A topological existence proof is presented for certain symmetrical periodic orbits of the collinear three-body problem with two equal masses, called Schubart orbits. The proof is based on the construction of a Wazewski setW in the phase space. The periodic orbits are found by a shooting argument in which symmetrical initial conditions enteringW are followed under the flow until they exit W. Top...

The multivariate reduced rank regression model plays an important role in econometrics. Examples include co-integration analysis and models with a factor structure. Geweke (1996) provided the foundations for a Bayesian analysis of this model. Unfortunately several of the full conditional posterior distributions, which forms the basis for constructing a Gibbs sampler for the poster distribution,...

Let G be a compact definable C group, X a compact affine definable CG manifold and 2 ≤ r < ∞. We prove that the set of equivariant definable Morse functions on X whose loci are finite unions of nondegenerate critical orbits is open and dense in the set of G invariant definable C functions with respect to the definable C topology.

Sequences are denoted by x — although C functions are involved in the sequel, their derivative are not explicitly used so this notation for sequences will not interfere with the usual one for derivatives. A function f : R −→ P(R) is a subset of R. Notations and theorems related to manifolds are taken from Hirsch[1]. Points belonging to manifolds will be denoted with tildes. The closed n-dimensi...

We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of n elements supporting access in time O(1) and insertion and deletion in time O(n ) for > 0 while using o(n) extra space. We consider several different implementation optimizations in C++ and compare their performance to that of vector and multiset from the standard library on sequences...

Alizadeh, Brandt, and Diebold [2002. Journal of Finance 57, 1047–1091] propose estimating stochastic volatility models by quasi-maximum likelihood using data on the daily range of the log asset price process. We suggest a related Bayesian procedure that delivers exact likelihood based inferences. Our approach also incorporates data on the daily return and accommodates a nonzero drift. We illust...

Memory leaks are a continuing problem in software developed with programming languages such as C and C++. A recent approach adopted by some researchers is to tolerate leaks in the software application and to reclaim the leaked memory by use of specially constructed memory allocation routines. However such routines replace the usual general purpose memory allocator and tend to be less efficient ...

A structured array is an array satisfying given constraints, such as being sorted or having no duplicate values. Generation of all arrays with a given structure up to some given length has many applications, including bounded exhaustive testing. A sequential generator of structured arrays can be defined by two C functions: the first one computes an initial array, and the second one steps from o...

In this paper, non-standard tight closure is proposed as an alternative for classical tight closure on finitely generated algebras over C. It has the advantage that it admits a functional definition, similar to the characteristic p definition of tight closure, where instead of the characteristic p Frobenius, its ultraproduct, the non-standard Frobenius, is used. This new closure operation cl(·)...

Some of the well-known fuzzy clustering algorithms are based on Euclidean distance function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, the former needs added constraint of fuzzy covariance matrix, the later can only be used for the d...