New Applications of the <Emphasis Type="Italic">p</Emphasis>-Adic Nevanlinna Theory

Let IK be an algebraically closed field of characteristic 0 complete for an ultrametric absolute value. Following results obtained in complex analysis, here we examine problems of uniqueness for meromorphic functions having finitely many poles, sharing points or a pair of sets (C.M. or I.M.) defined either in the whole field IK or in an open disk, or in the complement of an open disk. Following previous works in C, we consider functions fⁿ(x)f^m(ax + b), gⁿ(x)g^m(ax + b) with |a| = 1 and n ≠ m, sharing a rational function and we show that f/g is a n + m-th root of 1 whenever n + m ≥ 5. Next, given a small function w, if n, m ∈ IN are such that |n ? m|_∞ ≥ 5, then fⁿ(x)f^m(ax + b) ? w has infinitely many zeros. Finally, we examine branched values for meromorphic functions fⁿ(x)f^m(ax + b).     

Optimal stopping of strong Markov processes

We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings for Lévy processes obtained essentially via the Wiener–Hopf factorization. The main ingredient in our approach is the representation of the β$\beta$-excessive functions as expected suprema. A variety of examples is given.     

Magnetooptical force in the resonance field formed by elliptically polarized light waves

The screening of the Coulomb interaction is studied with regard to Friedel oscillations in multicomponent electron plasma structure. A double quantum well (QW) and a superlattice are considered. The groundstate energy of a donor (exciton) in a double quantum well is calculated by a variational method as a function of the population of subbands.     

Large‐Area Synthesis of Superclean Graphene via Selective Etching of Amorphous Carbon with Carbon Dioxide

Contamination commonly observed on the graphene surface is detrimental to its excellent properties and strongly hinders its application. It is still a great challenge to produce large‐area clean graphene film in a low‐cost manner. Herein, we demonstrate a facile and scalable chemical vapor deposition approach to synthesize meter‐sized samples of superclean graphene with an average cleanness of 99 %, relying on the weak oxidizing ability of CO₂ to etch away the intrinsic contamination, i.e., amorphous carbon. Remarkably, the elimination of amorphous carbon enables a significant reduction of polymer residues in the transfer of graphene films and the fabrication of graphene‐based devices and promises strongly enhanced electrical and optical properties of graphene. The facile synthesis of large‐area superclean graphene would open the pathway for both fundamental research and industrial applications of graphene, where a clean surface is highly needed.     

Linear dichroism in resonant inelastic x-ray scattering to molecular spin-orbit states

Polarization-dependent resonant inelastic x-ray scattering (RIXS) is shown to be a new probe of molecular-field effects on the electronic structure of isolated molecules. A combined experimental and theoretical analysis explains the linear dichroism observed in Cl 2p RIXS following Cl 1s excitation in HCl and CF3Cl as due to molecular-field effects, including singlet-triplet exchange, indicating polarized-RIXS provides a direct probe of spin-orbit-state populations applicable to any molecule.     

Exact Solutions of Klein-Gordon Equation with Exponential Scalar and Vector Potentials

We obtain the exact analytical solution of the Klein-Gordon equation for the exponential vector and scalar potentials by using the asymptotic iteration method. For the scalar potential greater than the vector potential case, the exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunction solutions are obtained in terms of the confluent hypergeometric functions.     

Optimization in a Nonlinear Lanchester-Type Model Involving Supply Units $$^* $$

Journal of Applied and Industrial Mathematics - In this paper, we introduce a nonlinear Lanchester-type model involving supply units. The model describes a battle where the Blue party consisting of...     

The β‐Agostic Structure in (C5Me5)2Sc(CH2CH3): Solid‐State NMR Studies of (C5Me5)2Sc−R (R=Me,Ph, Et)

Multinuclear solid‐state NMR studies of Cp*₂Sc?R (Cp*=pentamethylcyclopentadienyl; R=Me, Ph, Et) and DFT calculations show that the Sc?Et complex contains a β‐CH agostic interaction. The static central transition ⁴⁵Sc NMR spectra show that the quadrupolar coupling constants (C_q) follow the trend of Ph≈Me>Et, indicating that the Sc?R bond is different in Cp*₂Sc?Et compared to the methyl and phenyl complexes. Analysis of the chemical shift tensor (CST) shows that the deshielding experienced by Cβ in Sc?CH₂CH₃ is related to coupling between the filled σ_C‐C orbital and the vacant orbital.     

Photopolymerized injectable RGD-modified fumarated poly(ethylene glycol) diglycidyl ether hydrogels for cell growth

In this study, photopolymerized hydrogels of fumarated poly(ethylene glycol) diglycidyl-co- poly(ethylene glycol) diacrylate have been synthesized and modified with cell adhesion peptide, Arg-Gly-Asp (RGD). The structural and mechanical properties of the hydrogels are found to be poly(ethylene glycol) diacrylate (PEGDA) dependent. The percentage of gelation is increased from 72 to 89 wt.-% when the amount of the crosslinker co-monomer (PEGDA) in the hydrogel formulation is increased from 20 to 40 wt.-%. In the present case, the equilibrium mass swelling is decreased from 216 to 93%. The viscosities of the uncured formulations have also been measured and likewise, the results were influenced by the increasing amount of PEGDA that reduced the value from 83 to 36 cP. The compressive modulus of the prepared hydrogels was improved with the addition of the PEGDA. Cell growth experiments have been performed by comparing the properties of the hydrogels with and without RGD units. The results show that RGD units enhance the adhesion of cells to the surface of the hydrogels. SEM-EDS studies reveal that nitrogen and calcium are produced on the osteoblast-seeded surface of the scaffold within the culture time period. [Figure: see text].     

Asymmetric dehydration of β-hydroxy esters and application to the syntheses of flavane derivatives

Catalytic asymmetric dehydration of β-aryl or alkyl substituted β-hydroxy esters via kinetic resolution has been investigated. A brief survey of 10 different chiral ligands is conducted to examine the effects of chiral ligand structure on selectivity of the dehydration. The kinetic resolution of a variety of rac-β-hydroxy tert-butyl esters in the presence of prolinol chiral ligand 2 and BrZnCH₂CO₂-t-Bu can provide highly enantioenriched β-hydroxy esters 14-21 with selectivity factors ranging from 11 to 66. Also, application of this asymmetric synthetic methodology to the preparation of enantioenriched flavane derivatives 25-29 is demonstrated.