$$\mathcal {F}_\pi $$Fπ-residuality of generalized Baumslag–Solitar groups

Archiv der Mathematik - A generalized Baumslag–Solitar group is a finitely generated group that acts on a tree with infinite cyclic edge and vertex stabilizers. A group G is residually a...     

Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.     

The Landscape of the Spiked Tensor Model

We consider the problem of estimating a large rank-one tensor u ^⊗k ∈ (ℝⁿ)^⊗k , k ≥ 3 , in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio λ  _Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no polynomial-time algorithm is known that achieved this goal unless λ ≥ Cn^{(k − 2)/4} , and even powerful semidefinite programming relaxations appear to fail for 1 ≪ λ ≪ n^{(k − 2)/4} . In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-k homogeneous polynomial over the unit sphere in n dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions n , and give exact formulas for the exponential growth rate. We show that (for λ larger than a constant) critical points are either very close to the unknown vector u or are confined in a band of width Θ(λ^{−1/(k − 1)}) around the maximum circle that is orthogonal to u . For local maxima, this band shrinks to be of size Θ(λ^{−1/(k − 2)}) . These “uninformative” local maxima are likely to cause the failure of optimization algorithms. © 2019 Wiley Periodicals, Inc.     

Fractional damping enhances chaos in the nonlinear Helmholtz oscillator

Nonlinear Dynamics - The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional-order damping. For that...     

Controlled synthesis of ZnO nanoparticles from a Zn(II) coordination polymer: Structural characterization,optical properties and photocatalytic activity

A zinc coordination polymer derived from pyridine-2,6-dicarboxylate (PDC), {[Zn₂(PDC)₂]}_n, was successfully prepared via conventional, sonication and microwave-irradiation methods. The composition and characteristics of the obtained coordination polymers (CPs) were investigated by elemental analysis, TGA/DTA, X-ray diffraction and spectroscopic techniques. The so obtained CPs were heat-treated in the air at 600 °C for 2 h to produce ZnO of nanosized particles (NPs). It is of interest to note that the synthesis approach of the precursor greatly affects both the nanoparticle size and the structure of the resulting ZnO NPs. Moreover, the smallest particle size was associated with the sample derived from the ultrasonically prepared precursor. TEM analysis revealed that all samples have sphere-like morphologies. Structural analysis of the prepared ZnO samples was conducted and compared using Rietveld analysis of their PXRD patterns. Optical band gap calculations based on analysis of the UV–vis spectra of ZnO samples using Tauc's power law were achieved. The highest band gap of 3.63 eV was observed for ZnO sample obtained from the ultrasonically prepared precursor. Furthermore, the photocatalytic activity of ZnO NPs for the removal of Eosin Y color was monitored. The highest removal efficiency was recorded for ZnO originated from the ultrasonically synthesized precursor. Enhancement of removal efficiency that reached 98% was attained in only a period of 8 min. Its recycling test showed that it can be reused without structural changes over four cycling experiments.     

Anti-neuraminidase activity of chemical constituents of Balanophora involucrata

Balanophora involucrata J. D. Hooker has been known to possess potential anti-inflammatory and antibacterial activities; however, its antiviral activity has not been evaluated so far. In order to find new neuraminidase inhibitors (NAIs), the neuraminidase (NA) inhibition activity of different B. involucrata extracts was evaluated. In this study, an in vitro NA inhibition assay was performed to identify which extract of B. involucrata exhibits (maximal) inhibitory activity against NA. Ultra high performance liquid chromatography/quadrupole time-of-flight–tandem mass spectroscopy (MS/MS) and molecular docking techniques were used to identify the specific compounds responsible for the anti-influenza activity of the extract, and to explore the potential natural NAIs. The ethyl acetate extract of B. involucrata exhibited significant inhibitory activity against NA with 50% inhibitory concentration (IC₅₀) value of 159.5 μg/mL. Twenty compounds were identified according to the MS/MS spectra; among them two compounds (quercitrin and phloridzin) showed obvious inhibitory activity against NA, with IC₅₀ of 311.76 and 347.32 μmol/L, respectively. This study suggested that B. involucrata can be a potential natural source of NAIs and may be useful in the fight against ferocious influenza viruses.     

Probing the Catalytic Activity of Reduced Graphene Oxide Decorated with Au Nanoparticles Triggered by Visible Light

Hybrid materials in which reduced graphene oxide (rGO) is decorated with Au nanoparticles (rGO–Au NPs) were obtained by the in situ reduction of GO and AuCl₄^?_(aq) by ascorbic acid. On laser excitation, rGO could be oxidized as a result of the surface plasmon resonance (SPR) excitation in the Au NPs, which generates activated O₂ through the transfer of SPR‐excited hot electrons to O₂ molecules adsorbed from air. The SPR‐mediated catalytic oxidation of p‐aminothiophenol (PATP) to p,p′‐dimercaptoazobenzene (DMAB) was then employed as a model reaction to probe the effect of rGO as a support for Au NPs on their SPR‐mediated catalytic activities. The increased conversion of PATP to DMAB relative to individual Au NPs indicated that charge‐transfer processes from rGO to Au took place and contributed to improved SPR‐mediated activity. Since the transfer of electrons from Au to adsorbed O₂ molecules is the crucial step for PATP oxidation, in addition to the SPR‐excited hot electrons of Au NPs, the transfer of electrons from rGO to Au contributed to increasing the electron density of Au above the Fermi level and thus the Au‐to‐O₂ charge‐transfer process.     

Synthesis and structural characterization of (η5-Dp)Ru(PPh3)2H (Dp = C8H9−, 1,2-dihydropentalenyl)

Transition Metal Chemistry - (η5-Dp)Ru(PPh3)2H (Dp?=?C8H9?, 1,2-dihydropentalenyl) was synthesized in 90% yield by reaction of (η5-Dp)Ru(PPh3)2Cl with sodium formate....     

Purcell Effect and Nonlinear Behavior of the Emission in a Periodic Structure Composed of InAs Monolayers Embedded in a GaAs Matrix

Enhancement of spontaneous emission in a resonant Bragg quantum well (QW) structure with 60 periods of triple InAs monolayers embedded in a GaAs matrix is studied experimentally and theoretically. From measurements of the time‐resolved photoluminescence, besides the QW exciton at 1.47 eV, a specific super‐radiant (SR) emission demonstrating nonlinear properties is found. The SR mode shows a near‐quadratic dependence of intensity on excitation power, while its energy position follows the Bragg condition. It is revealed that the SR mode shows a peculiar non‐monotonic dependence of intensity on direction, with a maximum observed at approximately 40°. The enhancement in the SR emission at a specific direction is correlated well with suggested theoretical consideration of the modal Purcell factor for periodic quantum well structures.     

The Möbius Transformation and Smirnov’s Inequality for Polynomials

Differential inequalities for polynomials generalizing the well-known Smirnov, Rahman, Schmeisser, and Bernstein inequalities are obtained.