In the paper, the authors nd a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

As an export commodity coffee industry contributes to the economies of both exporting and importing countries. The aim of the study involves competitiveness and determinant of coffee export in Ethiopia through the period of 1990–2018 observations. To explain the level of comparative advantage and competitiveness respectively Revealed Comparative Advantage and Syematric Revealed Comparative Advantage were employed. To capture determinans of coffee ARDL model with bound testing to co-integration approach was employed to investigate the long-run association between Ethiopian total coffee export in bags (60kg each) with domestic coffee production, world coffee price, real exchange rate, FDI, world coffee production and price ratio. Even though Ethiopia has the comparative advantage in the export of coffee, however, the share it in the international market low in amount and not inlined with RCA. Bound testing to co-integration approach result confirmed the existence of a long-run relationship between total coffee exports of Ethiopia with its independent variables. The analysis pointed out that in the long run the extent of domestic coffee production, world price, and real exchange rate positively and significantly affects total coffee export. However, FDI, price ratio, world production of coffee have negative & significant effects. In the short-run Ethiopian total coffee export defined as a positive significant function of domestic coffee production and real exchange rate positive but insignificant effect with Level of RCA and world price as well as a negative function of FDI, price ratio, and world production of coffee. Coefficient Error Correction Model (ECM (-1)) was negative and significant with a value of 134.4 % of the adjustment would make each year and return to its long-run equilibrium after 1.3 years. The policy implication calls for addressing issues of the combined effect of the policy setting, institutions, and market failures to avoid the evil effect of the sector.

Currently, the pesticides are the global core concern because it is a boon to farmers against increasing disease-pest and simultaneously, pesticide residue is the major anxiety regarding human health. For that reason, identification and determination of factors affecting the application of pesticides are essential. To identify and evaluate determinants of pesticides application in Nepal, a household survey of 300 households was carried-out and an empirical analysis was done using multivariate probit model. Moreover, powder and liquid forms of pesticides were considered for summer and winter season in vegetable farming, which was assigned as outcome variables. Likewise, socio-economic, demographic, farm-level and perception data were considered as explanatory variables. Use of chemical fertilizers, age and gender of head of household, household size and access to weather information were found the most influencing factors. Moreover, forms of pesticides and growing seasons were found complementary to each other. Therefore, devising the policy options accordingly should balance needs of farmers and health of consumers.

Let ${\mathcal{SR}}^*$ be the class of starlike functions with real coefficients, i.e., the class of analytic functions $f$ which satisfy the condition $f(0)=0=f'(0)-1$, Re{z f'(z) / f (z)} > 0, for $z\in\mathbb{D}:=\{z\in\mathbb{C}:|z|<1 \}$ and $a_n:=f^{(n)}(0)/n!$ is real for all $n\in\mathbb{N}$. In the present paper, the sharp estimates of the third Hankel determinant $H_{3,1}$ over the class ${\mathcal{SR}}^*$ are computed.

In the paper, by a very simple approach, the author establishes an expression in terms of a lower Hessenberg determinant for the Euler polynomials. By the determinantal expression, the author finds a recurrence relation for the Euler polynomials. By the way, the author derives the corresponding expression and recurrence relation for the Euler numbers.

For the solution existence condition of the Navier-Stokes equation, we propose a conjecture as follows: "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"