$q$-analogues of two supercongruences of Z.-W. Sun

Abstract

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Oxygen self-doped g-C3N4with tunable electronic band structure for unprecedentedly enhanced photocatalytic performance

“…The peak at 284.6 eV originates from adventitious carbon (sp 3 C-C), while the peaks at 288.0 eV or 288.1 eV (N=C-N) and 288.6 eV (C=N) are ascribed to carbon at the two different spatial locations in the basic aromatic CN heterocycles. 13,16 Two new peaks at 286.8 eV and 289.1 eV correspond to C-O-C and C-O bonds in the C 1s spectrum of CNO-4. This is consistent with the assumption that O atoms are doped into the matrix of CN heterocycles by bonding with C atoms.…”

Constructing 2D/2D Fe2O3/g‐C3N4 Direct Z‐Scheme Photocatalysts with Enhanced H2 Generation Performance

“…[1][2][3][4][5][6][7][8][9] To date, a myriad of photocatalysts have been developed for various applications. [10][11][12][13][14][15] However, the major bottleneck of these photocatalysts lies in the narrow light response range and fast recombination of photogenerated electron and hole pairs. [16][17][18][19] To address these issues, the development of efficient and robust photocatalysts for accelerating the water splitting reaction is of high priority.…”

A family of <inline-formula><tex-math id="M1">$ q $</tex-math></inline-formula>-congruences modulo the square of a cyclotomic polynomial

“…The m = 1 case of (1.3) was first conjectured by the author and Zudilin [9, Conjecture 4.13] and has already been proved by themselves in a recent paper [11]. For some other recent progress on q-congruences, the reader may consult [2,3,4,5,6,7,8,10,15].…”