The fourth power mean of the general 2-dimensional Kloostermann sums mod <Emphasis Type="Italic">p</Emphasis>

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it.     

A Near-Infrared Dye That Undergoes Multiple Interconversions through Acid–Base Equilibrium and Reversible Redox Processes

A near-infrared (NIR) polymethine dye ( 1 ), consisting of a cyclohepta[1,2-b;4,3-b′]dithiophene and two phenol moieties, was synthesized. This dye exhibited pH-responsive changes in its photophysical properties due to a two-step acid–base equilibrium that produced a protonated cation ( 1H⁺ ) and an anion ( 1⁻ ). While 1H⁺ showed an intense fluorescence in the red region of the visible spectrum, 1⁻ exhibited a strong absorption in the NIR region. The tropylium ion character in 1H⁺ induces high pK_a1 and pK_a2 values for 1 . Moreover, a stable radical ( 1^. ) was prepared, which showed a NIR absorption band with a maximum at circa 1600 nm. The cyclic voltammogram of 1^. revealed a two-step reversible redox process that produced 1⁻ and the cation 1⁺ , which is different from 1H⁺ . These redox processes accompany drastic electrochromic changes in the vis–NIR region. Overall, 1 is susceptible to multiple interconversions between five forms, due to the multifaceted character of the cycloheptadithiophene skeleton.     

Evidence of Structure Sensitivity in the Fischer–Tropsch Reaction on Model Cobalt Nanoparticles by Time-Resolved Chemical Transient Kinetics

The Fischer–Tropsch process, or the catalytic hydrogenation of carbon monoxide (CO), produces long chain hydrocarbons and offers an alternative to the use of crude oil for chemical feedstocks. The observed size dependence of cobalt (Co) catalysts for the Fischer–Tropsch reaction was studied with colloidally prepared Co nanoparticles and a chemical transient kinetics reactor capable of measurements under non-steady-state conditions. Co nanoparticles of 4.3 nm and 9.5 nm diameters were synthesized and tested under atmospheric pressure conditions and H₂/CO=2. Large differences in carbon coverage (Θ_C) were observed for the two catalysts: the 4.3 nm Co catalyst has a Θ_C less than one while the 9.5 nm Co catalyst supports a Θ_C greater than two. The monomer units present on the surface during reaction are identified as single carbon species for both sizes of Co nanoparticles, and the major CO dissociation site is identified as the B₅-B geometry. The difference in activity of Co nanoparticles was found to be a result of the structure sensitivity caused by the loss of these specific types of sites at smaller nanoparticle sizes.     

A Metal–Organic Compound as Cathode Material with Superhigh Capacity Achieved by Reversible Cationic and Anionic Redox Chemistry for High-Energy Sodium-Ion Batteries

Although sodium-ion batteries (SIBs) are considered as alternatives to lithium-ion batteries (LIBs), the electrochemical performances, in particular the energy density, are much lower than LIBs. A metal–organic compound, cuprous 7,7,8,8-tetracyanoquinodimethane (CuTCNQ), is presented as a new kind of cathode material for SIBs. It consists of both cationic (Cu^II↔Cu^I) and anionic (TCNQ⁰↔TCNQ⁻↔ TCNQ²⁻) reversible redox reactions, delivering a discharge capacity as high as 255 mAh g⁻¹ at a current density of 20 mA g⁻¹. The synergistic effect of both redox-active metal cations and organic anions brings an electrochemical transfer of multiple electrons. The transformation of cupric ions to cuprous ions occurs at near 3.80 V vs. Na⁺/Na, while the full reduction of TCNQ⁰ to TCNQ⁻ happens at 3.00–3.30 V. The remarkably high voltage is attributed to the strong inductive effect of the four cyano groups.     

Host (dealuminated Y zeolite)–guest (zirconium tetraphenylporphyrin) nanocomposite materials. An efficient catalyst in the oximation of aldehydes

In this research, zirconium tetraphenylporphyrin encapsulated into dealuminated Y zeolite (ZrTPP–DAZY) was prepared through a template synthesis method. This heterogeneous catalyst was characterized by XRD, FT-IR, DRS, UV–Vis, EDX and FESEM techniques. The amount of ZrTPP in the nanocage of dealuminated Y zeolite was estimated to be 0.0156 g/g of support. This catalytic system was employed for an efficient oximation of aldehydes under magnetic stirring conditions at room temperature and the corresponding products were obtained in 50–90% yields. This catalytic system also indicated good shape selectivity towards linear aldehydes. ZrTPP–DAZY was reused several times without any significant loss in catalytic activity.     

Photoinduced electron transfer in a triarylamine-organoboron-Ru(2,2′-bipyridine)32+ compound

Long-range electron transfer reactions play a key role in biological photosynthesis, and they are likely to play an important role for future artificial photosynthetic endeavors as well. The possibility to control the rates for long-range electron transfer with external stimuli is of particular interest in this context. In the work presented herein, we explored a donor–bridge–acceptor compound in which intramolecular electron transfer from a triarylamine donor to a photoexcited Ru(bpy)₃²⁺ (bpy = 2,2′-bipyridine) acceptor occurs across an organoboron bridge over a distance of approximately 22 Å. Fluoride has a high binding affinity to the organoboron bridge in apolar solutions, and the resulting organofluoroborate has a significantly different electronic structure. We explored to what extent the change from an electron-deficient organoboron wire to an electron-rich organofluoroborate bridge affects long-range electron transfer between the distant triarylamine donor and the Ru(bpy)₃²⁺ acceptor.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

Study on convergence and error of a numerical method for solving systems of nonlinear Fredholm–Volterra integral equations of Hammerstein type

The aim of this paper is to present an efficient analytical and numerical procedure for solving systems of nonlinear Fredholm–Volterra integral equations of the Hammerstein type with the aid of fixed point techniques and the usual Schauder basis in an adequate Banach space.     

Polarization tensors of planar domains as functions of the admittivity contrast

(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support of the inhomogeneities and on their admittivity contrast. Corresponding asymptotic formulas are of particular interest in the design of reconstruction algorithms for determining the locations and the material properties of inhomogeneities inside a body from measurements of current flows and associated voltage potentials on the body’s surface. In this work, we consider the two-dimensional case only and provide an analytic representation of the polarization tensor in terms of spectral properties of the double layer integral operator associated with the support of simply connected conductivity inhomogeneities. Furthermore, we establish that an (infinitesimal) simply connected inhomogeneity has the shape of an ellipse, if and only if the polarization tensor is a rational function of the admittivity contrast with at most two poles whose residues satisfy a certain algebraic constraint. We also use the analytic representation to provide a proof of the so-called Hashin–Shtrikman bounds for polarization tensors; a similar approach has been taken previously by Golden and Papanicolaou and Kohn and Milton in the context of anisotropic composite materials.