Composition and structural formulas of ODP Site 200-1224 Eocene ferrobasalt minerals

The ~46-m.y.-old igneous basement cored during Leg 200 in the North Pacific represents one of the few cross sections of Pacific oceanic crust with a total penetration into basalt of >100 m. The rocks, emplaced during the Eocene at a fast-spreading rate (~14 cm/yr; full rate) are strongly differentiated tholeiitic basalts (ferrobasalts) with 7-4.5 wt% MgO, relatively high TiO2 (2-3.5 wt%), and total iron as Fe2O3 (9.1-16.8 wt%). The differentiated character of these lavas is related to unusually large amounts of crystallization differentiation of plagioclase, clinopyroxene, and olivine. The lithostratigraphy of the basement (cored to ~170 meters below seafloor) is divided into three units. The deepest unit (lithologic Unit 3), is a succession of lava flows of no more that a few meters thickness each. The intermediate unit (lithologic Unit 2) is represented by intermixed thin flows and pillows, whereas the shallowest unit (lithologic Unit 1), comprises two massive flows. The rocks range from aphyric to sparsely clinopyroxene-plagioclase-phyric (phenocryst content = <3 vol%) and from holocrystalline to hypohyaline. Chilled margins of pillow fragments show holohyaline to sparsely vitrophyric textures. Site 1224 oxide minerals present a type of alteration not previously seen, where titanomagnetite is only partially destroyed and the pure magnetite component is partially removed from the mineral, leaving, in the most extreme case, a nearly pure ulvöspinel residuum. As a result of this dissolution, iron, mainly in the oxidized state, is added to the circulating solvent fluids. This means that a considerable metal source can result from low-temperature reactions throughout the upper ocean crust. The coarsest-grained lithologic Unit 1 rocks have interstitial myrmekitic intergrowths of quartz and sodic plagioclase (~An12), roughly similar in mineralogy and bulk composition to tonalite/trondhjemite veinlets in abyssal gabbros from the southwest Indian Ocean and Hess Deep, eastern equatorial Pacific. Based on idiomorphic relationships and projections into the simplified Q-Ab-Or-H2O granite ternary system, the myrmekitic intergrowths formed at the same time as, or just after, the oxide minerals coprecipitated and at low water vapor pressure (~0.5 kbar). Their compositions correspond to SiO2-oligoclase intergrowths that are considerably less potassic than dacitic glasses that erupt, although rarely, along the East Pacific Rise or that have been produced experimentally by partial melting of gabbro. Based on the crystallization history and comparison to experimental data, the original interstitial siliceous liquids resulted from late-stage immiscible separation of siliceous and iron-rich liquids. The rare andesitic lavas found along the East Pacific Rise may be hybrid rocks formed by mixing of these immiscible siliceous melts with basaltic magma.

Differential resultant formulas for linear od-polynomials.

Ponencia

Reflexiones sobre los contratos maritimos : sacadas del Derecho Ciuil, y Canonico, del Consulado de Mar, y de los usos maritimos, con las formulas de los tales contratos ...

Sign.: [calderón]-3[calderón]4, 4[calderón]2, A-Z4, Aa-Tt4

Linear Sparse Differential Resultant Formulas

Let P be a system of n linear nonhomogeneous ordinary differential polynomials in a set U of n-1 differential indeterminates. Differential resultant formulas are presented to eliminate the differential indeterminates in U from P. These formulas are determinants of coefficient matrices of appropriate sets of derivatives of the differential polynomials in P, or in a linear perturbation Pe of P. In particular, the formula dfres(P) is the determinant of a matrix M(P) having no zero columns if the system P is ``super essential". As an application, if the system PP is sparse generic, such formulas can be used to compute the differential resultant dres(PP) introduced by Li, Gao and Yuan.

Sparse differential resultant formulas: between the linear and the nonlinear case

A matrix representation of the sparse differential resultant is the basis for efficient computation algorithms, whose study promises a great contribution to the development and applicability of differential elimination techniques. It is shown how sparse linear differential resultant formulas provide bounds for the order of derivation, even in the nonlinear case, and they also provide (in many cases) the bridge with results in the nonlinear algebraic case.