We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar, R, of arbitrary degree, n, in arbitrary dimension, D. The global properties of all such solutions are derived by studying the phase space of field equations in the equivalent theory of gravity coupled to a scalar field, which is obtained by a field redefinition and conformal transf...

Numerical methods for eigenvalue problems associated to alternating matrix pencils and polynomials are discussed. These problems arise in a large number of control applications for differential-algebraic equations ranging from regular and singular linear-quadratic optimal and robust control to dissipativity checking. We present a survey of several of these applications and give a systematic ove...

A general theory is given for discretized versions of the Galerkin method for solving Fredholm integral equations of the second kind. The discretized Galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the Galerkin method. The theoretical framework that is given parallels that of the regular Galerkin method, including the error analysis of the sup...

Combining the FH entropy of mixing and the standard RS enthalpy of mixing yields the FH solution theory for polymers: ∆G N = Bφ1φ2 + RT (φ1 lnφ1 + φ2 N lnφ2). As written above, this equation is comparable to the free energy of mixing from the Regular Solution Model. Notice that the expressions differ in two ways: first, FH is cast in volume fractions rather than mole fractions, and second, FH i...

Four dimensional N = 1 theories are engineered by compactifying six dimensional (2, 0) theory on a Riemann surface with regular punctures. A generalized Hitchin’s equation involving two Higgs fields is proposed as the BPS equation for N = 1 compactification. The puncture is interpreted as the singular boundary condition of this equation, and regular puncture is shown to be labeled by a nilpoten...

A fluorescence probe study on micellization of the binary surfactant system formed by n-octyl-d-thioglucopyranoside (OTG) and sodium dodecyl sulphate (SDS) in 0.1 M NaCl aqueous solutions has been carried out. The CMC experimental data, as obtained by the pyrene 1:3 ratio method, have been analyzed in the context of the pseudophase separation model. The interaction parameter (β12) determined by...

In this paper we show that ωBand ωS-regular languages satisfy the following separation-type theorem If L1, L2 are disjoint languages of ω-words both recognised by ωB(resp. ωS)automata then there exists an ω-regular language Lsep that contains L1, and whose complement contains L2. In particular, if a language and its complement are recognised by ωB(resp. ωS)automata then the language is ω-regula...

We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang-Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind of scalar graviton, or as approximate solutions of Einstein-Yang-Mills theory. We focus on platonic solutions with cubic symmetry, related to a rational map o...

In this paper, we exhibit a one-to-one correspondence between ω-regular languages and a subclass of regular cost functions over finite words, called ω-regular like cost functions. This bridge between the two models allows one to readily import classical results such as the last appearance record or the McNaughton-Safra constructions to the realm of regular cost functions. In combination with ga...

The numerical solution of boundary value problems for linear systems of first order equations with a regular singular point at one endpoint is considered. The standard procedure of expanding about the singularity to get a nonsingular problem over a reduced interval is justified in some detail. Quite general boundary conditions are included which permit unbounded solutions. Error estimates are g...