Spectral heat content for Lévy processes

In this paper we study the spectral heat content for various Lévy processes. We establish the small time asymptotic behavior of the spectral heat content for Lévy processes of bounded variation in , . We also study the spectral heat content for arbitrary open sets of finite Lebesgue measure in with respect to symmetric Lévy processes of unbounded variation under certain conditions on their characteristic exponents. Finally, we establish that the small time asymptotic behavior of the spectral heat content is stable under integrable perturbations to the Lévy measure.     

Switchable control of hydrophilicity and hydrophobicity in conjugated polymer nanoparticles by carbon dioxide

Abstract

We synthesized yellow-emissive, fluorine-based conjugated polymer to fabricate CO₂-responsive conjugated polymer nanoparticles (CPNPs). The CPNPs were functionalized with tertiary amine to have responsiveness to CO₂. The amine-functionalized CPNPs became hydrophilic by CO₂, bubbling because the bubbling led to formation of cationic ammonium ions at the side chains of the hydrophobic CPNPs. This resulted in high dispersion stability in aqueous phase even after vigorous mixing in the presence of organic phase (1-octanol). Subsequent N₂ bubbling was done to remove CO₂ present in water, leading to deprotonation of the side chains of CPNPs. The CPNPs became hydrophobic and moved to the organic phase. The CO₂-responsive property was based on the amine groups in the side chain of polymer that reversibly interacted with bicarbonate ion (HCO₃^-), formed by dissolving CO₂ in water, generating switchable hydrophilicity and hydrophobicity.     

Sharp Estimates on the Green Functions of Perturbations of Subordinate Brownian Motions in Bounded \boldsymbol{\kappa}-Fat Open Sets

In this paper we study perturbations of a large class of subordinate Brownian motions in bounded κ-fat open sets, which include bounded John domains. Suppose that X is such a subordinate Brownian motion and that J is the Lévy density of X. The main result of this paper implies, in particular, that if Y is a symmetric Lévy process with Lévy density J ^Y satisfying |J ^Y (x)???J(x)|?≤?c max {|x|^???d?+?ρ , 1} for some c?>?0,ρ?∈?(0, d), then for any bounded John domain D the Green function $G^Y_D$ of Y in D is comparable to the Green function G _D of X in D. One of the main tools of this paper is the drift transform introduced in Chen and Song (J Funct Anal 201:262–281, 2003). To apply the drift transform, we first establish a generalized 3G theorem for X.     

Effect of thermal annealing sequence on the crystal phase of HfO2 and charge trap property of Al2O3/HfO2/SiO2 stacks

In this study, we investigated the effect of a post annealing sequence on the HfO₂ crystal phase and the memory window of charge trap devices with TiN-Al₂O₃-HfO₂-SiO₂-Si stacks. The charge trap dielectrics of HfO₂ were deposited by atomic layer deposition and were annealed in an oxygen environment with or without Al₂O₃ blocking oxides. X-ray diffraction analysis showed that, after thermal annealing, the predominant crystal phase of HfO₂ is divided into tetragonal and monoclinic phase depending on the presence or absence of Al₂O₃ blocking oxide. In addition, deconvolution of X-ray diffraction spectra showed that, with increasing annealing temperature, the fraction of the tetragonal phase in the HfO₂ film was enhanced with the Al₂O₃ blocking oxide, while it was reduced without the Al₂O₃ blocking oxide. Finally, measurements of program/erase and increase-step-pulse programming showed that the charge trap efficiency and the memory window of the charge trap devices increased with decreasing fraction of tetragonal HfO₂.     

Contact area lithography and pattern transfer of self-assembled organic monolayers on SiO2/Si substrates

We describe a procedure for one-step patterning and transfer of self-assembled organic monolayers (SAMs) on SiO(2)/Si substrates. This procedure was inspired from an idea of pattern formation at contact area, which realizes high patterning fidelity, and enables a universal approach for the micro/nanometre scale patterning of SAMs.     

Enhanced bipolar resistive switching of HfO2 with a Ti interlayer

The characteristics of resistive switching of TiN/HfO₂/Ti/HfO₂/Pt/Ti stacks on SiO₂/Si substrates were investigated and compared to TiN/HfO₂/Pt/Ti stacks in order to study Ti interlayer effects on resistive switching. The Ti interlayers were deposited in situ during the reactive sputtering of HfO₂ films. The current–voltage measurements showed that the Ti interlayers enhanced the memory window but reduced the endurance of SET/RESET operations. The energy filtered images by TEM showed asymmetric oxygen accumulation at the Ti/HfO _x interfaces. Subsequent heat treatment improved the endurance of SET/RESET operation of TiN/HfO₂/Ti/HfO₂/Pt/Ti stacks.     

Spectral heat content on a class of fractal sets for subordinate killed Brownian motions

We study the spectral heat content for a class of open sets with fractal boundaries determined by similitudes in ${\mathbb{R}}^d$, $d\ge 1$, with respect to subordinate killed Brownian motions via $\alpha /2$-stable subordinators and establish the asymptotic behavior of the spectral heat content as $t\to 0$ for the full range of $\alpha \in (0,2)$. Our main theorems show that these asymptotic behaviors depend on whether the sequence of logarithms of the coefficients of the similitudes is arithmetic when $\alpha \in [d-\mathfrak{b},2)$, where $\mathfrak{b}$ is the interior Minkowski dimension of the boundary of the open set. The main tools for proving the theorems are the previous results on the spectral heat content for Brownian motions and the renewal theorem.