Experimental evidence on the origin of Ca-rich carbonated melts formed by interaction between sedimentary limestones and mantle-derived ultrabasic magmas

In this experimental study, we documented the formation of strongly ultrabasic and ultracalcic melts through the interaction of melilititic and basanitic melts with calcite. Three strongly to moderately SiO2-undersaturated volcanic rocks from the Bohemian Massif (central Europe) were mixed with 10, 30, and 50 wt% CaCO3 and melted at 1100, 1200, and 1300 °C at 2 kbar to evaluate the maximum amount of carbonate that can be assimilated by natural ultrabasic melts at shallow depths. Experiments revealed a surprisingly complete dissolution of the CaCO3, only rarely reaching carbonate saturation, with typical liquidus phases represented by olivine, spinel, melilite, and clinopyroxene. Only in the runs with the most SiO2-undersaturated compositions did abundant monticellite form instead of clinopyroxene. For all starting mixtures, strongly ultrabasic (SiO2 down to 15.6 wt%), lime-rich (CaO up to 43.6 wt%), ultracalcic (CaO/Al2O3 up to ~27) melt compositions were produced at 1200 and 1300 °C, with up to ~25 wt% dissolved CO2. When present, quenched olivine showed much higher forsterite content (Fo95–97) than olivine in the natural samples (Fo79–85). The two major results of this study are (1) silicate-carbonatite melt compositions do not necessarily imply the existence of carbonatitic components in the mantle, because they are also produced during limestone assimilation, and (2) Fo-rich olivines cannot be used to infer any primitive character of the melt nor high potential temperature (Tp).

Bartók and the Violin Music of Maramureș

The Second Rhapsody, one of Bartók’s technically most demanding concert pieces for violin, arranges archaic-improvisatory bagpipe imitations for concert performance. The arrangement itself shows a well-designed, coherent structure: the succession of dances, tonally and motivically related between each other, outline a kind of evolutionary progression from free motive-structure to strophic form. Bagpipe-music had a long-term influence on Bartók’s violin music, figuring as episodes in original works like the two Violin Sonatas or the Violin Concerto; but none exploits the genre to such an extent as the Second Rhapsody. The violin pieces with motive-structure of fascinatingly wild and virtuoso character were among Bartók’s major discoveries of the collecting trips to the Maramureş region. For the Rhapsody Bartók chose melodies from the one-time Ugocsa county, whose music, closely related to that of Maramureş county, was considered by him “the most interesting in our country [i.e., Hungary of the time], due exactly to its primitive character.” In Maramureş these melodies are less eccentric; instead, the violinists have a broader and more varied repertoire of dance music. In my article I discuss the different types of violin music of this region, focusing on structural, melodic, or interpretational elements that were of special interest for the composer. For this investigation I have made use of the primary sources of the respective collections: phonogram recordings, field notations, later transcriptions.

A Pólya–Vinogradov inequality for short character sums

In this paper, we obtain a variation of the Pólya–Vinogradov inequality with the sum restricted to a certain height. Assume $\chi $ to be a primitive character modulo q, $ \epsilon>0$ and $N\le q^{1-\gamma }$ , with $0\le \gamma \le 1/3$ . We prove that $$ \begin{align*} |\sum_{n=1}^N \chi(n) |\le c (\tfrac{1}{3} -\gamma+\epsilon )\sqrt{q}\log q \end{align*} $$ with $c=2/\pi ^2$ if $\chi $ is even and $c=1/\pi $ if $\chi $ is odd. The result is based on the work of Hildebrand and Kerr.

Short Character Sums and the Pólya–Vinogradov Inequality

We show in a quantitative way that any odd primitive character χ modulo q of fixed order g ≥ 2 satisfies the property that if the Pólya–Vinogradov inequality for χ can be improved to $$\begin{equation*} \max_{1 \leq t \leq q} \left|\sum_{n \leq t} \chi(n)\right| = o_{q \rightarrow \infty}(\sqrt{q}\log q) \end{equation*}$$ then for any ɛ > 0 one may exhibit cancellation in partial sums of χ on the interval [1, t] whenever $t \gt q^{\varepsilon}$, i.e., $$\begin{equation*} \sum_{n \leq t} \chi(n) = o_{q \rightarrow \infty}(t)\ \text{for all } t \gt q^{\varepsilon}. \end{equation*}$$ We also prove a converse implication, to the effect that if all odd primitive characters of fixed order dividing g exhibit cancellation in short sums then the Pólya–Vinogradov inequality can be improved for all odd primitive characters of order g. Some applications are also discussed.

Irreducible products of characters

We introduce the notion of Fitting characters for arbitrary finite groups, and prove that under some conditions the product of these characters is irreducible and the unique factorization of this form also holds. Moreover, we show that any nonlinear quasi-primitive character of solvable groups can be uniquely factored (up to multiplication by linear characters) as the product of certain Fitting characters on some extension groups.

______ is necessary for interpreting a proposition

In Natural propositions (2014), Stjernfelt contends that the interpretation of a proposition or dicisign requires the joint action of two kinds of signs. A proposition must contain a sign that conveys a general quality. This function can be served by a similarity-based icon or code-based symbol. In addition, a proposition must situate or apply this general quality, so that the predication can become liable of being true or false. This function is served by an index. Stjernfelt rightly considers the co-localization of these two parts to be a primitive phenomenon. Although this primitive character would seem to bar any further analysis, I endeavor to clarify the degree of proximity sufficient to enable co-localization. Siding with Pietarinen (2014), who argues that the whole issue should not be construed in metric terms, I conclude that one cannot make sense of propositional co-localization without appealing to some form of first-person perspective.

On quasi-primitive characters of solvable groups

Let [Formula: see text] be a quasi-primitive character with odd degree, and suppose that [Formula: see text] is a [Formula: see text]-solvable group. Wilde associated to [Formula: see text] a unique conjugacy class of subgroups [Formula: see text] satisfying [Formula: see text]. We construct in this situation a sequence of character pairs [Formula: see text], where [Formula: see text] is quasi-primitive and each [Formula: see text] is uniquely determined up to conjugacy in [Formula: see text], such that [Formula: see text] and [Formula: see text]. Furthermore, we have [Formula: see text] for each [Formula: see text], and in particular [Formula: see text]. We also prove that the subgroups [Formula: see text] and [Formula: see text] are conjugate in [Formula: see text], and thus present a new description for Wilde’s result.

Primitive characters of maximal subgroups of M-groups

Let [Formula: see text] be a maximal subgroup of an [Formula: see text]-group [Formula: see text] with odd index and let [Formula: see text] be primitive. Lewis proved in this situation that [Formula: see text] divides [Formula: see text], and Isaacs and Wilde further refined this result by showing that either [Formula: see text] or [Formula: see text]. In this paper, we present an independent and simpler proof for these remarkable results and thereby obtain more detailed information regarding the structure of the group [Formula: see text] and the primitive character [Formula: see text]. In particular, [Formula: see text] is strongly irreducible in the sense of Brauer.