Local laws for non-Hermitian random matrices

The product of m ∈ N independent random square matrices whose elements are independent identically distributed random variables with zero mean and unit variance is considered. It is known that, as the size of the matrices increases to infinity, the empirical spectral measure of the normalized eigenvalues of the product converges with probability 1 to the distribution of the mth power of the random variable uniformly distributed on the unit disk of the complex plane. In particular, in the case of m = 1, the circular law holds. The purpose of this paper is to prove the validity of the local circular law (as well as its generalization to the case of any fixed m) in the case where the distribution of the matrix elements has finite absolute moment of order 4 + δ,δ > 0,. Recent results of Bourgade, Yau, and Yin, of Tao and Vu, and of Nemish are generalized.     

On distributional solutions of local and nonlocal problems of porous medium type

We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of

(0.1)${?}_{t}u?{\mathfrak{L}}^{\sigma ,\mu }[\phi (u)]=g(x,t)\text{in}{\mathbb{R}}^N\times (0,T),$

where φ is merely continuous and nondecreasing, and ${\mathfrak{L}}^{\sigma ,\mu }$ is the generator of a general symmetric Lévy process. This means that ${\mathfrak{L}}^{\sigma ,\mu }$ can have both local and nonlocal parts like, e.g., ${\mathfrak{L}}^{\sigma ,\mu }=\mathrm{\Delta }?{(?\mathrm{\Delta })}^{\frac{1}{2}}$. New uniqueness results for bounded distributional solutions to this problem and the corresponding elliptic equation are presented and proven. A key role is played by a new Liouville type result for ${\mathfrak{L}}^{\sigma ,\mu }$. Existence and a priori estimates are deduced from a numerical approximation, and energy-type estimates are also obtained.     

Relative Reduction and Buchberger’s Algorithm in Filtered Free Modules

In this paper we develop a relative Gröbner basis method for a wide class of filtered modules. Our general setting covers the cases of modules over rings of differential, difference, inversive difference and difference–differential operators, Weyl algebras and multiparameter twisted Weyl algebras (the last class of rings includes the classes of quantized Weyl algebras and twisted generalized Weyl algebras). In particular, we obtain a Buchberger-type algorithm for constructing relative Gröbner bases of filtered free modules.     

Discovery of Novel Sultone Fused Berberine Derivatives as Promising Tdp1 Inhibitors

A new type of berberine derivatives was obtained by the reaction of berberrubine with aliphatic sulfonyl chlorides. The new polycyclic compounds have a sultone ring condensed to C and D rings of a protoberberine core. The reaction conditions were developed to facilitate the formation of sultones with high yields without by-product formation. Thus, it was shown that the order of addition of reagents affects the composition of the reaction products: when sulfochlorides are added to berberrubine, their corresponding 9-O-sulfonates are predominantly formed; when berberrubine is added to pre-generated sulfenes, sultones are the only products. The reaction was shown to proceed stereo-selectively and the cycle configuration was confirmed by 2D NMR spectroscopy. The inhibitory activity of the synthesized sultones and their 12-brominated analogs against the DNA-repair enzyme tyrosyl-DNA phosphodiesterase 1 (Tdp1), an important target for a potential antitumor therapy, was studied. All derivatives were active in the micromolar and submicromolar range, in contrast to the acyclic analogs and 9-O-sulfonates, which were inactive. The significance of the sultone cycle and bromine substituent in binding with the enzyme was confirmed using molecular modeling. The active inhibitors are mostly non-toxic to the HeLa cancer cell line, and several ligands show synergy with topotecan, a topoisomerase 1 poison in clinical use. Thus, novel berberine derivatives can be considered as candidates for adjuvant therapy against cancer.     

Nanocomposite Polymer Electrolytes of Sodium Alginate and Montmorillonite Clay

Nanocomposite polymer electrolytes (NPEs) were synthesized using sodium alginate (Alg) and either sodium (SCa-3-Na⁺)- or lithium (SCa-3-Li⁺)-modified montmorillonite clays. The samples were characterized by structural, optical, and electrical properties. SCa-3-Na⁺ and SCa-3-Li⁺ clays’ X-ray structural analyses revealed peaks at 2θ = 7.2° and 6.7° that corresponded to the interlamellar distances of 12.3 and 12.8 Å, respectively. Alg-based NPEs X-ray diffractograms showed exfoliated structures for samples with low clay percentages. The increase of clay content promoted the formation of intercalated structures. Electrochemical Impedance Spectroscopy revealed that Alg-based NPEs with 5 wt% of SCa-3-Na⁺ clay presented the highest conductivity of 1.96 × 10⁻² S/cm², and Alg with 10 wt% of SCa-3-Li⁺ showed conductivity of 1.30 × 10⁻² S/cm², both measured at 70 °C. From UV-Vis spectroscopy, it was possible to infer that increasing concentration of clay promoted a decrease of the samples’ transmittance and, consequently, an increase of their reflectance.     

Switch From Pauli-Lowering to LUMO-Lowering Catalysis in Brønsted Acid-Catalyzed Aza-Diels-Alder Reactions

Brønsted acid-catalyzed inverse-electron demand (IED) aza-Diels-Alder reactions between 2-aza-dienes and ethylene were studied using quantum chemical calculations. The computed activation energy systematically decreases as the basic sites of the diene progressively become protonated. Our activation strain and Kohn-Sham molecular orbital analyses traced the origin of this enhanced reactivity to i) “Pauli-lowering catalysis” for mono-protonated 2-aza-dienes due to the induction of an asynchronous, but still concerted, reaction pathway that reduces the Pauli repulsion between the reactants; and ii) “LUMO-lowering catalysis” for multi-protonated 2-aza-dienes due to their highly stabilized LUMO(s) and more concerted synchronous reaction path that facilitates more efficient orbital overlaps in IED interactions. In all, we illustrate how the novel concept of “Pauli-lowering catalysis” can be overruled by the traditional concept of “LUMO-lowering catalysis” when the degree of LUMO stabilization is extreme as in the case of multi-protonated 2-aza-dienes.     

A PYRIDYL-TRIAZINE COMPLEX OF Co(II): SPECTROSCOPIC,STRUCTURAL, AND DOCKING STUDIES

Journal of Structural Chemistry - A new cobalt(II) complex of 5-phenyl-3-(pyridin-2-yl)-1,2,4-triazine (PPTA), [Co(PPTA)2(NO3)2] (1), is prepared and identified by the elemental analysis, FTIR...     

Synthesis and Optoelectronic Properties of a Quinoxalino-Phenanthrophenazine (QPP) Extended Tribenzotriquinacene (TBTQ)

A six-step synthesis towards a tribenzotriquinacene (TBTQ) bearing three quinoxalinophenanthrophenazine (QPP) units is presented. The optoelectronic properties are investigated and the effect of the three-dimensional arrangement of the individual QPP planes is examined using optical spectroscopy, electrochemical analysis and quantum-chemical calculations.     

Magnetic State of Layered Cobalt Chalcogenides Co7Se8 and Co7Te8

JETP Letters - The structural and magnetic properties of the Co7Te8 layered compound have been studied for the first time using X-ray diffraction, measurements of the magnetic susceptibility, and...     

Synthesis and Investigation of Piezophotocatalytic Properties of Polyvinylidene Fluoride Nanofibers Modified with Titanium Dioxide

Moscow University Chemistry Bulletin - A piezoactive nanofiber composite PVDF film with TiO2 nanoparticles included in it was synthesized by electrospinning. The composition, morphology and...