Atomic force microscopy investigation of surface roughness generated between SiO2 micro-pits in CHF3/Ar plasma

The present paper investigates the surface roughness generated by reactive ion etching (RIE) on the location between silicon dioxide (SiO₂) micro-pits structures. The micro-pit pattern on polymethyl methacrylate (PMMA) mask was created by an electron beam lithography tool. By using PMMA as a polymer resist mask layer for pattern transfer in RIE process, the carbon (C) content in etching process is increased, which leads to decrease of F/C ratio and causes domination of polymerization reactions. This leads to high surface roughness via self-organized nanostructure features generated on SiO₂ surface which was analyzed using atomic force microscopy (AFM) technique. The etching chemistry of CHF₃ plasma on PMMA masking layer and SiO₂ is analyzed to explain the polymerization. The surface root-mean-square (RMS) roughness below 1 nm was achieved by decreasing the RF power to 150 W and process pressure lower than 10 mTorr.     

Selective surface chemistry of allyl alcohol and allyl aldehyde on Si(1 0 0)2×1: Competition of [2 + 2] CC cycloaddition with O-H dissociation and with [2 + 2] CO cycloaddition in bifunctional molecules

Competition between the CC functional group with the OH group in allyl alcohol and with the CO group in allyl aldehyde in the adsorption and thermal chemistry on Si(1 0 0)2×1 has been studied by X-ray photoelectron spectroscopy (XPS) and temperature-programmed desorption (TPD), as well as density-functional theory (DFT) calculations. The similarities found in the C 1s and O 1s spectra for both molecules indicate that the O-H dissociation product for allyl alcohol and [2 + 2] CO cycloaddition product for allyl aldehyde are preferred over the corresponding [2 + 2] CC cycloaddition products. Temperature-dependent XPS and TPD studies further show that thermal evolution of these molecules gives rise to the formation of ethylene, acetylene, and propene on Si(1 0 0)2×1, with additional CO evolution only from allyl alcohol. The formation of these desorption products also supports that the [2 + 2] CC cycloaddition reaction does not occur. In addition, the formation of SiC at 1090 K is observed for both allyl alcohol and allyl aldehyde. We propose plausible surface-mediated reaction pathways for the formation of these thermal evolution products. The present work illustrates the crucial role of the Si(1 0 0)2×1 surface in selective reactions of the Si dimers with the O−H group in allyl alcohol and with the CO group in allyl aldehyde over the CC functional group common to both molecules.     

On the global convergence rate of the gradient descent method for functions with Hölder continuous gradients

The gradient descent method minimizes an unconstrained nonlinear optimization problem with \({\mathcal {O}}(1/\sqrt{K})\), where K is the number of iterations performed by the gradient method. Traditionally, this analysis is obtained for smooth objective functions having Lipschitz continuous gradients. This paper aims to consider a more general class of nonlinear programming problems in which functions have Hölder continuous gradients. More precisely, for any function f in this class, denoted by \({{\mathcal {C}}}^{1,\nu }_L\), there is a \(\nu \in (0,1]\) and \(L>0\) such that for all \(\mathbf{x,y}\in {{\mathbb {R}}}^n\) the relation \(\Vert \nabla f(\mathbf{x})-\nabla f(\mathbf{y})\Vert \le L \Vert \mathbf{x}-\mathbf{y}\Vert ^{\nu }\) holds. We prove that the gradient descent method converges globally to a stationary point and exhibits a convergence rate of \({\mathcal {O}}(1/K^{\frac{\nu }{\nu +1}})\) when the step-size is chosen properly, i.e., less than \([\frac{\nu +1}{L}]^{\frac{1}{\nu }}\Vert \nabla f(\mathbf{x}_k)\Vert ^{\frac{1}{\nu }-1}\). Moreover, the algorithm employs \({\mathcal {O}}(1/\epsilon ^{\frac{1}{\nu }+1})\) number of calls to an oracle to find \({\bar{\mathbf{x}}}\) such that \(\Vert \nabla f({{\bar{\mathbf{x}}}})\Vert <\epsilon \).     

