Two-dimensional fin with convective base condition

When solving a two-dimensional model of an isolated fin, researchers have mainly concentrated on either a constant or a periodic fin base temperature. It is possible to obtain a numerical solution by a convective boundary condition on the fin base. However, in an analytical solution, one cannot calculate an arbitrary constant because of the convective boundary condition of the separation of variables. Therefore a heat balance is applied here to resolve this difficulty. In addition, a modified solution is presented which does not involve any additional mathematics with respect to the classical approach of solving a one-dimensional model. For different values of the Biot number $B_{22}$, a comparison of one- and two-dimensional solutions is given. Relative errors of the heat flow rates predicted by the classical and modified one-dimensional solutions, and the respective exact two-dimensional solution with respect to an, are computed. It is found that, for large values of $B_{22}$ (say 50.0) modified solution, by using a convective condition at the fin base gives significant accuracy improvements in comparison to the classical one-dimensional technique.     

Nicholas reactions in the construction of cyclohepta[de]naphthalenes and cyclohepta[de]naphthalenones. The total synthesis of microstegiol

The application of the Nicholas reaction chemistry of 2,7-dioxygenated naphthalenes in the synthesis of cyclohepta[de]napthalenes and in the synthesis of (±)-microstegiol (1) is presented. The substitution profile of Nicholas monosubstitution (predominantly C-1) and disubstitution reactions (predominantly 1,6-) on 2,7-dioxygenated napthalenes is reported. Application of a 1,8-dicondensation product and selected C-1 monocondensation products to the construction of cyclohepta[de]naphthalenes by way of ring closing metathesis and intramolecular Friedel-Crafts reactions, respectively, is described. Deprotection of the C-7 oxygen function to the corresponding naphthol allows tautomerization to cyclohepta[de]naphthalene-1-ones upon seven-membered-ring closure in most cases, and replacement of the C-2 oxygen function in the naphthalene by a methyl group ultimately allows the synthesis of (±)-microstegiol.     

Efficient aerial oxidation of different types of alcohols using ZnO nanoparticle–MnCO3-graphene oxide composites

Graphene–metal nanocomposites have been found to remarkably enhance the catalytic performance of metal nanoparticle-based catalysts. In continuation of our previous report, in which highly reduced graphene oxide (HRG)-based nanocomposites were synthesized and evaluated, we present nanocomposites of graphene oxide (GRO) and ZnO nanoparticle-doped MnCO₃ ([ZnO–MnCO₃/(1%)GRO]) synthesized via a facile, straightforward co-precipitation technique. Interestingly, it was noticed that the incorporation of GRO in the catalytic system could noticeably improve the catalytic efficiency compared to a catalyst (ZnO–MnCO₃) without GRO, for aerial oxidation of benzyl alcohol (BzOH) employing O₂ as a nature-friendly oxidant under base-free conditions. The impacts of various reaction factors were thoroughly explored to optimize reaction conditions using oxidation of BzOH to benzaldehyde (BzH) as a model substrate. The catalysts were characterized using X-ray diffraction, thermogravimetric analysis, Fourier transform infrared spectroscopy, field-emission scanning electron microscopy, Energy dispersive X-ray spectroscopy (EDX), Brunauer-Emmett-Teller (BET), and Raman spectroscopy. The (1%)ZnO–MnCO₃/(1%)GRO exhibited significant specific activity (67 mmol.g⁻¹.hr⁻¹) with full convversion of BzOH and >99% BzH selectivity within just 6 min. The catalytic efficiency of the (1%)ZnO–MnCO₃/(1%)GRO nanocomposite was significantly better than the (1%)ZnO–MnCO₃/(1%)HRG and (1%)ZnO–MnCO₃ catalysts, presumably due to the existence of oxygen-possessing groups on the GRO surface and as well as a very high surface area that could have been instrumental in uniformly dispersing the active sites of the catalyst, i.e., ZnO–MnCO₃. Under optimum circumstances, various kinds of alcohols were selectively transformed to respective carbonyls with full convertibility over the (1%)ZnO–MnCO₃/(1%)GRO catalyst. Furthermore, the highly effective (1%)ZnO–MnCO₃/(1%)GRO catalyst could be successfully reused and recycled over five consecutive runs with a marginal reduction in its performance and selectivity.     

加权ebyev-Ostrowski型不等式

关于著名的ebyev不等式,已有众多的研究成果.通过建立积分不等式,来建立全新的加权ebyev型积分不等式.给予了独立的证明,并给出了此类不等式的新评价.     

Analysis of electro-active regions and conductivity of BaMnO3 ceramic by impedance spectroscopy

Polycrystalline BaMnO₃ ceramic powders were prepared using the conventional mixed oxide route accompanied with several milling processes. Single phase formation was verified by recording the X-ray diffraction pattern of the powder as well as sintered pellet at room temperature. Scanning electron micrograph and energy dispersive X-ray spectrum of cross-sectional view have shown that sintered pellet is highly porous and contains only Ba, Mn and O elements, respectively. Analysis of impedance spectroscopy was carried out via the complex impedance and complex modulus formalisms. These results have shown that BaMnO₃ behave as semiconducting material. Furthermore, as a consequence of electrically inhomogeneous nature of the sample, it was observed that the electroactive regions (such as grain, grain boundary and sample-electrode interface) are overlapped in the applied frequency domain with dominant grain boundary effect. An equivalent circuit model (R _g C _g)(R _gb Q _gb)(R _e Q _e) was employed to fit the temperature dependent impedance spectroscopy data. Study of grain and grain boundary conductivities suggest that grains are more conductive than grain boundaries and conduction mechanism followed correlated barrier hopping (CBH) model.     

Bis(ammonium) tris­(hexa­aqua­magnesium) tetra­kis(hydrogen phosphite)

The structure of the title compound, (NH₄)₂[Mg(H₂O)₆]₃(HPO₃)₄, consists of [Mg(H₂O)₆]²⁺ and (NH₄)⁺ cations and (HPO₃)²⁻ anions held together by an intricate network of hydrogen bonds involving all H atoms except for one linked directly to a P atom. The Mg²⁺ cations are octa­hedrally coordinated by six water mol­ecules. One of the Mg atoms is located on a site with 2/m symmetry, whereas the other Mg atom and the P and N atoms occupy sites with m symmetry.     

On Mann iteration in Hilbert spaces

Let K$K$ be a compact convex subset of a real Hilbert space H$H$; T:K→K$T:K\to K$ a hemicontractive map. Let {_αn}$\left\{{\alpha }_n\right\}$ be a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary _x0∈K$x_0\in K$, the sequence {_xn}$\left\{x_n\right\}$ defined iteratively by _xn=_αnxn−1+(1−_αn)T_xn$x_n={\alpha }_n{x}_{n-1}+(1-{\alpha }_n)T{x}_n$, n≥1$n\ge 1$ converges strongly to a fixed point of T$T$.