Uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for nth order differential equations

For the nth order differential equation, y(n)=f(x,y,y^′,…,y(n−1)), we consider uniqueness implies existence results for solutions satisfying certain nonlocal (k+2)-point boundary conditions, 1?k?n−1. Uniqueness of solutions when k=n−1 is intimately related to uniqueness of solutions when 1?k?n−2. These relationships are investigated as well.     

Regulating the surface of nanoceria and its applications in heterogeneous catalysis

Ceria (CeO₂) as a support, additive, and active component for heterogeneous catalysis has been demonstrated to have great catalytic performance, which includes excellent thermal structural stability, catalytic efficiency, and chemoselectivity. Understanding the surface properties of CeO₂ and the chemical reactions occurred on the corresponding interfaces is of great importance in the rational design of heterogeneous catalysts for various reactions. In general, the reversible Ce³⁺/Ce⁴⁺ redox pair and the surface acid-base properties contribute to the superior intrinsic catalytic capability of CeO₂, and hence yield enhanced catalytic phenomenon in many reactions. Particularly, nanostructured CeO₂ is characterized by a large number of surface-bound defects, which are primarily oxygen vacancies, as the surface active catalytic sites. Many efforts have therefore been made to control the surface defects and properties of CeO₂ by various synthetic strategies and post-treatments. The present review provides a comprehensive overview of recent progress in regulating the surface structure and composition of CeO₂ and its applications in catalysis.     

Extended one-dimensional supramolecular assembly on a stepped surface

2,6-naphthalene-dicarboxylic acid was adsorbed on a Ag110 surface with an average terrace width of only some tens of a nm. Scanning tunneling microscopy shows that the adsorbates self-assemble into one-dimensional mesoscale length chains. These extend over several hundred nanometers and thus the structure exhibits an unprecedented tolerance to monatomic surface steps. Density functional theory and x-ray photoelectron spectroscopy explain the behavior by a strong intermolecular hydrogen bond plus a distinct template-mediated directionality and a high degree of molecular backbone flexibility.     

Asphaltene precipitation from latin american heavy crude oils. Effects of solvent aromaticity and agitation on particle size reduction

Asphaltenes from three crudes were precipitated with a mixture of n-heptane and toluene, the size of the particles formed under different solvent mixtures and different agitation regimes were studied. The kinetic size reduction of aggregates formed with an excess of precipitant agent is followed, contrary to other published studies where the kinetic followed is of growing particles. It was found that the particle size of precipitated asphaltenes decreases as precipitant aromaticity increases and agitation energy rises, which indicates the formation of aggregates bonded by weak forces, since the agitation applied was not of high energy, except for the ultrasonic device.     

Elusive Zintl Ions [μ‐HSi4]3− and [Si5]2− in Liquid Ammonia: Protonation States,Sites, and Bonding Situation Evaluated by NMR and Theory

The existence of [μ‐HSi₄]^3? in liquid ammonia solutions is confirmed by ¹H and ²⁹Si NMR experiments. Both NMR and quantum chemical calculations reveal that the H atom bridges two Si atoms of the [Si₄]^4? cluster, contrary to the expectation that it is located at one vertex Si of the tetrahedron. The calculations also indicate that in the formation of [μ‐HSi₄]^3?, protonation is driven by a high charge density and an increase of electron delocalization compared to [Si₄]^4?. Additionally, [Si₅]^2? was detected for the first time and characterized by NMR. Calculations show that it is resistant to protonation, owing to a strong charge delocalization, which is significantly reduced upon protonation. Thus, our methods reveal three silicides in liquid ammonia: unprotonated [Si₅]^2?, terminally protonated [HSi₉]^3?, and bridge‐protonated [μ‐HSi₄]^3?. The protonation trend can be roughly predicted by the difference in charge delocalization between the parent compound and the product, which can be finely tuned by the presence of counter ions in solution.     

The properties and geodesics related to the NUT--Taub-like spacetime

Some properties related to the NUT--Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT--Taub-like black hole are discussed. Furthermore, the geodesics in the NUT--Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT--Taub spacetime when m^*=0 and m^*\ll M, respectively.     

Upper and Lower Solution Methods for Fully Nonlinear Boundary Value Problems

Sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions. The conditions assume the existence of a strong upper solution-lower solution pair, a concept that is defined in the paper. The differential equation has nonlinear dependence on all lower order derivatives of the unknown; in particular, appropriate Nagumo conditions are obtained and employed.     

Ethylene dissociation on flat and stepped Ni(1 1 1): A combined STM and DFT study

The dissociative adsorption of ethylene (C₂H₄) on Ni(1 1 1) was studied by scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. The STM studies reveal that ethylene decomposes exclusively at the step edges at room temperature. However, the step edge sites are poisoned by the reaction products and thus only a small brim of decomposed ethylene is formed. At 500 K decomposition on the (1 1 1) facets leads to a continuous growth of carbidic islands, which nucleate along the step edges.DFT calculations were performed for several intermediate steps in the decomposition of ethylene on both Ni(1 1 1) and the stepped Ni(2 1 1) surface. In general the Ni(2 1 1) surface is found to have a higher reactivity than the Ni(1 1 1) surface. Furthermore, the calculations show that the influence of step edge atoms is very different for the different reaction pathways. In particular the barrier for dissociation is lowered significantly more than the barrier for dehydrogenation, and this is of great importance for the bond-breaking selectivity of Ni surfaces.The influence of step edges was also probed by evaporating Ag onto the Ni(1 1 1) surface. STM shows that the room temperature evaporation leads to a step flow growth of Ag islands, and a subsequent annealing at 800 K causes the Ag atoms to completely wet the step edges of Ni(1 1 1). The blocking of the step edges is shown to prevent all decomposition of ethylene at room temperature, whereas the terrace site decomposition at 500 K is confirmed to be unaffected by the Ag atoms.Finally a high surface area NiAg alloy catalyst supported on MgAl₂O₄ was synthesized and tested in flow reactor measurements. The NiAg catalyst has a much lower activity for ethane hydrogenolysis than a similar Ni catalyst, which can be rationalized by the STM and DFT results.