Diophantine equationAx 2+B=y n

Cao, Zhenfu; Dong, Xiaole

doi:10.1007/bf02883090

Cited by 7 publications

(7 citation statements)

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“…PMMA with a melt flow index of 1.8 g/10 min and Mw 5 90,400 g/mol was obtained from Chimei Co. (PMMA, Agryrex 205). GNPs were purchased from Graphene Expert Co. GNPs are obtained from reduction of graphene oxide by Hummer method [51] with average thickness of approximately 7-10 layers, based on company statement. The required FG was prepared by this research team which will be explained in the following section.…”

Section: F5supporting

confidence: 55%

“…This most probably means a better interaction of FG with polymer phases but more conversion of atom hybridization, resulting in less inherent conductivity of FG in comparison with GNPs. The presence of S and N components in the samples is due to oxidation by H 2 SO 4 and reduction of GO by hydrazine (NH 2 NH 2 ) through GNP preparation by Hummer method [51,53].…”

Section: Characterization Of Graphenic Materialsmentioning

confidence: 92%

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Electrical conductivity of graphene filled PLA/PMMA blends: Experimental investigation and modeling

et al. 2018

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In order to gain a fundamental understanding about the influences of filler characteristic on the electrical properties of polymer blend nanocomposites two types of graphene, graphene nanoplates (GNPs) and functionalized graphene (FG), were added to immiscible blend of poly (lactic acid)/poly(methyl methacrylate) (PLA/PMMA) and experimental and theoretical studies were carried out. Structure and properties of graphenic nanoparticles were investigated by Raman spectroscopy, elemental analysis, thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy (FTIR) and X‐ray diffraction (XRD). The state of dispersion and distribution of fillers within the blend were examined by field emission scanning electron microscopy, Atomic force microscopy, transmission electron microscopy as well as XRD patterns. Theoretical modeling was carried out by several statistical and thermodynamic based models. Results showed that FG was more homogenously dispersed in the PLA matrix compared with GNP which results in lower percolation threshold and better electrical conductivity in the FG filled blends, despite its poor intrinsic electrical conductivity. For the PLA/PMMA blends filled composites, electrical conductivity modeling results showed that thermodynamic‐based models exhibit more satisfactory estimations than Power law statistical model. Thus, the electrical conductivity of two‐phase polymer blend filled with graphenic materials is predictable with thermodynamic models. POLYM. COMPOS., 40:704–715, 2019. © 2018 Society of Plastics Engineers

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Section: F5supporting

confidence: 55%

Section: Characterization Of Graphenic Materialsmentioning

confidence: 92%

Electrical conductivity of graphene filled PLA/PMMA blends: Experimental investigation and modeling

et al. 2018

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“…The equation x 2 +4 = y n , n > 1 has the only positive integral solutions (x, y, n) = (2, 2, 3) or (11,5,3). [15] extended the above lemma and provided an elementary proof.…”

Section: Other Resultsmentioning

confidence: 92%

THE EXPONENTIAL DIOPHANTINE EQUATION AX2 + BY 2 = λkZ AND ITS APPLICATIONS

Cao

Chu²,

Shiu³

2008

Taiwanese J. Math.

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Let A, B ∈ N with A > 1, B > 1 and gcd(A, B) = 1, k ≥ 2 be an integer coprime with AB, and let λ ∈ {1, 2, 4} be such that if λ = 4, then A = 4 and B = 4; and if k is even, then λ = 4. In this paper, we shall describe all solutions of the equationwhere the symbol X| * A means that every prime divisor of X divides A. Then, using this result, we give some more general results on the number of solutions of the equation la x + mb y = λc z , x > 1, y > 1, z > 1. In addition, using Cao's result on Pell equation, we obtain some improvement of Terai's results on the equations a x + 2 = c z , a x + 4 = c z and a x + 2 y = c z .

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“…Yangtze River sediments have more oxides than Yellow River sediments in the content of K 2 O, Fe 2 O 3 , MgO, Al 2 O 3 , etc. while the situation is reverse in the content of Na 2 O and CaO [3][4][5][6][7][8][9][10][11][12] (Table 1).…”

Section: Characteristics Of Sediments In River Coursementioning

confidence: 99%

Identification of Yangtze River and Yellow River Paleochannels in South Yellow Sea Shelf

Song

Zhou

Chen

et al. 2013

AMR

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research of submarine paleochannels has not only a great significance in exploring the evolution of palaeoenvironment of continental shelf but also a practical application value in solving problems on disaster geology and environmental geology in the continental shelf development. Yellow River and Yangtze River both were concentrated in the northern Jiangsu to enter the South Yellow Sea Basin in the Last Glacial, playing an important role in the palaeoenvironment evolution of the South Yellow Sea. On the basis of integrating previous research results and researching a large number of shallow stratigraphic sections of paleochannels in the South Yellow Sea Shelf in detail, identification and research of Yangtze River and Yellow River paleochannels in the South Yellow Sea Shelf are carried out in this paper. Research results show that: the Yangtze River and Yellow River paleochannels in the South Yellow Sea continental shelf are significantly different in the river section, river pattern, major elements, as well as trace elements, clay minerals, carbonate content and heavy mineral assemblages in the river sediments and other aspects. These differences can be used as the evidence for identification of the Yangtze River and Yellow River paleochannels.

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Diophantine equationAx 2+B=y n

Cited by 7 publications

References 1 publication

Electrical conductivity of graphene filled PLA/PMMA blends: Experimental investigation and modeling

Electrical conductivity of graphene filled PLA/PMMA blends: Experimental investigation and modeling

THE EXPONENTIAL DIOPHANTINE EQUATION AX2 + BY 2 = λkZ AND ITS APPLICATIONS

Identification of Yangtze River and Yellow River Paleochannels in South Yellow Sea Shelf

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