Proof That a Dominant Endmember Formula Can Always Be Written for a Mineral or a Crystal Structure

An endmember formula must be: (1) conformable with the crystal structure of the mineral, (2) electroneutral (i.e., not carry a net electric charge), and (3) irreducible [i.e., not capable of being factored into components that have the same bond topology (atomic arrangement) as that of the original formula]. The stoichiometry of an endmember formula must match the “stoichiometry” of the sites in the structure; for ease of expression, I denote such a formula here as a chemical endmember. In order for a chemical endmember to be a true endmember, the corresponding structure must obey the valence-sum rule of bond-valence theory. For most minerals, the chemical endmember and the (true) endmember are the same. However, where local order would lead to strong deviation from the valence-sum rule for some local arrangements, such arrangements cannot occur and the (true) endmember differs from the chemical endmember. I present heuristic and algebraic proofs that a specific chemical formula can always be represented by a corresponding dominant endmember formula. That dominant endmember may be derived by calculating the difference between the mineral formula considered and all of the possible endmember compositions; the endmember formula which is closest to the mineral formula considered is the dominant endmember.

Optical phase curve of the ultra-hot Jupiter WASP-121b

We present the analysis of TESS optical photometry of WASP-121b, which reveals the phase curve of this transiting ultra-hot Jupiter. Its hotspot is located at the sub-stellar point, showing inefficient heat transport from the dayside (2870 ± 50 K) to the nightside (<2500 K at 3σ) at the altitudes probed by TESS. The TESS eclipse depth, measured at the shortest wavelength to date for WASP-121b, confirms the strong deviation from blackbody planetary emission. Our atmospheric retrieval on the complete emission spectrum supports the presence of a temperature inversion, which can be explained by the presence of VO and possibly TiO and FeH. The strong planetary emission at short wavelengths could arise from an H− continuum.

WORDS DENOTING WRESTLING IN KHAKAS AND TUVIN LANGUAGES (ON THE ORIGIN OF THE WORD KüRES / HүREš)

The article analyzes the possibilities of word variation in the development of the semantic (lexical) system of language. The necessity of this study is determined by the fact that in Khakass and Tuva linguistics there are not enough works devoted to development patterns of categorical semantics of the word. The article defines how the meaning of words found in proto-languages is advanced at further stages of language development. The obtained results demonstrate that the original words with the semantics in question already existed in the Old-Turkic era. Their semantic development is characterized by its own logic: the vector is set by the inner form of an ancient root (kүš, küs); during affixation (küres, hүreš), the choice of the motivating root is observed. The hypothesis is proven that for different Turkic languages, the vector can be either “the same” or different. In the second case, the distinctive lines, although visible enough, extend within certain limits: even with a sufficiently strong deviation from a given line of variation, they maintain a deep bond with the semantics of the original root...