Multiresolution based adaptive schemes for second order hyperbolic PDEs in elastodynamic problems

An enhanced interpolation wavelet-based adaptive-grid scheme is implemented for simulating high gradient smooth solutions (as well as, discontinuous ones) in elastodynamic problems in domains with irregular boundary shapes. In the method, spatially adaptive smoothing is used to improve interpolation property of the solution in high gradient zones. In hyperbolic systems, in fact, there are no certain inherent regularities; hence, the erroneous adapted grid may be achieved because of small spurious oscillations in the solution domain. These oscillations, mainly formed in the vicinity of high gradient and discontinuity zones, make the adaptation procedure strongly unstable. To cover this drawback, enhanced smoothing splines are used to denoise directly non-physical oscillations in the irregular grid points, a kind of ill-posed problem. Controllable smoothing is achieved using non-uniform weight coefficients. As the smoothing splines are a kind of the Thikhonov regularization method, they work stably in irregular grid points. Regarding the Thikhonov regularization method, L-curve scheme could be used to investigate trade-off between accuracy and smoothness of the solutions. This relationship, in fact, could not be reliably captured by common computational methods. The proposed method, in general, is easy and conceptually straightforward; as all calculations are carried out in the physical domain. This concept is verified using a variety of 2D numerical examples.     

DFT based insights into reactivity descriptors of encapsulated B<Subscript>24</Subscript>N<Subscript>24</Subscript> nanocages

The purpose of this study is to probe the DFT based chemical reactivity parameter, electrophilicity index as a possible molecular engineering of endohedral BN-nanocages. The structure and electronic properties of endohedral boron nitride nanocages have been investigated as a function of alkali atom inside the nanocage using density functional theory. We have calculated and analyzed basic characteristic related to the reactive behavior, such as HOMO–LUMO band gap, chemical hardness, chemical potential, vertical electron affinity, and vertical ionization potential, as well as the global electrophilicity index, ω(I, A) of the encapsulated B₂₄N₂₄ nanocages. We also investigated the MQZVP basis set effect on total electronic energy of the clusters.     

Existence of Nondecreasing Positive Solutions for a System of Singular Integral Equations

In this paper, a monotonicity property of the superposition operator in higher dimensions will be proved. Then by using the concept of measure of noncompactness, we will establish the existence of nondecreasing positive solutions for a system of singular integral equations. Furthermore, the results will be used to investigate the solvability of the system of k ^th -order initial value problems.     

The influence of NH3 -attaching on the NMR parameters in the zigzag BN nanotube

Two models of (10, 0) boron nitride nanotubes (BNNTs), perfect and Ammonia-attached, were studied in order to evaluate the influence of NH₃-attaching on the B-11 and N-15 nuclear magnetic resonance in the (10, 0) boron-nitride nanotube (BNNT) for the first time. At first, based on density functional theory (DFT) each of the structures was optimized using B3LYP/6-31G (d) model chemistry. At the next step, the chemical-shielding (CS) tensors were calculated using the B3LYP/6-31G (d, p) level of theory in both of the relaxed forms and were converted to experimentally measurable nuclear magnetic resonance (NMR) parameters, i.e. chemical-shielding isotropic (CSI) and chemical-shielding anisotropic (CSA). Our calculation revealed that in the NH₃-attached BNNT (the most stable model) the B atom chemically bonded to the NH₃ molecule has the largest chemical-shielding isotropic (CSI) and the smallest chemical-shielding anisotropic (CSA) values among the other boron nuclei. Additionally, the NMR parameters of those nuclei directly bonded to the boron dramatically change while those of the other B nuclei remain almost unchanged.     

TiO2 supported cobalt-manganese nano catalysts for light olefins production from syngas

Cobalt-manganese nano catalysts were prepared by sol-gel method. This research investigated the effects of different cobalt-manganese (Co/Mn = 1/1) loading, pH and calcination conditions on the catalytic performance of Co-Mn/TiO2 catalysts for Fischer-Tropsch synthesis (FTS) in a fixed bed reactor. It was found that the catalyst containing 30wt%(Co-Mn)/TiO2 was an optimal catalyst for the conversion of synthesis gas to light olefins especially propylene. The activity and selectivity of optimal catalyst were studied under different operational conditions. The results showed that the best operational conditions were H2 /CO = 1/1 molar feed ratio at 250℃ and GHSV = 1300 h-1 under atmospheric pressure. Characterization of catalysts was carried out by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), N2 adsorption-desorption measurements.     

TiO2 supported cobalt-manganese nano catalysts for light olefins production from syngas

Cobalt-manganese nano catalysts were prepared by sol-gel method. This research investigated the effects of different cobalt-manganese (Co/Mn = 1/1) loading, pH and calcination conditions on the catalytic performance of Co-Mn/TiO₂ catalysts for Fischer-Tropsch synthesis (FTS) in a fixed bed reactor. It was found that the catalyst containing 30wt%(Co-Mn)/TiO₂ was an optimal catalyst for the conversion of synthesis gas to light olefins especially propylene. The activity and selectivity of optimal catalyst were studied under different operational conditions. The results showed that the best operational conditions were H₂/CO= 1/1 molar feed ratio at 250 °C and GHSV= 1300 h^?1 under atmospheric pressure. Characterization of catalysts was carried out by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), N₂ adsorption-desorption measurements.     

Common fixed point results for four mappings satisfying almost generalized (S, T)-contractive condition in partially ordered metric spaces

In this paper, we define the concept of almost generalized (S, T)-contractive condition, and prove some common fixed point results for four mappings satisfying almost generalized (S, T)-contractive condition in partially ordered metric space. An example is given to support the usability of our results.     

The 0-Homogenous Complete Lift Metric

The complete lift of a Riemannian metric g on a differentiable manifold M is not 0-homogeneous on the fibers of the tangent bundle TM. In this paper we introduce a new kind of lift G of g, which is 0-homogeneous. It determines a pseudo-Riemannian metric on ${\widetilde {TM}}$ , which depends only on the metric g. We obtain the Levi-Civita connection of this metric and study conformal vector fields on ( ${\widetilde {TM},G}$ ). Finally, we introduce the almost product and complex structures which preserve homogeneity and study certain geometrical properties of these structures.