On Le’s and Bugeaud’s Papers about the Equation ax 2?+ b 2m?1 ?=?4 c p

 We correct an inaccuracy in the papers of Le, Mignotte, and Bugeaud on the generalized Ramanujan-Nagell equation. Received June 23, 2001     

Thin-Layer Chromatographic Analysis of Flavonoids,Phenolic Acids,and Amino Acids in Some Croatian Hypericum Taxa

JPC – Journal of Planar Chromatography – Modern TLC - The flowering tops of Hypericum hirsutum, H. montanum, H. perforatum subsp. angustifolium, H. perforatum subsp. perforatum, and H....     

金属性二维过渡金属硫化物的溶剂热合成及电催化析氢性能

采用溶剂热法制备了多种二维过渡金属硫化物(TMDCs), 在合成过程中通过调控反应前驱体的滴加速率来控制所得TMDCs的形貌和结构. 然后采用高温热处理来提高TMDCs的结晶性, 从而提升了其电催化活性. 在酸性电解液中进行电催化析氢性能测试. 结果表明, “花状”结构的金属性二维二硫化铌(NbS₂)具有最佳的催化活性和稳定性, 在电流密度为10 mA/cm²时, 其过电位仅为146 mV, 持续工作24 h后电流密度几乎不衰减. 研究发现, 可充分暴露面内活性位点的“花状”结构以及高温处理后材料导电性的提高是二维NbS₂具有优异电催化性能的主要因素.     

Diophantine equations with products of consecutive members of binary recurrences

We prove a finiteness result for the number of solutions of a Diophantine equation of the form \(u_n u_{n+1}\cdots u_{n+k}\pm 1 =\pm u_m^2\), where \(\{ u_n\}_{n\ge 1}\) is a binary recurrent sequence whose characteristic equation has roots which are real quadratic units.     

A Polarized Gel Electrolyte for Wide-Temperature Flexible Zinc-Air Batteries

The development of flexible zinc-air batteries (FZABs) has attracted broad attention in the field of wearable electronic devices. Gel electrolyte is one of the most important components in FZABs, which is urgent to be optimized to match with Zn anode and adapt to severe climates. In this work, a polarized gel electrolyte of polyacrylamide-sodium citric (PAM-SC) is designed for FZABs, in which the SC molecules contain large amount of polarized −COO⁻ functional groups. The polarized −COO⁻ groups can form an electrical field between gel electrolyte and Zn anode to suppress Zn dendrite growth. Besides, the −COO⁻ groups in PAM-SC can fix H₂O molecules, which prevents water from freezing and evaporating. The polarized PAM-SC hydrogel delivers a high ionic conductivity of 324.68 mS cm⁻¹ and water retention of 96.85 % after being exposed for 96 h. FZABs with the PAM-SC gel electrolyte exhibit long cycling life of 700 cycles at −40 °C, showing the application prospect under extreme conditions.     

High temperature selective growth of single-walled carbon nanotubes with a narrow chirality distribution from a CoPt bimetallic catalyst

Chirality-controlled synthesis of single-walled carbon nanotubes (SWCNTs) is a prerequisite for their practical applications in electronic and optoelectronic devices. We report here a novel bimetallic CoPt catalyst for the selective growth of high quality SWCNTs with a narrow chirality distribution at relatively high temperatures of 800 °C and 850 °C using atmospheric pressure alcohol chemical vapor deposition. The addition of Pt into a Co catalyst forms a CoPt alloy and significantly reduces the diameters of the as-grown SWCNTs and narrows their chirality distributions.     

Chevalley–Weil theorem and subgroups of class groups

We prove, under some mild hypothesis, that an ´etale cover of curves defined over a number field has infinitely many specializations into an everywhere unramified extension of number fields. This constitutes an “absolute” version of the Chevalley–Weil theorem. Using this result, we are able to generalise the techniques of Mestre, Levin and the second author for constructing and counting number fields with large class group.     

Sum-Free Sets and Related Sets

A   of integers is sum-free if . Cameron conjectured that the number of sum-free sets is . As a step towards this conjecture, we prove that the number of sets satisfying

HPTLC Determination of Flavonoids and Phenolic Acids in Some Croatian Stachys Taxa

JPC – Journal of Planar Chromatography – Modern TLC - Stachys is a large genus belonging to the family Lamiaceae. In common with many other representatives of this family, the aerial...