On Semi-Slant $${\varvec{\xi ^\perp }}$$-Riemannian Submersions

The aim of the present paper is to define and study semi-slant \(\xi ^\perp \)-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant \(\xi ^\perp \)-Riemannian submersions, semi-invariant \(\xi ^\perp \)-Riemannian submersions and slant Riemannian submersions. We obtain characterizations, investigate the geometry of foliations which arise from the definition of this new submersion. After we investigate the geometry of foliations, we obtain necessary and sufficient condition for base manifold to be a locally product manifold and proving new conditions to be totally umbilical and totally geodesicness, respectively. Moreover, some examples of such submersions are mentioned.     

Non-linear vibrations of suspension bridges with external excitation

Non-linear coupled vertical and torsional vibrations of suspension bridges are investigated. Method of Multiple Scales, a perturbation technique, is applied to the equations to find approximate analytical solutions. The equations are not discretized as usually done, rather the perturbation method is applied directly to the partial differential equations. Free and forced vibrations with damping are investigated in detail. Amplitude and phase modulation equations are obtained. The dependence of non-linear frequency on amplitude is described. Steady-state solutions are analyzed. Frequency-response equation is derived and the jump phenomenon in the frequency-response curves resulting from non-linearity is considered. Effects of initial amplitude and phase values, amplitude of excitation, and damping coefficient on modal amplitudes, are determined.     

Synthesis of dihydrofurans containing trifluoromethyl ketone and heterocycles by radical cyclization of fluorinated 1,3-dicarbonyl compounds with 2-thienyl and 2-furyl substituted alkenes

Manganese(III) acetate based radical cyclization of various fluorinated 1,3-dicarbonyl compounds with 2-thienyl and 2-furyl substituted alkenes produced 3-trifluoroacetyl and 2-trifluoromethyl-dihydrofurans in good yields. The radical cyclizations of 2-methyl-5-[(E)-2-phenylvinyl]furan 2b and 2-[(E)-2-phenylvinyl]thiophene 2c led to the formations of 5-(5-methyl-2-furyl)-4,5-dihydrofuran and 5-(2-thienyl)-4,5-dihydrofuran, respectively. In the reactions of 1,3-dicarbonyls with alkenes, 2-thienyl substituted alkenes formed 4,5-dihydrofurans in higher yields than 2-furyl substituted alkenes.     

Preparation and properties of a new solid state borate ion selective electrode and its application

A new borate ion selective electrode using solid salts of Ag₃BO₃, Ag₂S and Cu₂S has been developed. Detailed information is provided concerning the composition, working pH and conditioning of the electrode. An analytically useful potential change occurred from 1 × 10⁻⁶ to 1 × 10⁻¹ M borate ion. The slope of the linear portion was 31 ± 2 mV/10-fold changes in borate concentration. The measurements were made at constant ionic strength (0.1 M NaNO₃) and at room temperature. The effect of Cl⁻, Br⁻, NO₃⁻, SO⁼₄, H₂PO₄⁻ anions and K⁺, Na⁺, Cu²⁺, Ag⁺, Ca²⁺ cations on borate response is evaluated and it was found that only Ag⁺ had a small interference effect. The lifetime of the electrode was more than two years, when used at least 4-5 times a day, and the response time was about 20-30 s. Borate content in waste water of borax factory, tap water of a town situated near to the borax factory and city tap water far from these mines were also determined. The validation was made with differential pulse polarography for the same water sample, and high consistency was obtained.     

Synthesis,molecular conformation,vibrational, electronic transition,and chemical shift assignments of 4-(thiophene-3-ylmethoxy)phthalonitrile: a combined experimental and theoretical analysis

This work presents the synthesis and characterization of a novel compound, 4-(thiophene-3-ylmethoxy)phthalonitrile (TMP). The spectroscopic properties of the compound were examined by FT-IR, FT-Raman, NMR, and UV techniques. FT-IR and FT-Raman spectra in solid state were observed in the region 4000–400 cm⁻¹ and 3500–50 cm⁻¹, respectively. The ¹H and ¹³C NMR spectra were recorded in CDCl₃ solution. The UV absorption spectrum of the compound that dissolved in THF was recorded in the range of 200–800 nm. The structural and spectroscopic data of the molecule in the ground state were calculated using density functional theory (DFT) employing B3LYP exchange correlation and the 6-311++G(d,p) basis set. The vibrational wavenumbers were calculated and scaled values were compared with experimental FT-IR and FT-Raman spectra. The complete assignments were performed on the basis of the experimental results and total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. Isotropic chemical shifts (¹³C NMR and ¹H NMR) were calculated using the gauge-invariant atomic orbital (GIAO) method. A study on the electronic properties, such as HOMO and LUMO energies, were performed by time-dependent DFT (TD-DFT) approach. The HOMO and LUMO analyses have been used to elucidate information regarding charge transfer within the molecule. Comparison of the calculated frequencies, NMR chemical shifts, absorption wavelengths with the experimental values revealed that DFT method produces good results.     

Selective detection of dopamine with poly(diphenylamine sulfonic acid) modified electrode in the presence of ascorbic acid

A glassy carbon electrode was modified with electropolymerized film of diphenylamine sulfonic acid (DPASA). Electropolymerization was performed by cyclic voltammetry in 0.1 M KCl solution. The modified electrode showed an excellent electrocatalytic effect towards oxidation of dopamine (DA) and ascorbic acid (AA). Electrostatic interaction between the negatively charged poly(DPASA) film and either cationic DA species or anionic AA species favorably contributed to the redox response of DA and AA. Anodic peaks of DA and AA in their mixture were well separated by ca 168 and −11.8 mV. The proposed modified electrode was utilized for selective determination of dopamine in the concentration range of 5.0 × 10^t7–2.0 × 10⁻⁵ M in the presence of high concentration of ascorbic acid. Detection limit was 6.5 × 10⁻⁹ M.     

Large-scale plasmonic microarrays for label-free high-throughput screening

Microarrays allowing simultaneous analysis of thousands of parameters can significantly accelerate screening of large libraries of pharmaceutical compounds and biomolecular interactions. For large-scale studies on diverse biomedical samples, reliable, label-free, and high-content microarrays are needed. In this work, using large-area plasmonic nanohole arrays, we demonstrate for the first time a large-scale label-free microarray technology with over one million sensors on a single microscope slide. A dual-color filter imaging method is introduced to dramatically increase the accuracy, reliability, and signal-to-noise ratio of the sensors in a highly multiplexed manner. We used our technology to quantitatively measure protein-protein interactions. Our platform, which is highly compatible with the current microarray scanning systems can enable a powerful screening technology and facilitate diagnosis and treatment of diseases.     

Derivation of Korteweg-de Vries flow equations from the regularized long-wave (RLW) equation

We perform a multiple-time scales analysis and compatibility condition to the regularized long-wave (RLW) equation. We derive Korteweg-de Vries (KdV) flow equation in the bi-Hamiltonian form as an amplitude equation.     

A collocation approach for the numerical solution of certain linear retarded and advanced integrodifferential equations with linear functional arguments

This article presents a Taylor collocation method for the approximate solution of high‐order linear Volterra‐Fredholm integrodifferential equations with linear functional arguments. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. Some numerical examples, which consist of initial and boundary conditions, are given to show the properties of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011