Random walks with different directions

As an extension of Polya’s classical result on random walks on the square grids (\({\mathbf {Z}}^d\)), we consider a random walk where the steps, while still have unit length, point to different directions. We show that in dimensions at least 4, the returning probability after n steps is at most \(n^{-d/2 - d/(d-2) +o(1) }\), which is sharp. The real surprise is in dimensions 2 and 3. In dimension 2, where the traditional grid walk is recurrent, our upper bound is \(n^{-\omega (1) }\), which is much worse than in higher dimensions. In dimension 3, we prove an upper bound of order \(n^{-4 +o(1) }\). We find a new conjecture concerning incidences between spheres and points in \({\mathbf {R}}^3\), which, if holds, would improve the bound to \(n^{-9/2 +o(1) }\), which is consistent to the \(d \ge 4\) case. This conjecture resembles Szemerédi-Trotter type results and is of independent interest.     

The consensus string problem for a metric is NP-complete

Given a set S of strings, a consensus string of S based on consensus error is a string w that minimizes the sum of the distances between w and all the strings in S. In this paper, we show that the problem of finding a consensus string based on consensus error is NP-complete when the penalty matrix is a metric.     

Scanning transmission X‐ray microscopy probe for in situ mechanism study of graphene‐oxide‐based resistive random access memory

Here, an in situ probe for scanning transmission X‐ray microscopy (STXM) has been developed and applied to the study of the bipolar resistive switching (BRS) mechanism in an Al/graphene oxide (GO)/Al resistive random access memory (RRAM) device. To perform in situ STXM studies at the C K‐ and O K‐edges, both the RRAM junctions and the I₀ junction were fabricated on a single Si₃N₄ membrane to obtain local XANES spectra at these absorption edges with more delicate I₀ normalization. Using this probe combined with the synchrotron‐based STXM technique, it was possible to observe unique chemical changes involved in the BRS process of the Al/GO/Al RRAM device. Reversible oxidation and reduction of GO induced by the externally applied bias voltages were observed at the O K‐edge XANES feature located at 538.2 eV, which strongly supported the oxygen ion drift model that was recently proposed from ex situ transmission electron microscope studies.     

The hub covering flow problem

The hub covering flow problem (HCFP) seeks to find the minimal cost hub-and-spoke network by optimally locating hub nodes and assigning non-hub nodes to the hub nodes subject to a coverage constraint. The cost of establishing such a hub network is based on a fixed cost of opening hubs and the cost of transporting demand flow through the network. We also present an extension called the multi-aircraft HCFP. The results from computational experiments are presented and discussed.     

Laser-driven high-resolution patterning of indium tin oxide thin film for electronic device

We here introduce a laser-driven process to pattern transparent thin films on transparent substrates. This method utilizes a pre-patterned metal film as the dynamic release layer and the transparent thin film is selectively removed by a thermo-elastic force laser-induced in the underlying metal layer. High-fidelity indium tin oxide (ITO) thin film patterns were fabricated on plastic and glass substrates using a pulsed Nd:YAG laser. Tens of square centimeters could be patterned with several pulse shots. We fabricated a pentacene thin film transistor with ITO source and drain electrodes and observed a very low off-current level. This tells that the channel area between ITO electrodes was completely etched out by this laser-driven process. Combined with the absence of photoresist and chemical etching steps, this method provides a simple high-resolution route to pattern transparent thin films over large areas at low temperatures.     

Understanding the junction degradation mechanism in CdS/CdTe solar cells using a Cd-deficient CdTe layer

It is known that CdTe solar cells are often degraded under solar illumination. But the degradation mechanism is not fully proved because it does not appear consistently. The junction degradation in CdS/CdTe solar cells was investigated using a CdTe layer with Cd deficient composition, where Cd vacancy concentration is high. It was found that the Cu atoms easily filled the Cd vacancies in CdTe and transport to junction area from Cu back contact. PL measurement and spectral quantum efficiency measurement showed that the incorporation of Cu atoms in CdS forms a defect energy level at 1.55 eV below the conduction band in CdS. As a result, the junction built-in potential is decreased and light penetration into CdTe absorber is shielded. For reliable and stable CdTe cells, the formation of Cd vacancy in CdTe should be avoided by careful control of CdTe.     

Magnetic nanofibers with core (Fe3O4 nanoparticle suspension)/sheath (poly ethylene terephthalate) structure fabricated by coaxial electrospinning

One-dimensional magnetic nanostructures have recently attracted much attention because of their intriguing properties that are not realized by their bulk or particle form. These nanostructures are potentially useful for the application to ultrahigh-density data storages, sensors and bulletproof vest. The magnetic particles in magnetic nanofibers of blend types cannot fully align along the external magnetic field because magnetic particles are arrested in solid polymer matrix. To improve the mobility of magnetic particles, we used magneto-rheological fluid (MRF), which has the good mobility and dispersibility. Superparamagnetic core/sheath composite nanofibers were obtained with MRF and poly (ethylene terephthalate) (PET) solution via a coaxial electrospinning technique. Coaxial electrospinning is suited for fabricating core/sheath nanofibers encapsulating MRF materials within a polymer sheath. The magnetic nanoparticles in MRF were dispersed within core part of the nanofibers. The core/sheath magnetic composite nanofibers exhibited superparamagnetic behavior at room temperature and the magnetic nanoparticles in MRF well responded to an applied magnetic field. Also, the mechanical properties of the nanofiber were improved in the magnetic field. This study aimed to fabricate core/sheath magnetic composite nanofibers using coaxial electrospinning and characterize the magnetic as well as mechanical properties of composite nanofibers.     

An unexpected Pummerer rearrangement in the synthetic route to ethyl (2′-hydroxy-4′,5′-methylenedioxyphenyl)acetate: An alternative approach to 2,3-dimethylthio benzofurans

The synthesis of ethyl (2′-hydroxy-4′,5′-methylendioxophenyl)acetate, a fragment of the antihyperglycemic natural coumarin subcoriacin, is reported. We found an expeditious route to the title compound in five steps. Final metal catalyzed acid ethanolysis of the vinylic 1,1-methylthio methylsulfoxide derivative afforded the required aryl acetic ester, but in the absence of metal catalyst, an unexpected Pummerer rearrangement produced the 2,3-dimethylthiofuran derivative as the major product. This last result provides an alternative entry to 2,3-dimethlythiobenzofurans.     

MAO‐free and extremely active catalytic system for ethylene tetramerization

The original Sasol catalytic system for ethylene tetramerization is composed of a Cr source, a PNP ligand, and MAO (methylaluminoxane). The use of expensive MAO in excess has been a critical concern in commercial operation. Many efforts have been made to replace MAO with non‐coordinating anions (e.g., [B(C₆F₅)₄]^?); however, most of such attempts were unsuccessful. Herein, an extremely active catalytic system that avoids the use of MAO is presented. The successive addition of two equivalent [H(OEt₂)₂]⁺[B(C₆F₅)₄]^? and one equivalent CrCl₃(THF)₃ to (acac)AlEt₂ and subsequent treatment with a PNP ligand [CH₃(CH₂)₁₆]₂C(H)N(PPh₂)₂ ( 1 ) yielded a complex presumably formulated as [ 1 ‐CrAl (acac)Cl₃(THF)]²⁺[B(C₆F₅)₄]^?₂, which exhibited high activity when combined with iBu₃Al (1120 kg/g‐Cr/h; ~4 times that of the original Sasol system composed of Cr (acac)₃, iPrN(PPh₂)₂, and MAO). Via the introduction of bulky trialkylsilyl substituents such as –SiMe₃, –Si(nBu)₃, or –SiMe₂(CH₂)₇CH₃ at the para‐position of phenyl groups in 1 (i.e., by using [CH₃(CH₂)₁₆]₂C(H)N[P(C₆H₄‐p‐SiR₃)₂]₂ instead of 1 ), the activities were dramatically improved, i.e., tripled (2960–3340 kg/g‐Cr/h; more than 10 times that of the original Sasol system). The generation of significantly less PE (<0.2 wt%) even at a high temperature is another advantage achieved by the introduction of bulky trialkylsilyl substituents. NMR studies and DFT calculations suggest that increase of the steric bulkiness on the alkyl‐N and P‐aryl moieties restrict the free rotation around (alkyl)N–P (aryl) bonds, which may cause the generation of more robust active species in higher proportion, leading to extremely high activity along with the generation of a smaller amount of PE.