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G.E. Farr 《Discrete Mathematics》2019,342(5):1510-1519
This paper continues the study of combinatorial properties of binary functions — that is, functions f:2E? 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.  相似文献   
154.
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.  相似文献   
155.
Ganenkova  E. G.  Starkov  V. V. 《Mathematical Notes》2019,105(1-2):216-226

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

  相似文献   
156.
Radiophysics and Quantum Electronics - We present the results of comparing the total electron content measurements based on GLONASS satellite signals and the EISCAT UHF incoherent scatter radar...  相似文献   
157.
The first examples of the catalytic asymmetric 1,3‐dipolar cycloaddition of azomethine ylides with acyclic activated 1,3‐dienes (and 1,3‐enynes) are described. Under copper catalysis, a selective cycloaddition at the terminal γ,δ‐C?C bond is observed. In addition, depending on the ligand used, either the exo or the endo adduct can be obtained with high selectivity. Under appropriate reaction conditions, the acyclic 1,6‐addition product is detected, suggesting a stepwise mechanism. The resulting C4‐alkenyl‐substituted pyrrolidines are suitable substrates for further access to polycyclic systems, as highlighted by the preparation of hexahydrochromeno[4,3‐b]pyrrole and the tetracyclic core of the alkaloid gracilamine.  相似文献   
158.
Journal of Structural Chemistry - An analysis is presented for the results obtained in the studies initiated by A. E. Shvelashivili, Corresponding Member, Academy of Sciences of Georgia, and...  相似文献   
159.
Tunneled metal oxides such as α-Mn8O16 (hollandite) have proven to be compelling candidates for charge-storage materials in high-density batteries. In particular, the tunnels can support one-dimensional chains of K+ ions (which act as structure-stabilizing dopants) and H2O molecules, as these chains are favored by strong H-bonds and electrostatic interactions. In this work, we examine the role of water molecules in enhancing the stability of K+-doped α-Mn8O16 (cryptomelane). The combined experimental and theoretical analyses show that for high enough concentrations of water and tunnel-ions, H2O displaces K+ ions from their natural binding sites. This displacement becomes energetically favorable due to the formation of K2+ dimers, thereby modifying the stoichiometric charge of the system. These findings have potentially significant technological implications for the consideration of cryptomelane as a Li+/Na+ battery electrode. Our work establishes the functional role of water in altering the energetics and structural properties of cryptomelane, an observation that has frequently been overlooked in previous studies.

Water displaces potassium ions and initiates the formation of a homonuclear dimer ion (K2+) in the tunnels of hollandite.  相似文献   
160.
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