Keller–Osserman estimates and removability result for the anisotropic porous medium equation with gradient absorption term

We study “large” nonnegative solutions for a class of quasilinear equations model of which is We give a sufficient condition on the exponents and for the removability of isolated singularities.     

Synthesis of Sub-100 nm Nanoparticles by Emulsifier-free Emulsion Polymerization of α-Methylstyrene,Methyl Methacrylate and Acrylic Acid

The emulsifier-free emulsion copolymerization of α-methylstyrene (AMS) and methyl methacrylate (MMA) in the presence of functional monomer acrylic acid (AA) was carried out in batch process, giving birth to sub-100 nm nanoparticles. The kinetics of polymerization was investigated. The morphology and size of particles were monitored by TEM. The influences of the functional monomer AA concentration, initiator ammonium persulfate (APS) concentration, and polymerization temperature were studied. It was found that AMS caused a drastic decrease in both the rate of polymerization and the average degree of polymerization. The activation energy calculated from Arrhenius plot turned out to be 83.6 kJ/mol.     

Hierarchical ZSM-11 with intergrowth structures:Synthesis,characterization and catalytic properties

Hierarchical ZSM-11 microspheres with intercrystalline mesoporous properties and rod-like crystals intergrowth morphology have been synthesized using a spot of tetrabutylammonium as a single template.XRD,FTIR,SEM,TEM and N2 adsorption analysis revealed that each individual particle was composed of nanosized rod crystals inserting each other and the intercrystalline voids existing among rods gave a significant mesopore size distribution.Steam treatment result demonstrated the excellent hydrothermal stability of samples.Various crystallization modes including constant temperature crystallization (one-stage crystallization) and two-stage temperature-varying crystallization with different 1st stage durations were investigated.The results suggested that the crystallization modes were mainly responsible for the adjustable particle size and textural properties of samples while the small amount of tetrabutylammonium bromide was mainly used to direct the formation of both ZSM-11 framework and its intergrowth morphology.Furthermore,the performance of optimal ZSM-11 as an active component for the catalytic pyrolysis of heavy oil was also investigated.Compared with the commercial pyrolysis catalyst,the hierarchical ZSM-11 catalyst exhibited a high selectivity to desired products(LPG+gasoline+diesel),as well as a much lower dry gas and coke yield,plus a high selectivity and yield of light olefins(C=3 C=4)and very poor selectivity to benzene.Therefore,fully open micropore-mesopore connectivity would make such hierarchically porous ZSM-11 zeolites very attractive for applications in clean petrochemical catalysis field.     

N‐methyl‐2‐pyrrolidonium methyl sulfonate acidic ionic liquid as a new dynamic coating for separation of basic proteins by capillary electrophoresis

A simple and economical CE method has been developed for the analysis of four model basic proteins by employing N‐methyl‐2‐pyrrolidonium methyl sulfonate ionic liquid (IL) as the dynamic coating material based on the interaction of both between electrostatic attraction and hydrogen bond, and between the organic cations of IL and the inner surface of bare fused‐silica capillary. The N‐methyl‐2‐pyrrolidonium‐based IL modified capillary not only generated a stable suppressed electroosmotic flow, but also effectively eliminated the wall adsorption of proteins. Several important parameters such as the IL concentration, pH values, and concentrations of the background electrolyte were optimized to improve the separation of basic proteins. Consequently, under the optimum separation conditions, a satisfied separation of basic proteins including lysozyme, cytochrome c, ribonuclease A, and α‐chymotrypsinogen A with theoretical plates ranging from 2.09 × 10⁵ to 4.48 × 10⁵ plates/m had been accomplished within 15 min. The proposed method first illustrated the effect of hydrogen bond between coating material and inner capillary surface on the coating, which should be a new strategy to design and select more effective coating materials to form more stable coatings in CE.     

A Silyliumylidene Cation Stabilized by an Amidinate Ligand and 4‐Dimethylaminopyridine

The synthesis and reactivity of a silyliumylidene cation stabilized by an amidinate ligand and 4‐dimethylaminopyridine (DMAP) are described. The reaction of the amidinate silicon(I) dimer [ L Si:]₂ ( 1 ; L =PhC(NtBu)₂) with one equivalent of N‐trimethylsilyl‐4‐dimethylaminopyridinium triflate [4‐NMe₂C₅H₄NSiMe₃]OTf and two equivalents of DMAP in THF afforded [ L Si(DMAP)]OTf ( 2 ). The ambiphilic character of 2 is demonstrated from its reactivity. Treatment of 2 with 1 in THF afforded the disilylenylsilylium triflate [ L′ ₂( L )Si]OTf ( 3 ; L′ = L Si:) with the displacement of DMAP. The reaction of 2 with [K{HB(iBu)₃}] and elemental sulfur in THF afforded the silylsilylene [ L SiSi(H){(NtBu)₂C(H)Ph}] ( 4 ) and the base‐stabilized silanethionium triflate [ L Si(S)DMAP]OTf ( 5 ), respectively. Compounds 2 , 3 , and 5 have been characterized by X‐ray crystallography.     

Electrochemical‐Reduction‐Assisted Assembly of a Polyoxometalate/Graphene Nanocomposite and Its Enhanced Lithium‐Storage Performance

Herein, we present an electrochemically assisted method for the reduction of graphene oxide (GO) and the assembly of polyoxometalate clusters on the reduced GO (rGO) nanosheets for the preparation of nanocomposites. In this method, the Keggin‐type H₄SiW₁₂O₄₀ (SiW₁₂) is used as an electrocatalyst. During the reduction process, SiW₁₂ transfers the electrons from the electrode to GO, leading to a deep reduction of GO in which the content of oxygen‐containing groups is decreased to around 5 %. Meanwhile, the strong adsorption effect between the SiW₁₂ clusters and rGO nanosheets induces the spontaneous assembly of SiW₁₂ on rGO in a uniformly dispersed state, forming a porous, powder‐type nanocomposite. More importantly, the nanocomposite shows an enhanced capacity of 275 mAh g^?1 as a cathode active material for lithium storage, which is 1.7 times that of the pure SiW₁₂. This enhancement is attributed to the synergistic effect of the conductive rGO support and the well‐dispersed state of the SiW₁₂ clusters, which facilitate the electron transfer and lithium‐ion diffusion, respectively. Considering the facile, mild, and environmentally benign features of this method, it is reasonable as a general route for the incorporation of more types of functional polyoxometalates onto graphene matrices; this may allow the creation of nanocomposites for versatile applications, for example, in the fields of catalysis, electronics, and energy storage.     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

Homoclinic orbits for first order Hamiltonian systems with some twist conditions

In this paper, we study the nonperiodic first-order Hamiltonian system ù = J L(t)u +J H(t, u), where H ∈ C1(R × R2n). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation,we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin.