Three-weight linear codes from Weil sums

Journal of Algebraic Combinatorics - By appropriately choosing a defining set, we define a class of linear codes and establish their complete weight enumerators and weight enumerators using Weil...     

A general stability result for the semilinear viscoelastic wave model under localized effects

Our main goal in the present work is to address an integro-differential model under localized viscoelastic and frictional effects arising in the Boltzmann theory of viscoelasticity. More precisely, we consider a general version in the history context of the pioneer localized viscoelastic problem approached by Cavalcanti and Oquendo (2003) in the null history scenario, and more recently by Cavalcanti et al. (2018) in the history framework. By means of a new observability inequality, we prove a general stability result to the model under a weaker assumption on the localized frictional damping and a slower condition on the decreasing memory kernel (of polynomial type) than the previously mentioned works. To achieve such stability results, we still work in a general setting by removing the assumption on complementary damping mechanisms and show, in some reasonable situations concerning the density coefficient, that the localized viscoelastic effect is enough to ensure the general stability (of polynomial type) to the problem.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

Proton conductivity study on three CS/IL@fle-MOF membranes

The low-cost, high specific surface area and porosity, controlled pore size, and chemical properties of metal–organic framework (MOF) materials have attracted much attention in the exploration of proton conduction. The method of chemically modifying MOF structures or introducing conductive medium into the holes can effectively improve the proton conductivities of the materials. Here, the structural tunability of ionic liquid (IL) and flexible MOF (fle-MOF) materials are matched to give full play to the conductivity of IL, the framework support, and the microporous effect of MOFs, which achieves the synergistic effect of performance and expands the temperature range of proton transfer. Three kinds of CS/IL@fle-MOF membranes were prepared by combining three fle-MOFs with 1-carboxymethyl-3-methylimidazole (CMMIM) in different proportions to obtain 15 pieces of membranes. The comparative analyses show that CS/IL@fle-MOF membranes have excellent proton conduction performance at a wider temperature range (263–353 K) and lower relative humidity (75% RH). Among them, the proton conductivities of CS/CMMIM@MIL-88A-25% and CS/CMMIM@MIL-88B-125% are up to 1.33 and 1.42 S cm⁻¹ at 75% RH and 353 K, respectively; whereas those of CS/CMMIM@MIL-53(Fe)-75% and CS/CMMIM@MIL-88B-125% reach up to 2.1 × 10⁻³ and 1.28 × 10⁻³ S cm⁻¹ at 75% RH and 263 K, respectively. The E_a of CS/CMMIM@fle-MOFs is in the range of 0.1–0.5 eV, suggesting that the proton transport follows predominantly the typical Grotthuss transfer mechanism. The results of this study indicate that the CS/CMMIM@fle-MOF membranes combinations offer great potential for the design of composite porous proton-conducting materials.     

Two cubane-like [M4O4] {M = nickel(II), cobalt(II)} complexes: syntheses,crystal structures and magnetic properties

Transition Metal Chemistry - Two cubane-like complexes, namely [Ni4L4(HOEt)4] (1), [Co4L4(HOEt)4] (2) (H2L?=?(E)-2-((3-hydroxypropylimino)methyl)-6-methoxyphenol), were prepared under...     

Dimeric Manganese-Catalyzed Hydroarylation and Hydroalkenylation of Unsaturated Amides

An unprecedented Mn(I)-catalyzed selective hydroarylation and hydroalkenylation of unsaturated amides with commercially available organic boronic acids is reported. Alkenyl boronic acids have been successfully employed for the first time in Mn(I)-catalyzed carbon–carbon bond formation. A wide array of β-alkenylated amide products can be obtained in moderate to good yields, which offers practical access to five- and six-membered lactams. This protocol has predictable regio- and chemoselectivity, excellent functional group compatibility and ease of operation in air, representing a significant step-forward towards manganese-catalyzed C−C coupling.     

分数阶Schrodinger—Kirchhoff方程无穷多高能量解的存在性

本文研究如下带有变号势函数的分数阶Schrodinger Kirchhoff方程(a+b∫∫R^N|u(x)-u(y)|^p/|x-y|^N+p^sdxdy)^p-1(-△)p^su+λV(x)|u|^p-2u=f(x,u)-μg(x)|u|^q-2u,x∈R^N.其中s∈(0,1),p∈[2,∞),q∈(l,p),a,b>0,λ,μ>0均为正常数,在V,f,g等函数合适的条件下,运用喷泉定理获得该系统无穷多高能量解的存在性.     

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

The ground and excited states of a donor impurity at the center of a spherical quantum dot subject to a magnetic field are calculated within the effective-mass approximation. The barriers are infinitely high and the differential equation is solved by combining the finite-difference method with the Richardson extrapolation. The binding and transition energies are more accurate than the available variational values, and excellent agreement is found with the hydrogen atom. The transition energies for a medium-size quantum dot are given.