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Abstract Amorphous carbons can have drastically different physical properties depending on synthetic methods. Among these, hydrogenated diamond-like carbon (HDLC) produced via plasma-enhanced chemical vapor deposition is unique in that it exhibits superlubricity with a coefficient of friction (COF) less than 0.01 in proper environmental conditions. It is known that HDLC undergoes friction-induced graphitization at the shear interface and forms a highly hydrogenated transfer film at the counter-surface sliding against it. In contrast, glassy carbon (GC) produced via pyrolysis of organic precursors rarely exhibits superlubricious behavior even though the graphitic nature probed with Raman spectroscopy is similar to that of the transfer film formed from HDLC. This study addresses this drastic difference in friction of HDLC and GC and identifies key parameters that can be tuned to achieve (nearly) superlubricious behaviors with GC. The factors influencing the superlubricity of amorphous carbon include the composition and structure of the initial carbon coating, which strongly depend on the synthetic method, and the coating failure and transfer film stability, which depend on the surface chemistry of the substrate. 

Let $E/\mathbf{Q}$be an elliptic curve and let $p$be an odd prime of good reduction for $E$. Let $K$be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which $p$splits. The goal of this paper is two-fold: (1) we formulate a $p$-adic BSD conjecture for the $p$-adic $L$-function $L_{\mathfrak{p}}^{\mathrm{B}\mathrm{D}\mathrm{P}}$introduced by Bertolini–Darmon–Prasanna [Duke Math. J. 162 (2013), pp. 1033–1148]; and (2) for an algebraic analogue $F_{\stackrel{¯<\#comment/>}{\mathfrak{p}}}^{\mathrm{B}\mathrm{D}\mathrm{P}}$of $L_{\mathfrak{p}}^{\mathrm{B}\mathrm{D}\mathrm{P}}$, we show that the “leading coefficient” part of our conjecture holds, and that the “order of vanishing” part follows from the expected “maximal non-degeneracy” of an anticyclotomic $p$-adic height. In particular, when the Iwasawa–Greenberg Main Conjecture $\left(F_{\stackrel{¯<\#comment/>}{\mathfrak{p}}}^{\mathrm{B}\mathrm{D}\mathrm{P}}\right)=\left(L_{\mathfrak{p}}^{\mathrm{B}\mathrm{D}\mathrm{P}}\right)$is known, our results determine the leading coefficient of $L_{\mathfrak{p}}^{\mathrm{B}\mathrm{D}\mathrm{P}}$at $T=0$up to a $p$-adic unit. Moreover, by adapting the approach of Burungale–Castella–Kim [Algebra Number Theory 15 (2021), pp. 1627–1653], we prove the main conjecture for supersingular primes $p$under mild hypotheses. In the $p$-ordinary case, and under some additional hypotheses, similar results were obtained by Agboola–Castella [J. Théor. Nombres Bordeaux 33 (2021), pp 629–658], but our method is new and completely independent from theirs, and apply to all good primes. 

By investigating second coordination sphere effects on the magnetic anisotropy of a Co(ii) single molecule magnet (SMM), we aim to clarify their role in magneto-structural correlations to enhance the performance of transition metal SMMs.