Graphene layer number dependent size distribution of silver nanoparticles

We observe that silver atoms deposited by thermal evaporation deposition onto n-layer graphene films condense upon annealing to form nanoparticles with an average diameter and density that is determined by the layer numbers of graphene films. The optical microscopy and Raman spectroscopy were utilized to identify the number of the graphene layers and the SEM (scanning electron microscopy) was used to observe the morphologies of the particles. Systematic analysis revealed that the average sizes of the nanoparticles increased with the number of graphene layers. The density of nanoparticles decreased as the number of graphene layers increased, revealing a large variation in the surface diffusion strength of nanoparticles on the different substrates. The mechanisms of formation of these layer-dependent morphologies of silver nanoparticles are related to the surface free energy and surface diffusion of the n-layer graphenes.     

An MRA approach to surface completion and image inpainting

The objective of this paper is to introduce a multi-resolution approximation (MRA) approach to the study of continuous function extensions with emphasis on surface completion and image inpainting. Along the line of the notion of diffusion maps introduced by Coifman and Lafon with some “heat kernels” as integral kernels of these operators in formulating the diffusion maps, we apply the directional derivatives of the heat kernels with respect to the inner normal vectors (on the boundary of the hole to be filled in) as integral kernels of the “propagation” operators. The extension operators defined by propagations followed by the corresponding sequent diffusion processes provide the MRA continuous function extensions to be discussed in this paper. As a case study, Green's functions of some “anisotropic” differential operators are used as heat kernels, and the corresponding extension operators provide a vehicle to transport the surface or image data, along with some mixed derivatives, from the exterior of the hole to recover the missing data in the hole in an MRA fashion, with the propagated mixed derivative data to provide the surface or image “details” in the hole. An error formula in terms of the heat kernels is formulated, and this formula is applied to give the exact order of approximation for the isotropic setting.     

Synthesis of ethyl 6‐aryl‐4‐oxo‐4,6‐dihydro‐1(12)(13)h‐pyrimido‐[2′,1′:4,5][1,3,5]triazino[1,2‐a]benzimidazole‐3‐carboxylates

The synthesis of ethyl 6‐aryl‐4‐oxo‐4,6‐dihdro‐1(12)(13)H‐pyrimido[2′,1′:4,5][1,3,5]triazino[1,2‐a]‐benzimidazole‐3‐carboxylates ( 4a‐p ) was described via pyrimidine ring annulation to 4‐aryl‐3,4‐dihydro[1,3,5]triazino[1,2‐a]benzimidazole‐2‐amines ( 2a‐p ) which were obtained from 2‐guanidinobenzimidazole ( 1 ). Tautomerism in the prepared compounds was investigated using nmr spectroscopy. Compounds 2a‐p were found to be present in dimethyl sulfoxide solution predominantly as 3,4‐dihyhydro tautomeric form. Compounds 4a‐p existed in dynamic equilibrium of 1‐, 12‐ and 13H‐forms. It was found that methylation of 4a‐d led to 13‐methyl substituted derivatives 9a‐d exclusively.     

Homoleptic Platinum(II) and Palladium(II) Organothiolates and Phenylselenolates: Solvothermal Synthesis,Structural Determination,Optical Properties,and Single‐Source Precursors for PdSe and PdS Nanocrystals

Homoleptic d⁸‐metal organothiolates and phenylselenolates [M(EC₆H₅)₂]_∞ (E=S, M=Pt 1 , M=Pd 2 , M=Ni 5 ; E=Se, M=Pt 3 , M=Pd 4 ) were prepared as crystalline solids under solvothermal conditions. Their structures were solved using powder X‐ray diffraction data. In each case, the EC₆H₅ (E=S, Se) ligand binds to two metal ions (M=Pt, Pd, and Ni) to form chain‐like structures with planar (in 1 ) or zig‐zag (in 2 , 3 , 4 , 5 ) conformations. The [M(SR)₂]_∞ complexes (M=Pt, R=4‐tert‐butylphenyl 6 ; R=2‐naphthyl 8 ; R=4‐nitrophenyl 10 and M=Pd, R=4‐tert‐butylphenyl 7 ; R=2‐naphthyl 9 ; R=4‐nitrophenyl 11 ) were prepared under similar solvothermal conditions. Based on the XPS binding energies and elemental analyses, complexes 6 , 7 , 8 , 9 , 10 , 11 have the same [M(SR)₂]_∞ formulation as 1 and 2 . The cyclic complex [Pd₆(SCH₃)₁₂] 12 was prepared as a crystalline solid by solvothermal annealing treatment of the amorphous precipitate. A chain‐like polymer structure is proposed for both [Pd(SC₁₂H₂₅)₂]_∞ 13 and [Pd(SC₁₆H₃₃)₂]_∞ 14 ; these polymeric chains self‐assemble to give layer‐like structures. Solid‐state diffuse reflectance spectra reveal that the optical band gap E_g (eV) of complexes 1 , 6 , 8 , 10 and of 2 , 7 , 9 , 11 are in the range of 2.10–3.00 eV and 2.10–2.63 eV, respectively, and 5 has the lowest E_g value (1.72 eV). Heating solid samples of 4 and 13 under solvothermal conditions afforded phase‐pure Pd₁₇Se₁₅ and PdS nanocrystals, respectively. Field‐effect transistors fabricated with a drop‐cast thin film made from Pd₁₇Se₁₅ nanocrystals prior treated with an ethanolic solution of 1‐hexadecanethiol displayed ambipolar charge transporting properties with hole and electron mobility being 7×10^?2 cm² V^?1 s^?1 and 6×10^?2 cm² V^?1 s^?1, respectively.     

PDE models associated with the bilateral filter

The bilateral filter, introduced in 1998 by Tomasi and Manduchi for feature-preservation image noise-reduction, has recently made significant impacts to other engineering disciplines, particularly to certain research areas in image-based computer graphics. The popularity of this simple filtering approach has even attracted a lot of interest from the imaging sector of the high-tech industry as well. The objective of this paper is to develop the theoretical aspects of this ad hoc filter by deriving the class of nonlinear diffusion partial differential equations (PDE) associated with the bilateral filtering process.     

High-spin structure of yrast-band in 78Kr

Lifetime of levels up to 22⁺, have been measured in ⁷⁸Kr and an oblate shape is assigned to the ground state using the CSM and the configuration dependent shell correction calculations. Calculations further show that ⁷⁸Kr is highly γ-soft nucleus. The experimental Q _t values coupled with theoretical calculations indicate an oblate shape for ⁷⁸Kr at low spins and triaxial shape at higher spins     

On chagnes of signs in infinite series

Доказана теорема. Пус ть {а_n} — последовате льность положительн ых чисел, монотонно стре мящаяся к нулю, причем Σa _n =∞. Тогда найд ется такая последовательность знаковε(п)=±1 (п=1,2, ...), что для каждого натураль ного т и любого целого b с условием 0≦b≦m?1 выполнено равен ство $$\mathop \sum \limits_{n \equiv b(mod m)} \varepsilon (n)a_n = 0$$ . Приведены также неко торые родственные ре зультаты и указаны нерешенные в опросы.