An oxo‐bridged centrosymmetric tetranuclear titanium compound

The title compound, octa‐tert‐butoxybis­[μ₃‐2,2′‐(N‐methyl­imino)­diethanolato]­di‐μ‐oxo‐tetratitanium(IV), [Ti₂O{(OCH₂CH₂)₂(NCH₃)}{(CH₃)₃CO}₄]₂ or [Ti₄(C₅H₁₁NO₂)₂(C₄H₉O)₈O₂], lies about an inversion centre, and displays the less usual zigzag configuration. One O atom of the N‐methyl­diethoxo­amine ligand bridges the symmetry‐related Ti atoms, while the other bridges the two independent Ti atoms, with the N atom binding to give a facial configuration. Four ^tBuO⁻ ligands and a bridging oxide complete the respective five‐ and sixfold coordination of the two Ti atoms. The Ti—O bond lengths range in a self‐consistent fashion from 1.7624 (17) to 2.0878 (18) Å, while the Ti—N bond length is 2.374 (2) Å.     

A blow-up result in a Cauchy viscoelastic problem

In this work we consider a Cauchy problem for a nonlinear viscoelastic equation. Under suitable conditions on the initial data and the relaxation function, we prove a finite-time blow-up result.     

Rapid TLC Method for Estimation of Mevalonic Acid in the Leaves of Medicinal Plants

A simple, rapid, specific and sensitive thin layer chromatographic (TLC) method has been developed for the quantitative estimation of mevalonic acid (MVA) in leaves of medicinal plants; Artemisia annua, Psorelia corylifolia, Vinca rosea, Withania somnifera and Barleria proinites. The assay procedure involved conversion of MVA to its lactone, mevalonolactone (MVAL). Mevalonic acid was extracted from the leaf tissues of plants. Separation of MVAL was carried out on silica gel 60 F₂₅₄ TLC plates using benzene:acetone (3:2) as the mobile phase. The densitometric determination of MVAL was performed at 600 nm after derivatization with anisaldehyde reagent in absorption–reflectance mode. The method was validated over the linearity range of 100–500 ng spot^?1 and correlation coefficient for the calibration curve was >0.99. The average recovery of MVAL, used as internal standard, was higher than 98%. The lower limit of detection was found to be 50 ng spot^?1.     

Stimulated raman scattering in fiber optic systems

The effect of stimulated Raman scattering (SRS) in fiber optic communications is considered. On one hand, SRS limits the launch power in a multiple-channel communication system; while on the other hand, SRS can provide optical amplification in the 1.3-μm and 1.55-μm windows. In most of the previous work these issues have been treated separately by using different assumptions. A solution is usually obtained by solving differential equations. We present a numerical method that involves the simultaneous solution of integral equations describing SRS in optical fiber. The method is general enough to be applicable for wavelength division multiplexing (WDM), optic frequency division multiplexing (OFDM), and optical amplification. However, it is efficient and simple to program and uses just a few realistic assumptions. A WDM communication system with 10 optical channels in the 1.55-μm window is studied by using this method, The data rate is above 1 Gbps. The system parameters are such that the other nonlinear effects, such as stimulated Brillouin scattering and four-wave mixing, are less significant for the system. Launch power limitations imposed by SRS are investigated for IM / DD and coherent systems. The receiver dynamic range over the wavelengths of interest is an important factor in determining the launch power limitations. An optical amplifier in the 1.3-μm window is also analyzed. The two-pump technique is investigated. With pump power levels of about 500 mw 0-dB gain can be achieved for a 30-km repeaterless link. Finally, the calculated results agree with the experiments.     

Multidimensional modified fractional calculus operators involving a general class of polynomials

In the present work, we introduce and study essentially a class of multi-dimensional modified fractional calculus operators involving a general class of polynomials in the kernel. These operators are considered in the space of functionsM _γ (R ₊ ⁿ ). Some mapping properties and fractional differential formulas are obtained. Also images of some elementary and special functions are established.     

Ultraspherical Integral Method for Optimal Control Problems Governed by Ordinary Differential Equations

In this paper an ultraspherical integral method is proposed to solve optimal control problems governed by ordinary differential equations. Ultraspherical approximation method reduced the problem to a constrained optimization problem. Penalty leap frog method is presented to solve the resulting constrained optimization problem. Error estimates for the ultraspherical approximations are derived and a technique that gives an optimal approximation of the problems is introduced. Numerical results are included to confirm the efficiency and accuracy of the method.     

New cytotoxic isoprenoid derivatives from the Red Sea soft coral Sarcophyton glaucum

Chemical investigation of the soft coral Sarcophyton glaucum collected from the Red Sea led to isolation of 11 isoprenoidal metabolites (1–11). A new sesquiterpenoid, 6-oxo-germacra-4(15),8,11-triene (1), a new natural cembranoid, sarcophinediol, along with two known sesquiterpenoids (2 and 3) and seven known cembranoids (5–11) was obtained. The structures of the compounds were established based on their NMR, MS, IR and UV spectral data. All compounds were evaluated for their cytotoxicity employing three cancer cell lines (HepG2, MCF-7 and HCT116). Compounds 4 and 6 showed significant cytotoxicity towards HepG2 with IC₅₀ values of 18.8 ± 0.07 and 19.9 ± 0.02 μM; respectively. Compounds 5–7 exhibited potent cytotoxicity against MCF-7 cells with IC₅₀ values of 9.9 ± 0.03, 2.4 ± 0.04 and 3.2 ± 0.02 μM, respectively. Compounds 1, 4 and 5 showed significant activities towards HCT116 cells with IC₅₀ values of 29.4 ± 0.03, 19.4 ± 0.02 and 25.8 ± 0.03 μM, respectively.     

Novel synthesis of alkoxy substituted oxa[9]helicenes by the reaction of helical quinone with alcohols

The reaction of helical quinone with alcohols in the presence of Brønsted acid such as para-toluenesulfonic acid (pTSA) or HCl proceeded smoothly to produce the corresponding alkoxy substituted oxa[9]helicenes in good yields.     

Crystal supramolecularity in 2,2′-iminodipyridinium tetrahalometallate(II) salts: Supramolecular motifs that control tetrahedral halometallate solid state structures

N⁺–H$?$Br–M and (π)C–H$?$Br–M hydrogen bond synthons have been exploited in the crystallization of a series of 2,2′-iminodipyridinium(2+) dication (hereafter 2,2′-imdipyH₂), (C₁₀H₁₁N₃)[MX₄] salts (M = Co and Hg; X = Cl and Br) and 2,2′-iminodipyridinium(1+) cation (hereafter 2,2′-imdipyH), (C₁₀H₁₀N₃)₂[MX₄] salts (M = Co, Hg; X = Cl and Br). Intermolecular interactions and crystal supramolecularity adopted in these structures were analyzed and compared with reported similar structures, (C₁₀H₁₁N₃)[CuCl₄] and (C₁₀H₁₀N₃)₂[CoCl₄]. In these salts only one structural form for the halometallate species is observed namely mononuclear tetrahedral. The crystal supramolecularity in the (2,2′-imdipyH₂)[MX₄] series corresponds to three distinct structural motifs: Parallel ribbons of infinitely connected cyclic dimers of two dications and two anions found in the isomorphous salts of [CoCl₄]^2? and [CuCl₄]^2?; and cyclic dimer hearing-bone packing motif found in the isomorphous dication salts of [CoBr₄]^2? and [HgBr₄]^2?. Infinitely helical layers based on alternating $?$anion$?$two stacked cations $?$anion$?$ two stacked cations$?$ are found in the isomorphous salts of (2,2′-imdipyH)₂[CoCl₄] and (2,2′-imdipyH)₂[HgBr₄].