Some New Inequalities of Dirichlet Eigenvalues for Laplace Operator with any Order

In this paper, we establish several inequalities of Dirichlet eigenvalues for Laplace operator $\Delta$ with any order on \emph{n}-dimensional Euclidean space. These inequalities are more general than known Yang's inequalities and contain new consequences. To obtain them, we borrow the approach of Illias and Makhoul, and use a generalized Chebyshev's inequality

Interfacial Magnetoelectric Coupling in Tri-component Superlattices

Using first-principles density functional theory, we investigate the interfacial magnetoelectric coupling in a tri-component superlattice composed of a ferromagnetic metal (FM), ferroelectric (FE), and normal metal (NM). Using Fe/FE/Pt as a model system, we show that a net and cumulative interfacial magnetization is induced in the FM metal near the FM/FE interface. A carefully analysis of the magnetic moments in Fe reveals that the interfacial magnetization is a consequence of a complex interplay of interfacial charge transfer, chemical bonding, and spin dependent electrostatic screening. The last effect is linear in the FE polarization, is switchable upon its reversal, and yields a substantial interfacial magnetoelectric coupling.Comment: 5 pages, 6 figure

Sensitive voltammetric detection of yeast RNA based on its interaction with Victoria Blue B

Voltammetric studies of the interaction of yeast RNA (y-RNA) with Victoria Blue B (VBB) are described in this paper. Furthermore, a linear sweep voltammetric method for the detection of y-RNA was established. The reaction conditions, such as acidity and amount of buffer solution, the concentration of VBB, the reaction time and temperature, etc., were carefully investigated by second order derivative linear sweep voltammetry. Under the optimal conditions, the reduction peak current of VBB at –0.75 V decreased greatly after the addition of y-RNA to the solution without any shift of the reduction peak potential. Based on the decrease of the peak current, a new quantitative method for the determination of y-RNA was developed. The effects of co-existing substances on the determination were carefully investigated and three synthetic samples were determined with satisfactory results. The stoichiometry of the VBB–y-RNA complex was calculated by linear sweep voltammetry and the interaction mechanism is discussed

Voltammetric determination of heparin based on its interaction with malachite green

In this paper malachite green (MG) was used as a bioprobe to determine heparin concentration by linear sweep voltammetry on the dropping mercury working electrode (DME). In Britton-Robinson (B-R) buffer solution of pH 1.5, MG had a well-defined second order derivative linear sweep voltammetric reductive peak at         –0.618 V (vs. SCE). After the addition of heparin into the MG solution, the reductive peak current decreased apparently without the movement of peak potential. Based on the difference of the peak current, a new voltammetric method for the determination of heparin was established. The conditions for the binding reaction and the electrochemical detection were optimized. Under the selected experimental conditions the difference of peak current was directly proportional to the concentration of heparin in the range from 0.3 to 10.0 mg/L with the linear regression equation as ∆ip″ (nA) = 360.19 C (mg/L) + 178.88 (n = 15, γ = 0.998) and the detection limit as 0.28 mg/L (3σ). The effects of coexisting substances such as metal ions, amino acids on the determination of heparin were investigated and the results showed that this method had good selectivity. This method was further applied to determine the heparin content in heparin sodium injection samples with satisfactory results and good recovery. The stoichiometry of the biocomplex was calculated by the electrochemical method and the binding mechanism was further discussed. KEY WORDS: Heparin, Malachite green, Voltammetry, Binding reaction  Bull. Chem. Soc. Ethiop. 2008, 22(2), 165-172

Magnetoelectric Coupling and Electric Control of Magnetization in Ferromagnet-Ferroelectric-Metal Superlattices

Ferromagnet-ferroelectric-metal superlattices are proposed to realize the large room-temperature magnetoelectric effect. Spin dependent electron screening is the fundamental mechanism at the microscopic level. We also predict an electric control of magnetization in this structure. The naturally broken inversion symmetry in our tri-component structure introduces a magnetoelectric coupling energy of $P M^2$. Such a magnetoelectric coupling effect is general in ferromagnet-ferroelectric heterostructures, independent of particular chemical or physical bonding, and will play an important role in the field of multiferroics.Comment: 5 pages including 3 figures and 1 tabl

Strong correlation of the neutron star core-crust transition density with the σ\sigma-meson mass via vacuum polarization

We study the neutron star core-crust transition density $\rho_t$ with the inclusion of the vacuum polarization in the dielectric function in the nonlinear relativistic Hartree approach (RHAn). It is found that the strong correlation between the $\rho_{t}$ and the scalar meson mass $m_{\sigma}$ strikingly overwhelms the uncertainty of the nuclear equation of state in the RHAn models, in contrast to the usual awareness that $\rho_{t}$ is predominantly sensitive to the isovector nuclear potential and symmetry energy. The accurate extraction of $\rho_{t}$ through the future gravitational wave measurements can thus provide a strong constraint on the longstanding uncertainty of $m_{\sigma}$, which is of significance to better infer the vacuum property. As an astrophysical implication, it suggests that the correlation between $\rho_t$ and $m_\sigma$ is very favorable to reconcile the difficulty in reproducing the large crustal moment of inertia for the pulsar glitches with the well constrained symmetry energy.Comment: 11 pages, 4 figure