A pseudo-Anosov surface automorphism φ has associated to it an algebraic unit λφ called the dilatation of φ. It is known that in many cases λφ appears as the spectral radius of a Perron–Frobenius matrix preserving a symplectic form L. We investigate what algebraic units could potentially appear as dilatations by first showing that every algebraic unit λ appears as an eigenvalue for some integra...

In this paper, we introduce a method of generating the dual graph of the minimal normal resolution of the algebraic curve singularities. Using factorization of polynomials over algebraic extension field, we can calculate the dual graph from the coefficients of the given polynomial exactly. The computing process includes no approximation. We constructed the system to generate the dual graph on R...

A minor error in the necessary conditions for the algebraic form of the Lamé equation to have a finite projective monodromy group, and hence for it to have only algebraic solutions, is pointed out. [See F. Baldassarri, “On algebraic solutions of Lamé’s differential equation”, J. Differential Equations 41 (1) (1981), 44–58.] It is shown that if the group is the octahedral group , then the degree...

A computationally efficient method is proposed for computing the simplest normal forms of vector fields. A simple, explicit recursive formula is obtained for general differential equations. The most important feature of the approach is to obtain the “simplest” formula which reduces the computation demand to minimum. At each order of the normal form computation, the formula generates a set of al...

The Personal Responsibility and Work Opportunity Reconciliation Act of 1996 can be considered the centerpiece of welfare reform. Peter H. Rossi’s paper examines the contributions of current research projects to PRWORA evaluation, including the Urban Institute’s Assessing the New Federalism (ANF) project and its National Survey of America’s Families. Rossi seems to prefer social experiments to s...

The model of the human Type I ANF developed in this study is verified against measured temporal characteristic data from literature. In Chapter 2 a review is presented on the temporal characteristics investigated in this study. For the sake of completeness , the temporal characteristics not covered are briefly reviewed in this addendum. These are: 1. discharge rate 2. adaptation 3. alternation ...

Function synthesis is the problem of automatically constructing functions that fulfil a given specification. Using templates to limit the form of those functions is a popular way of reducing the search-space while still allowing interesting functions to be found. We present an investigation of restrictions to templates over Boolean functions of polynomial shape, based on their algebraic normal ...

Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generaliz...

In this paper a method is presented for computing the simplest normal form of differential equations associated with the singularity of a double zero eigenvalue. Based on a conventional normal form of the system, explicit formulae for both generic and nongeneric cases are derived, which can be used to compute the coefficients of the simplest normal form and the associated nonlinear transformati...