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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 such that , where 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
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Differential inequalities for polynomials generalizing the well-known Smirnov, Rahman, Schmeisser, and Bernstein inequalities are obtained.
相似文献146.
Tereshchenko E. D. Cherniakov S. M. Yurik R. Yu. Rietveld M. T. Häggström I. 《Radiophysics and Quantum Electronics》2020,62(10):667-676
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
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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
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Facile non‐lithographic route to highly aligned silica nanopatterns using unidirectionally aligned polystyrene‐block‐polydimethylsiloxane films 下载免费PDF全文
Zhe Qiang Maurice L. Wadley Bryan D. Vogt Kevin A. Cavicchi 《Journal of Polymer Science.Polymer Physics》2015,53(15):1058-1064
Thin films (monolayer and bilayer) of cylinder forming polystyrene‐block‐polydimethylsiloxane (PS‐b‐PDMS) were shear aligned by the swelling and deswelling of a crosslinked PDMS pad that was physically adhered to the film during solvent vapor annealing. The nanostructures formed by self‐assembly were exposed to ultraviolet‐ozone to partially oxidize the PDMS, followed by calcination in air at 500 °C. In this process, the PS segments were fully decomposed, while the PDMS yielded silica nanostructures. The highly aligned PDMS cylinders were thus deposited as silica nanolines on the silicon substrate. Using a bilayer film, the center‐to‐center distance of these features were effectively halved from 38 to 19 nm. Similarly, by sequential shear‐alignment of two distinct layers, a rhombic array of silica nanolines was fabricated. This methodology provides a facile route to fabricating complex topographically patterned nanostructures. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1058–1064 相似文献