Diophantine approximation with mild divisibility constraints

Given an irrational number α and a sequence B of coprime positive integers with the sum of inverses convergent, we investigate the problem of finding small values of nα, with n B-free.     

Pair correlation of torsion points on elliptic curves

We prove the existence of the pair correlation measure associated to torsion points on the real locus E(R) of an elliptic curve E and provide an explicit formula for the limiting pair correlation function.     

Engineered 3D tissue models for cell-laden microfluidic channels

Delivery of nutrients and oxygen within three-dimensional (3D) tissue constructs is important to maintain cell viability. We built 3D cell-laden hydrogels to validate a new tissue perfusion model that takes into account nutrition consumption. The model system was analyzed by simulating theoretical nutrient diffusion into cell-laden hydrogels. We carried out a parametric study considering different microchannel sizes and inter-channel separation in the hydrogel. We hypothesized that nutrient consumption needs to be taken into account when optimizing the perfusion channel size and separation. We validated the hypothesis by experiments. We fabricated circular microchannels (r = 400 μm) in 3D cell-laden hydrogel constructs (R = 7.5 mm, volume = 5 ml). These channels were positioned either individually or in parallel within hydrogels to increase nutrient and oxygen transport as a way to improve cell viability. We quantified the spatial distribution of viable cells within 3D hydrogel scaffolds without channels and with single- and dual-perfusion microfluidic channels. We investigated quantitatively the cell viability as a function of radial distance from the channels using experimental data and mathematical modeling of diffusion profiles. Our simulations show that a large-channel radius as well as a large channel to channel distance diffuse nutrients farther through a 3D hydrogel. This is important since our results reveal that there is a close correlation between nutrient profiles and cell viability across the hydrogel. Young Seok Song and Richard L. Lin have contributed equally to this contribution     

Magnetic and magnetocaloric results of magnetic field-induced transitions in La1−xCexMn2Si2 (x=0.35 and 0.45) compounds

The La_1−xCe_xMn₂Si₂ compounds (x=0.35 and 0.45) exhibit an antiferromagnetic-ferromagnetic transition caused by the changes in distance between Mn atoms due to temperature changes. A field-induced transition from antiferromagnetic state to ferromagnetic state at a critical field, which decreases with increase in temperature, can also be induced by applying a magnetic field. In this paper our aim is to study the magnetization and magnetocaloric effect, close to transition temperatures. Our subsidiary aim is to examine the temperature dependence of critical field and ferromagnetic fraction of compounds. The variation of magnetocaloric effect with temperature is correlated with the ferromagnetic-antiferromagnetic phase coexistence. Our final aim is to examine the harmony between magnetocaloric effect values calculated both by the Maxwell theory and by the Landau theory.     

Nanoporous structures on ZnO thin films

Porous structures were formed on ZnO thin films which were grown by an electrochemical deposition (ECD) method. The growth processes were carried out in a solution of dimethylsulfoxide (DMSO) zinc perchlorate, Zn(ClO₄)₂, at 120 ^°C on indium tin oxide (ITO) substrates. Optical and structural characterizations of electrochemically grown ZnO thin films have shown that the films possess high (0002) c$c$-axis orientation, high nucleation, high intensity and low FWHM of UV emission at the band edge region and a sharp UV absorption edge. Nanoporous structures were formed via self-assembled monolayers (SAMs) of hexanethiol (C₆SH) and dodecanethiol (C₁₂SH). Scanning electron microscope (SEM) measurements showed that while a nanoporous structure (pore radius 20 nm) is formed on the ZnO thin films by hexanathiol solution, a macroporous structure (pore radius 360 nm) is formed by dodecanethiol solution. No significant variation is observed in X-ray diffraction (XRD) measurements on the ZnO thin films after pore formation. However, photoluminescence (PL) measurements showed that green emission is observed as the dominant emission for the macroporous structures, while no variation is observed for the thin film nanoporous ZnO sample.     

High-pressure X-ray diffraction study of tungsten diselenide

Synchrotron X-ray diffraction was used in conjunction with a diamond anvil cell to investigate the properties of a tungsten diselenide (WSe₂) sample to 35.8 GPa at room temperature. By fitting the pressure-volume data to the third-order Birch-Murnaghan equation of state, the bulk modulus, K_0T, of WSe₂ was determined to be 72±1 GPa with its pressure derivative, , being 4.1±0.1. It was also found that the c-direction of the hexagonal structure is significantly more compressible than the a-direction. No phase transformation was clearly observed in the pressure range of our measurements.     

A new construction of Szász-Mirakyan operators

The paper aims to study a generalization of Szász-Mirakyan-type operators such that their construction depends on a function ρ by using two sequences of functions. To show how the function ρ play a crucial role in the design of the operator, we reconstruct the mentioned operators which preserve exactly two test functions from the set \(\left \{ 1,\rho ,\rho ^{2}\right \}\). We show that these operators provide weighted uniform approximation over unbounded interval. We establish the degree of approximation in terms of a weighted moduli of smoothness associated with the function ρ. Also a Voronovskaya type result is presented. Finally some graphical examples of the mentioned operators are given. Our results show that mentioned operators are sensitive or flexible to point of wive of the rate of convergence to f, depending on our selection of ρ.     

Boron-incorporated Sulfonated polysulfone/polyphosphoric acid electrolytes for supercapacitor application

In the present work, boron-doped multicomponent gel polymer electrolytes composed of host polymer, sulfonated polysulfone (SPSU) and the additives; ionic liquid, 1-ethyl-3-methyl-imidazolium tetrafluoroborate (IL), H₃BO₃, polyphosphoric acid (PPA) were prepared. Fourier transform infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA) techniques were used to characterize the sulfonated polysulfone-based electrolytes. Ion conductivity of these gel electrolytes were studied by dielectric impedance analyzer within the temperature from ?20 to 100°C. The ionic conductivity of the SPSU-5IL-1PPA and SPSU-5IL-1H₃BO₃-1PPA were measured as 4.8 × 10^?3 and 9 × 10^?4 S cm^?1, respectively. Supercapacitor having activated carbon-based composite electrode and electrolyte was constructed with the configuration: Al/C/electrolyte/C/Al. The electrochemical properties and ion transfer characteristics of the supercapacitor were investigated by the cyclic voltammetry (CV). Galvanostatic charge—discharge experiments exhibited good electrochemical reversibility and produced a specific capacitance value of 120 F g^?1 at 1 A g^?1. The symmetric supercapacitor system was retained almost 85% of its initial activity after 1000 cycle.     

Nonvanishing of Fourier coefficients of modular forms

Let be a cusp form with integer weight that is not a linear combination of forms with complex multiplication. For , let

Improving on work of Balog, Ono, and Serre we show that for almost all , where is any good function (e.g. such as ) monotonically tending to infinity with . Using a result of Fouvry and Iwaniec, if is a weight 2 cusp form for an elliptic curve without complex multiplication, then we show for all that . We also obtain conditional results depending on the Generalized Riemann Hypothesis and the Lang-Trotter Conjecture.

     

Simultaneous Preparation of Multiple Polymer Brushes under Ambient Conditions using Microliter Volumes

The fabrication of well‐defined, multifunctional polymer brushes under ambient conditions is described. This facile method uses light‐mediated, metal‐free atom‐transfer radical polymerization (ATRP) to grow polymer brushes with only microliter volumes required. Key to the success of this strategy is the dual action of N‐phenylphenothiazine (PTH) as both an oxygen scavenger and polymerization catalyst. Use of simple glass cover slips results in a high degree of spatial and temporal control and allows for multiple polymer brushes to be grown simultaneously. The preparation of arbitrary 3D patterns and functional/emissive polymer brushes demonstrates the practicality and versatility of this novel strategy.