On the homogeneity of additive mappings

LetK be a ring with an identity 1 0 andM, L two unitaryK-modules. Then, for any additive mappingf:M L, the setH _f :={ K f(x)=f(x) for allx M} forms a subring ofK, the homogeneity ring off. It is shown that, forM {0},L {0} and any subringS ofK for whichM is a freeS-module, there exists an additive mappingf:ML such thatH _f =S. This result is applied to the four Cauchy functional equations, and it leads also to an answer to the question as to whether it is possible to introduce onM a multiplication ·:M × M M makingM into a ring but not into aK-algebra.     

Established Liposome-Coated IMB16-4 Polymeric Nanoparticles (LNPs) for Increasing Cellular Uptake and Anti-Fibrotic Effects In Vitro

As a global health problem, liver fibrosis still does not have approved treatment. It was proved that N-(3,4,5-trichlorophenyl)-2(3-nitrobenzenesulfonamide) benzamide (IMB16-4) has anti-hepatic fibrosis activity. However, IMB16-4 displays poor water solubility and poor bioavailability. We are devoted to developing biodegraded liposome-coated polymeric nanoparticles (LNPs) as IMB16-4 delivery systems for improving aqueous solubility, cellular uptake, and anti-fibrotic effects. The physical states of IMB16-4−LNPs were analyzed using a transmission electron microscope (TEM), high-performance liquid chromatography (HPLC), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) and differential scanning calorimeter (DSC). The results show that IMB16-4−LNPs increased the drug loading compared to liposomes and enhanced cellular uptake behavior compared with IMB16-4−NPs. In addition, IMB16-4−LNPs could repress the expression of hepatic fibrogenesis-associated proteins, indicating that IMB16-4−LNPs exhibited evident anti-fibrotic effects.     

Spectroscopy of light nuclei with skyrme-type interactions

Deformed Hartree-Fock calculations are performed for some light nuclei in a large configuration space consisting of first four major shells. The interaction employed is the modified Skyrme interaction in which the deformed density is replaced by the band averaged scalar density that makes the Hamiltonian rotationally invariant rendering the spectroscopic calculations feasible. It is shown that the introduction of density dependence spreads out the energy spectra and that the Skyrme variant SIV which has a weak density dependence gives best overall agreement for energy spectra and the available data for the electromagnetic properties of the nuclei studied. It is found that the maximum contribution to the energy of any state in the low lying spectrum comes from thes-state attractive ands-state repulsive parts of the Skyrme interaction. It is also shown that when two-body density dependent version of Skyrme interaction is used, the Koopmans theorem no longer holds.     

Novel Inhibitors of 2′-O-Methyltransferase of the SARS-CoV-2 Coronavirus

The COVID-19 pandemic is still affecting many people worldwide and causing a heavy burden to global health. To eliminate the disease, SARS-CoV-2, the virus responsible for the pandemic, can be targeted in several ways. One of them is to inhibit the 2′-O-methyltransferase (nsp16) enzyme that is crucial for effective translation of viral RNA and virus replication. For methylation of substrates, nsp16 utilizes S-adenosyl methionine (SAM). Binding of a small molecule in the protein site where SAM binds can disrupt the synthesis of viral proteins and, as a result, the replication of the virus. Here, we performed high-throughput docking into the SAM-binding site of nsp16 for almost 40 thousand structures, prepared for compounds from three libraries: Enamine Coronavirus Library, Enamine Nucleoside Mimetics Library, and Chemdiv Nucleoside Analogue Library. For the top scoring ligands, semi-empirical quantum-chemical calculations were performed, to better estimate protein–ligand binding enthalpy. Relying upon the calculated binding energies and predicted docking poses, we selected 21 compounds for experimental testing.     

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 $u_q({\mathfrak{sl}}_2)$.     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

Universal deformation rings and self-injective Nakayama algebras

Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring $R(\mathrm{\Lambda },V)$ and we describe $R(\mathrm{\Lambda },V)$ explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups.     

On images of locally finite derivations and E-derivations

Some cases of the LFED Conjecture, proposed by the second author [15], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions $k(x)$ of the polynomial algebra $k[x]$, the formal power series algebra $k[[x]]$ and the Laurent formal power series algebra $k[[x]][x^{?1}]$, where $x=(x_1,x_2,\dots ,x_n)$ denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized.