Micro-patterning of vapor-phase polymerized poly(3,4-ethylenedioxythiophene) (PEDOT) using ink-jet printing/soft lithography

Highly conductive and transparent poly(3,4-ethylenedioxythiophene) (PEDOT) thin films can be prepared effectively via vapor-phase polymerization (VPP) with the addition of imidazole (Im) based derivatives. The addition of Im that has one and/or two alkyl substituents significantly improved the electrical conductivity of PEDOT thin films. In an effort to develop a facile PEDOT micro-patterning method, we investigated ink-jet printing and soft lithography. The procedure of oxidant patterning with a weak base followed by VPP of a 3,4-ethylenedioxythiophene (EDOT) monomer provides an effective and simple method for micro-patterning of an intrinsic conductive polymer (ICP).     

Peptide-induced patterning of gold nanoparticle thin films

In this work, the use of patterned proteins and peptides for the deposition of gold nanoparticles on several substrates with different surface chemistries is presented. The patterned biomolecule on the surface acts as a catalyst to precipitate gold nanoparticles from a precursor solution of HAuCl₄ onto the substrate. The peptide patterning on the surfaces was accomplished by physical adsorption or covalent attachment. It was shown that by using covalent attachment with a linker molecule, the influence of the surface properties from the different substrates on the biomolecule adsorption and subsequent nanoparticle deposition could be avoided. By adjusting the reaction conditions such as pH or HAuCl₄ concentration, the sizes and morphologies of deposited gold nanoparticle agglomerates could be controlled. Two biomolecules were used for this experiment, 3XFLAG peptide and bovine serum albumin (BSA). A micro-transfer molding technique was used to pattern the peptides on the substrates, in which a pre-patterned poly(dimethylsiloxane) (PDMS) mold was used to deposit a lift-off pattern of polypropylmethacrylate (PPMA) on the various substrates. The proteins were either physically adsorbed or covalently attached to the substrates, and an aqueous HAuCl₄ solution was applied on the substrates with the protein micropatterns, causing the precipitation of gold nanoparticles onto the patterns. SEM, AFM, and Electron Beam Induced Current (EBIC) were used for characterization.     

Comparing and ranking fuzzy numbers using ideal solutions

This paper presents a new approach for comparing and ranking fuzzy numbers in a simple manner in decision making under uncertainty. The concept of ideal solutions is sensibly used, and a distance-based similarity measure between fuzzy numbers is appropriately adopted for effectively determining the overall performance of each fuzzy number in comparing and ranking fuzzy numbers. As a result, all the available information characterizing a fuzzy number is fully utilized, and both the absolute position and the relative position of fuzzy numbers are adequately considered, resulted in consistent rankings being produced in comparing and ranking fuzzy numbers. The approach is computationally simple and its underlying concepts are logically sound and comprehensible. A comparative study is conducted on the benchmark cases in the literature that shows the proposed approach compares favorably with other approaches examined.     

A converse of Loewner–Heinz inequality and applications to operator means

Let f(t)$f(t)$ be an operator monotone function. Then A?B$A?B$ implies f(A)?f(B)$f(A)?f(B)$, but the converse implication is not true. Let A?B$A?B$ be the geometric mean of A,B?0$A,B?0$. If A?B$A?B$, then B⁻¹?A?I$B^{-1}?A?I$; the converse implication is not true either. We will show that if f(λB+I)⁻¹?f(λA+I)?I$f{(\lambda B+I)}^{-1}?f(\lambda A+I)?I$ for all sufficiently small λ>0$\lambda >0$, then f(λA+I)?f(λB+I)$f(\lambda A+I)?f(\lambda B+I)$ and A?B$A?B$. Moreover, we extend it to multi-variable matrices means.     

On Young and Heinz inequalities for τ-measurable operators

The purpose of this article is to prove Young and Heinz inequalities for τ-measurable operators.     

Multiple positive solutions for Robin problem involving critical weighted Hardy–Sobolev exponents with boundary singularities

This paper deals with the existence of positive solutions for Robin elliptic problems involving critical weighted Hardy–Sobolev exponents with boundary singularities. Using the Caffarelli–Kohn–Nirenberg inequalities and variational methods, we prove the existence and multiplicity of positive solutions.     

Positivity of Toeplitz operators via Berezin transform

In this paper, we study positive Toeplitz operators on the Bergman space via their Berezin transforms. Surprisingly we show that the positivity of a Toeplitz operator on the Bergman space is not completely determined by the positivity of the Berezin transform of its symbol. In fact, we show that even if the minimal value of the Berezin transform of a quadratic polynomial of |z|$|z|$ on the unit disk is positive, the Toeplitz operator with the function as the symbol may not be positive.     

A sufficient condition for the existence of a principal eigenvalue for nonlocal diffusion equations with applications

Considerable work has gone into studying the properties of nonlocal diffusion equations. The existence of a principal eigenvalue has been a significant portion of this work. While there are good results for the existence of a principal eigenvalue equations on a bounded domain, few results exist for unbounded domains. On bounded domains, the Krein–Rutman theorem on Banach spaces is a common tool for showing existence. This article shows that generalized Krein–Rutman can be used on unbounded domains and that the theory of positive operators can serve as a powerful tool in the analysis of nonlocal diffusion equations. In particular, a useful sufficient condition for the existence of a principal eigenvalue is given.