Abstract. Clinopyroxene-only thermobarometry is one of the most practical tools to reconstruct crystallization pressures and temperatures of clinopyroxenes. Because it does not require any information of coexisting silicate melt or other co-crystallized mineral phases, it has been widely used to elucidate the physiochemical conditions of crystallizing magmas. However, previously calibrated clinopyroxene-only thermobarometers display low accuracy when being applied to mafic and intermediate magmatic systems. Hence, in this study, we present new empirical nonlinear barometric and thermometric models, which were formulated to improve the performance of clinopyroxene-only thermobarometry. Particularly, a total of 559 experimental runs conducted in the pressure range of 1 bar to 12 kbar have been used for calibration and validation of the new barometric and thermometric formulation. The superiority of our new models with respect to previous ones was confirmed by comparing their performance on 100 replications of calibration and validation, and the standard error of estimate (SEE) of the new barometer and thermometer are 1.66 kbar and 36.6 ∘C, respectively. Although our new barometer and thermometer fail to reproduce the entire test dataset, which has not been used for calibration and validation, they still perform well on clinopyroxenes crystallized from subalkaline basic to intermediate magmas (i.e., basaltic, basalt-andesitic, dacitic magma systems). Thus, their applicability should be limited to basaltic, basalt-andesitic and dacitic magma systems. In a last step, we applied our new thermobarometer to several tholeiitic Icelandic eruptions and established magma storage conditions exhibiting a general consistency with phase equilibria experiments. Therefore, we propose that our new thermobarometer represents a powerful tool to reveal the crystallization conditions of clinopyroxene in mafic to intermediate magmas.

This paper investigates the multiuser power control problem in relay-assisted anti-jamming systems. Because of the hierarchical confrontation characteristics between users and jammer, we take the incomplete information and observation error into consideration and formulate an anti-jamming Bayesian three-layer Stackelberg game, in which primary users act as leaders, relay users act as vice-leaders, and jammer acts as a follower. Both users and jammer have the ability to sense others' transmission power and choose optimal power to realize the maximum of utility. Based on the backward induction method, we propose a multiuser hierarchical iterative algorithm to obtain the Stackelberg equilibrium (SE) and prove the existence and uniqueness of SE. Finally, simulation results are compared with the Nash equilibrium to verify the effectiveness of the proposed game. Moreover, both the influence of incomplete information and the observation error on utility are analyzed. INDEX TERMS Power control, anti-jamming, three-layer Stackelberg game, Stackelberg equilibrium.

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