Lifting via cocycle deformation

We develop a strategy to compute all liftings of a Nichols algebra over a finite dimensional cosemisimple Hopf algebra. We produce them as cocycle deformations of the bosonization of these two. In parallel, we study the shape of any such lifting.     

Synthesis of nanocomposites from cationic polyacrylamide and modified carbon black: Application as flocculants for oily sludge suspension

Carbon black was modified using various liquid‐phase oxidation methods (modified carbon black = m‐CB, m = (1, 2, 3): 1, sulfuric acid/potassium permanganate method; 2, nitric acid method; 3, hydrogen peroxide method). With acetone–ethylene glycol as initiator, dimethyldiallylammonium chloride (DMDAAC) and acrylamide (AM) as monomer, cationic polyacrylamide (CPAM) was prepared by UV excitation of the monomer. The m‐CB/CPAM nanocomposites were synthesized using a hydrothermal method. The factors that affected the molecular weight of CPAM were investigated, including the total monomer concentration, the dosage of the complex initiator, the mass ratio of m_AM:m_DMDAAC and the UV irradiation time. The chemical structures and morphologies of the samples were characterized using Fourier transform infrared spectroscopy, thermogravimetric analysis, elemental composition, X‐ray diffraction and scanning electron microscopy. 1‐CB/CPAM was utilized to flocculate oil sludge suspension, and the effects of 1‐CB quality, 1‐CB/CPAM dosage, temperature and pH value on the flocculation performance of 1‐CB/CPAM were investigated. The flocculation mechanism of 1‐CB/CPAM was also analyzed. The results show that 1‐CB/CPAM has an outstanding flocculation effect, and it flocculates oil sludge particles by adsorption bridging and charge neutralization in acidic and alkaline conditions.     

Spin-Spin Relaxation Process of 23Na-NMR in Na-Loaded NaY

Abstract

Spin-spin relaxation of ²³Na-NMR is observed by the spin echo method at room temperature for Y-type zeolite loaded with Na metal without hydration. For saturated and no levels of loading, the echo decay is well fitted by single exponential function. T ₂ decreases to be 0.25 times smaller by loading. This decrease of T ₂ is explained semiquantitatively with assuming nuclear dipole-dipole interaction between neighboring Na.     

An approach for solving a fuzzy multiobjective programming problem

In this paper we present a new approach, based on the Nearest Interval Approximation Operator, for dealing with a multiobjective programming problem with fuzzy-valued objective functions.     

On actions of Drinfel'd doubles on finite dimensional algebras

Let q be an nth root of unity for $n>2$ and let $T_n(q)$ be the Taft (Hopf) algebra of dimension $n^2$. In 2001, Susan Montgomery and Hans-Jürgen Schneider classified all non-trivial $T_n(q)$-module algebra structures on an n-dimensional associative algebra A. They further showed that each such module structure extends uniquely to make A a module algebra over the Drinfel'd double of $T_n(q)$. We explore what it is about the Taft algebras that leads to this uniqueness, by examining actions of (the Drinfel'd double of) Hopf algebras H “close” to the Taft algebras on finite-dimensional algebras analogous to A above. Such Hopf algebras H include the Sweedler (Hopf) algebra of dimension 4, bosonizations of quantum linear spaces, and the Frobenius–Lusztig kernel $u_q({\mathfrak{sl}}_2)$.     

Accurate prediction of norbornadiene cycle enthalpies by DLPNO-CCSD(T1)/CBS method

The DLPNO-CCSD(T₁)/CBS method combined with simple reactions containing small reference species leads to an improvement in the accuracy of theoretically evaluated enthalpies of formation of medium-sized polyalicyclic hydrocarbons when compared with the widely used composite approach. The efficiency of the DLPNO-CCSD(T₁)/CBS method is most vividly demonstrated by comparing with the results of G4 calculations for adamantane. The most important factor in choosing appropriate working reaction is the same number of species on both sides of the equation. Among these reactions, the reactions with small enthalpy change usually provide a better cancellation of errors. The DLPNO-CCSD(T₁)/CBS method was used to calculate the enthalpies of formation of compounds belonging to the norbornadiene cycle (norbornadiene, quadricyclane, norbornene, nortricyclane, and norbornane). The most reliable experimental enthalpies of formation are recommended for these compounds by comparing calculated values with conflicting experimental data.     

Cartan Invariants in the Category of Restricted Representation for gl(m|n)

Let k be an algebraically closed field of characteristic p 2, and gl(m|n) be the general linear Lie superalgebra over k. The Cartan invariants for the restricted supermodule category for gl(m|n) are presented.