On the Stability of a k-Cubic Functional Equation in Intuitionistic Fuzzy n-Normed Spaces

In this paper, we investigate some stability results concerning the k-cubic functional equation f(kx + y) + f(kx?y) = kf(x + y) + kf(x?y) + 2k(k²?1)f(x) in the intuitionistic fuzzy n-normed spaces.     

Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

Let ${(R, \mathfrak{m})}$ be a commutative Noetherian local ring of Krull dimension d, and let C be a semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing module if and only if the top local cohomology module of ${R, H _{\mathfrak{m}} ^{d} (R)}$ , has finite G _C -injective dimension. This generalizes a recent result due to Yoshizawa, where the ring is assumed to be complete Cohen-Macaulay.     

Bregman operator splitting with variable stepsize for total variation image reconstruction

This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form $\min\{\phi(Bu) +1/2\|Au-f\|_{2}^{2}\}$ , where ? may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a line search to achieve better efficiency. These schemes are applicable to total variation (TV)-based image reconstruction. The stepsize rule starts with a Barzilai-Borwein (BB) step, and increases the nominal step until a termination condition is satisfied. The stepsize rule is related to the scheme used in SpaRSA (Sparse Reconstruction by Separable Approximation). Global convergence of the proposed BOSVS algorithm to a solution of the optimization problem is established. BOSVS is compared with other operator splitting schemes using partially parallel magnetic resonance image reconstruction problems. The experimental results indicate that the proposed BOSVS algorithm is more efficient than the BOS algorithm and another split Bregman Barzilai-Borwein algorithm known as SBB.     

A hyperbranched polyamidoamine dendrimer grafted onto magnetized graphene oxide as a sorbent for the extraction of synthetic dyes from foodstuff

Microchimica Acta - Graphene oxide nanosheets were modified with magnetite nanoparticles, and a hyperbranched polyamidoamine dendrimer was then covalently attached to their surface. The resulting...     

Mizoroki–Heck and Suzuki–Miyaura reactions mediated by poly(2‐acrylamido‐2‐methyl‐1‐propanesulfonic acid)‐stabilized magnetically separable palladium catalyst

The purpose of this work was to synthesize and characterize a new magnetic polymer nanosphere‐supported palladium(II) acetate catalyst for reactions requiring harsh conditions. In this regard, an air‐stable, moisture‐stable and highly efficient heterogenized palladium was synthesized by the coordination of palladium(II) acetate with poly(2‐acrylamido‐2‐methyl‐1‐propanesulfonic acid)‐grafted modified magnetic nanoparticles with a core–shell structure. The structure of the newly developed catalyst was characterized using various techniques. The catalytic activity of the resultant nano‐organometallic catalyst was evaluated in Mizoroki–Heck and Suzuki–Miyaura reactions to afford the corresponding coupling products in good to excellent yields. High selectivity as well as outstanding turnover number (14 143, 4900) and turnover frequency (28 296, 7424) values were recorded for the catalyst in Suzuki–Miyaura and Mizoroki–Heck reactions, respectively. Magnetic separation and recycling of the catalyst for at least six runs became possible without any significant loss of efficiency or any detectable palladium leaching.     

Palladium nanoparticles immobilized on sepiolite–cyclodextrin nanosponge hybrid: Efficient heterogeneous catalyst for ligand‐ and copper‐free C─C coupling reactions

A novel hybrid system composed of sepiolite clay and cyclodextrin nanosponge (CDNS) was prepared via reaction of Cl‐functionalized sepiolite with amine‐functionalized CDNS. CDNS–sepiolite was then applied for immobilization of Pd(0) nanoparticles. The resulting hybrid system, Pd@CDNS‐sepiolite, was characterized using various techniques and successfully used as an efficient and heterogeneous catalyst for ligand‐ and copper‐free Sonogashira and Heck coupling reactions under mild reaction conditions. Recycling experiments confirmed that Pd@CDNS‐sepiolite was recyclable and could be used for several consecutive reaction runs with slight Pd leaching and loss of catalytic activity.