (x) = 1.011 + 0.448x + 0.186x 2 . Druga i treća prijelazna energija su (0.10 − 0.11 eV) odnosno (0.18 − 0.185 eV) više od primarne prijelazne energije. Pomoću građe slojeva objašnjavamo učinak toplinske obrade na vrijednosti energijskih procijepa. Prvotne prijelazne energije opuštenog CuGaxIn1−xSe2 mogu se predstaviti kvadratnim izrazom Eg1 (x) = 1.04 + 0.46x + 0.22x 2