Ultraslow optical waveguiding in an atomic Bose-Einstein condensate

We investigate waveguiding of ultraslow light pulses in an atomic Bose-Einstein condensate. We show that under the conditions of off-resonant electromagnetically induced transparency, waveguiding with a few ultraslow modes can be realized. The number of modes that can be supported by the condensate can be controlled by means of experimentally accessible parameters. Propagation constants and the mode conditions are determined analytically using a Wentzel-Kramers-Brillouin analysis. Mode profiles are found numerically.     

Image reversal for direct electron beam patterning of protein coated surfaces

Electron beam lithography (EBL) is used to create surfaces with protein patterns, which are characterized by immunofluorescence and atomic force microscopies. Both negative and positive image processes are realized by electron beam irradiation of proteins absorbed on a silicon surface, where image reversal is achieved by selectively binding a second species of protein to the electron beam exposed areas on the first protein layer. Biofunctionality at the cellular level was established by culturing cortical cells on patterned lines of fibronectin adsorbed on a bovine serum albumin background for 7 days in culture.     

Lyapunov-type integral inequalities for certain higher order differential equations

In this paper, first we will give a short survey of the most basic results on Lyapunov inequality, and next we obtain this-type integral inequalities for certain higher order differential equations. Our results are sharper than some results of Yang (2003) [20].     

Synthesis of zinc borate by inverse emulsion technique for lubrication

Lubricating oil additives based on boron compounds are promising materials for lubrication due to their tribological advantages such as antiwear efficiency, good film strength, and high temperature resistance. This article deals with the preparation of zinc borate particles that are well dispersed and colloidally stabilized in mineral oil. This method starts with preparing two inverse emulsions (water-in-oil) with sorbitan monostearate (Span 60) as a surfactant, light neutral oil as a continuous phase, and the aqueous solutions of borax decahydrate (Na₂B₄O₇·10H₂O) and zinc nitrate (Zn(NO₃)₂·6H₂O) as the dispersed phases. The produced particles were zinc borate crystals having both rod-like and spherical morphologies, and the diameters of spherical particles were changing between 20 and 30 nm. FTIR spectra of the obtained particles showed the characteristic peaks of trihedral borate (B(3)-O) and tetrahedral borate (B(4)-O) groups as well as the specific peaks of the sorbitan monostearate. TG showed 30.42% and 22.08% mass loss at 600 °C for the samples prepared by inverse emulsion and precipitation techniques, respectively. The endothermic peak at 50 °C is observed due to the melting of sorbitan monostearate and the heat of melting is evaluated as −3.50 J/g. Tribological studies revealed that sorbitan monostearate not only outperformed as a dispersing agent of inorganic particles, but also it proved to be an anti-wear agent. Zinc borate produced by precipitation decreased the wear scar diameter from 1.402 to 0.639 mm and the friction coefficient from 0.099 to 0.064. The inverse emulsion was effective in decreasing wear scar diameter and the friction coefficient by lowering them to 0.596 and 0.089 mm, respectively.     

On Lyapunov-type inequality for quasilinear systems

In this paper, we sketch some recent developments in the theory of Lyapunov-type inequalities and present some new results relating to a quasilinear system, special cases of which contain some well-known differential equations such as half-linear and linear equations. Our result generalize the Lyapunov-type inequality given in [18].     

Mn(III) acetate-mediated regioselective benzylation of various α,β-unsaturated and β-alkoxy-α,β-unsaturated ketones

We describe herein the results of manganese(III) acetate mediated α′-benzylation of various α,β-unsaturated and β-alkoxy-α,β-unsaturated ketones in moderate yields.     

Hamiltonian structure of multi component integrable systems

In this work we have generalized the super KdV equation into a multicomponent super KdV equation. It is shown that the system is bi-super Hamiltonian. The third super Hamiltonian in the multicomponent super KdV hierarchy is obtained and the corresponding first and second members of evolution equations are given. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. This work is supported by Yildiz Technical University Foundation under project No. 21-01-01-02.     

Bose-Einstein Condensate in a Linear Trap with a Dimple Potential

We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.     

On the oscillation of certain second-order nonlinear differential equations

In this paper, oscillation criteria for the nonlinear second-order ordinary differential equation