On Lyapunov-type inequality for a class of quasilinear systems

In this paper, we establish a new Lyapunov-type inequality for quasilinear systems. Our result in special case reduces to the result of Watanabe et al. [J. Inequal. Appl. 242(2012), 1-8]. As an application, we also obtain lower bounds for the eigenvalues of corresponding systems

Oscillation criteria for nonlinear delay differential equations of second order

We prove oscillation theorems for the nonlinear delay differential equation $\left( \left\vert y^{\prime }(t)\right\vert ^{\alpha -2}y^{\prime}(t)\right) ^{\prime }+q(t)\left\vert y(\tau (t))\right\vert ^{\beta-2}y(\tau (t))=0, t\geq t_{\ast }>0,$ where $\beta >1,$ $\alpha >1,$ $q(t)\geq 0$ and locally integrable on $[t_{\ast },\infty ),$ $\tau (t)$ is a continuous function satisfiying $0<\tau (t)\leq t$ and lim$_{t\rightarrow \infty }\tau (t)=\infty .$ The results obtained essentially improve the known results in the literature and can be applied to linear and half-linear delay type differential equations

Mean value theorem for holomorphic functions

This article presents a generalization of Myers' theorem and when the boundary assumption f'(a)=f'(b) is removed, and to prove this result for holomorphic functions of one complex variable. After that, the equivalence of Rolle's and mean value theorems in the complex plane are proved

LYAPUNOV-TYPE INEQUALITIES FOR THIRD-ORDER LINEAR DIFFERENTIAL EQUATIONS

In this article, we establish new Lyapunov-type inequalities for third-order linear differential equations y `''+q(t)y = 0 under the three-point boundary conditions y(a) = y(b) = y(c) = 0 and y(a) = y `'(d) = y(b) = 0 by bounding Green's functions G (t; s) corresponding to appropriate boundary conditions. Thus, we obtain the best constants of Lyapunov-type inequalities for three-point boundary value problems for third-order linear differential equations in the literature

Lyapunov-type inequalities for nonlinear systems involving the (p1,p2,...,pn)-Laplacian

We prove some generalized Lyapunov-type inequalities for n-dimensional Dirichlet nonlinear systems. We extend the results obtained by Cakmak and Tiryaki [6] for a parameter $1<p_k<2$. As an application, we obtain lower bounds for the eigenvalues of the corresponding system

On the Lyapunov-type inequalities of a three-point boundary value problem for third order linear differential equations

In this paper, by using Green's function for second order differential equations with Dirichlet boundary condition, we establish new Lyapunov-type inequalities for third order linear differential equation which improve all existing results in the literature. As an application, we obtain sharp lower bound for the eigenvalues of corresponding equations and for the distance between the end points in the three consecutive zeros of the solution of the equations. (C) 2015 Elsevier Ltd. All rights reserved

On Lyapunov-type inequalities for odd order boundary value problems

In this article, we construct new Lyapunov-type inequalities for odd order boundary value problems. The aim of this article is to find the maximum of Green's function |G2n+1(x,s)| corresponding to two-point boundary value problems. To the best of our knowledge, there is no paper dealing with Lyapunov-type inequalities for odd order boundary value problems by bounding the Green's function of the same problem. In addition, some applications of the obtained inequalities are also given

Optimization of macroelement contents in raspberry leaves by liming in an extremely acid soil

Raspberries thrive best in an acid soil. However, if the soil pH is lower than 5.6, lime application is necessary. In this study the effects of lime and dolomite application in combination with NPK 15:15:15 fertilizer (600 kg ha�1) on the macroelement contents (N, P, K, Ca, and Mg) in an extremely acid soil (pH 4.35) and raspberry leaves were evaluated during a three-year period. Optimal pH value for raspberry cultivation (5.84) was achieved with the application of 9 t ha�1 of lime. The mineral nitrogen (NH4+NO3)-N content and P content in the soil after liming increased significantly, but P concentration stayed below the optimal values. Additionally, no changes were noted in K concentration in the soil. The Ca concentration increased significantly in all treatments, while the Mg content increased significantly only in the treatment with dolomite. The N content in the raspberry leaves increased, but K content decreased after liming. There was no change in P content in the leaves affected by liming. Lime increased Ca content in the leaves above the optimal values, while it did not affect the initially optimal Mg content in the leaves. After liming and NPK fertilization, the concentrations of N, P and K in the leaves were still below the optimal values, indicating a need for the combination of higher rates of fertilizer with lime in raspberry cultivation in very acid soils.Los frambuesos crecen mejor en suelos ácidos. Sin embargo, si el pH del suelo es inferior a 5,6, es necesario aplicar cal. En este estudio se evaluaron durante un período de tres años los efectos de aplicar cal y dolomita, en combinación con fertilizantes NPK 15:15:15 (600 kg ha�1), en el contenido de macroelementos (N, P, K, Ca y Mg) en un suelo extremadamente ácido (pH 4,35) y en hojas de frambueso. El pH óptimo para el cultivo del frambueso (5,84) se logró con la aplicación de 9 t ha�1 de cal. En el caso del suelo, después del encalado el contenido en nitrógeno mineral (NH4+NO3)-N y de P aumentó significativamente, pero la concentración de P se mantuvo por debajo de los valores óptimos; además, no se observaron cambios en la concentración de K; la concentración de Ca aumentó significativamente en todos los tratamientos, pero el contenido de Mg aumentó significativamente sólo en el tratamiento con dolomita. En las hojas de frambueso, después del encalado el contenido de N aumentó, pero el contenido de K disminuyó; no hubo cambios en el contenido de P; el contenido de Ca aumentó por encima de los valores óptimos, mientras que no se afectó el contenido inicial óptimo de Mg. Después del encalado y la fertilización NPK, las concentraciones de N, P y K en las hojas estaban todavía por debajo de los valores óptimos, lo que indica la necesidad de combinar mayores tasas de abono con cal en el cultivo de frambueso en suelos muy ácidos

Minor cereals exhibit superior antioxidant effects on human epithelial cells compared to common wheat cultivars

In the present study, various minor cereals including rye, oat, spelt, primitive and wild wheat species (20 genotypes each) were tested for their antioxidative effects in cell biological studies, and the effects were compared with the effects of 12 common wheat genotypes. Ethanol soluble extracts of grains were used and studied in human cancer-derived cell lines including HeLa (cervical) and HCT116 (colorectal) cell lines by analyzing cellular levels of reactive oxygen species (ROS), mitochondrial health, DNA damage and cell survival. The cereal genotypes were also examined for the total phenolic concentration (TPC) and for the relationship between oxidative cell damage and TPC values. Most genotypes of the minor cereal species showed superior antioxidant effects in human cell cultures compared to the common wheat genotypes. Many of the minor cereal genotypes with high antioxidant capacities protected DNA and mitochondrial damage and prevented cell death in HeLa cells and colon-derived HCT116 human epithelial cells. There was no significant relationship between TPC values and oxidative cell damage. However, common wheat genotypes had, on average, lower TPC values. The results show that minor cereals contain potentially high levels of certain antioxidant substances which might be useful in preventing oxidative damage in cellular systems