Received (received date) Revised (revised date) Communicated by (Name of Editor) ABSTRACT In this paper we study the solution of stable generalized Lyapunov matrix equations with large-scale, dense coeecient matrices. Our iterative algorithms, based on the matrix sign function, only require scalable matrix algebra kernels which are highly ee-cient on parallel distributed architectures. This app...

Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifier Q into a first-order language enriched with a family of predicates Rs, for every arity i (or an infinitary predicate R) which takes Qz~(z, yl, . . . , y,~) to Vz(R(z, yl,..., g,~) --" ~b(x, Yl,..., Y,~)) (gl . . . . . g~ are precisely the free variables of Qzq~). The logic of Q (without ordinary quan...

One of the most important methods for solving the generalized eigenvalue problem Av = λBv is the QZ algorithm, which is a member of the larger class of GZ algorithms. These are normally implemented implicitly as bulge chasing algorithms. We show how to effect rational implicit GZ iterations by chasing bulges in both directions and passing them through each other. Application of this procedure t...

interest given by Wicksell.* It was obtained for the simplified system already mentioned, by Lange.f The remarks in this section are in fact a generalization or justification of this latter theory. The index relations are particularly interesting in discussing changes from one system to another consequent on the introduction or change of interest rate X. Thus, with the index of primary factors ...

A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties of the sequence of polynomials { 2Φ1(q−n, qb+1; q−c+b−n; q, qz)}n=0, where 0 < q < 1 and the complex parameters b, c and d are such that b = −1,−2, . . ., c− b+ 1 = −1,−2, . ...

with suggestions that fractionation of tholeiitic basalt in this pressure To model magmatic crystallization processes for mafic to intermediate range yields an alkalic basalt. Both trends may occur for natural compositions at high pressure, liquidus phase relations in the basalts depending on the Na2O content of the parental magma. forsterite–anorthite–diopside–silica (FADS) tetrahedron within ...

Natural fractures caused by tectonic stress in shale can not only improve the seepage capacity of shale, but also become migration and loss channel free gas. Calcite, quartz other minerals fracture veins record fluid evolution information shale. Through analysis different types cements Silurian–Ordovician Wufeng–Longmaxi Formations southern Sichuan Basin, effect on gas construction or destructi...

Holtz, F., Behrens, H., Dingwell, D.B. and Taylor, R.P., 1992. Water solubility in aluminosilicate melts of haplogranite composition at 2 kbar. In: Y. Bottinga, D.B. Dingwell and P. Richet (Guest-Editors), Silicate Melts. Chem. Geol., 96: 289-302. The compositional dependence of H20 solubility was investigated at 2 kbar and 800 °C in haplogranite melts (system SiO2-NaAISi3Os-KA1Si308 or Qz-Ab-O...