Self-Reciprocal Irreducible Pentanomials Over \mathbb{F}_2

Joseph Yucas and Gary Mullen conjectured that there is no self-reciprocal irreducible pentanomial of degree n over if n is divisible by 6. In this note we prove this conjecture for the case n ≡ 0, and disprove the conjecture for the case n ≡ 6 (mod 12) AMS Classifications: 11T55     

Some characterization and ordering results based on entropies of current records

The aim of this paper is to investigate the entropy properties of current records. Several characterizations are obtained based on the entropy of these statistics. It is proved that the equality of the entropy of the endpoints of record coverage is a characteristic property of symmetric distribution. It is shown that the parent distribution can be identified uniquely by the entropy properties of the endpoints of record coverage. Considering the records coming from distribution with decreasing (increasing) density, the monotonicity of entropy of current records is discussed. We also prove that the dispersive ordering of the parent distributions implies the entropy ordering of their respective current records.     

Analysis of strained double-lightly doped MOSCNT using NEGF

The effects of uniaxial and torsional strains on the double-lightly doped MOSCNT (DLD-MOSCNT) performances are investigated, using the non-equilibrium Green function (NEGF) formalism in mode space approach. The Hamiltonian of the device is obtained by a tight-binding approximation assuming that only p _z orbitals are contributing in carrier transport. In all simulation processes, one mode with the lowest subband is considered. DLD-MOSCNT has a small band-to-band tunneling and almost eliminates the ambipolar behavior of I _DS–V _GS characteristics because of the band engineering. We use a modified model to demonstrate the strain effects on such a low OFF-current device. The results show that the strain effects mainly depend on the chiral vector and diameter of CNT. The strain causes band gap and carrier velocity changes, which result in variation of ON- or OFF-current. In addition, the subthreshold swing of this device under uniaxial strain is calculated, which is about 61 mV/Dec for 2 % tensile strain in (16,0) and for ?2 % compressive strain in (17,0). Under the uniaxial strain, in the case that the energy band gap increases, the variation of DIBL is very small.     

The Potential Role of Nigella sativa Seed Oil as Epigenetic Therapy of Cancer

Nigella sativa oil, commonly known as black seed oil (BSO), is a well-known Mediterranean food, and its consumption is associated with beneficial effects on human health. A large number of BSO’s therapeutic properties is attributed to its pharmacologically active compound, thymoquinone (TQ), which inhibits cell proliferation and induces apoptosis by targeting several epigenetic players, including the ubiquitin-like, containing plant homeodomain (PHD) and an interesting new gene, RING finger domains 1 (UHRF1), and its partners, DNA methyltransferase 1 (DNMT1) and histone deacetylase 1 (HDAC1). This study was designed to compare the effects of locally sourced BSO with those of pure TQ on the expression of the epigenetic complex UHRF1/DNMT1/HDAC1 and the related events in several cancer cells. The gas chromatographs obtained from GC-MS analyses of extracted BSO showed that TQ was the major volatile compound. BSO significantly inhibited the proliferation of MCF-7, HeLa and Jurkat cells in a dose-dependent manner, and it induced apoptosis in these cell lines. BSO-induced inhibitory effects were associated with a significant decrease in mRNA expression of UHRF1, DNMT1 and HDAC1. Molecular docking and MD simulation showed that TQ had good binding affinity to UHRF1 and HDAC1. Of note, TQ formed a stable metal coordinate bond with zinc tom, found in the active site of the HDAC1 protein. These findings suggest that the use of TQ-rich BSO represents a promising strategy for epigenetic therapy for both solid and blood tumors through direct targeting of the trimeric epigenetic complex UHRF1/DNMT1/ HDAC1.     

Mucin-Inspired Single-Chain Polymer (MIP) Fibers as Potent SARS-CoV-2 Inhibitors

Mucins are the key component of the defensive mucus barrier. They are extended fibers of very high molecular weight with diverse biological functions depending strongly on their specific structural parameters. Here, we present a mucin-inspired nanostructure, produced via a synthetic methodology to prepare methacrylate-based dendronized polysulfates ( MIP-1 ) on a multi gram-scale with high molecular weight (MW=450 kDa) and thiol end-functionalized mucin-inspired polymer ( MIP ) via RAFT polymerization. Cryo-electron tomography (Cryo-ET) analysis of MIP-1 confirmed a mucin-mimetic wormlike single-chain fiber structure (length=144±59 nm) in aqueous solution. This biocompatible fiber showed promising activity against SARS-CoV-2 and its mutant strain, with a remarkable low half maximal (IC₅₀) inhibitory concentration (IC₅₀=10.0 nM). Additionally, we investigate the impact of fiber length on SARS-CoV-2 inhibition by testing other functional polymers ( MIPs ) of varying fiber lengths.