On the ternary complex analysis and its applications

Previouly a possible extension of the complex number, together with its connected trigonometry was introduced. In this paper we focuss on the simplest case of ternary complex numbers. Then, some types of holomorphicity adapted to the ternary complex numbers and the corresponding results upon integration of differential forms are given. Several physical applications are given, and in particuler one type of holomorphic function gives rise to a new form of stationary magnetic field. The movement of a monopole type object in this field is then studied and shown to be integrable. The monopole scattering in the ternary field is finally studied.Comment: LaTeX 28 page

On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere

Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. For these applications, it is of interest to obtain analytic expressions, and we present the reduction of a number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related series have additional applications in quantum and statistical physics and chemistry.Comment: 17 pages, no figure

A Generalization of Chetaev's Principle for a Class of Higher Order Non-holonomic Constraints

The constraint distribution in non-holonomic mechanics has a double role. On one hand, it is a kinematic constraint, that is, it is a restriction on the motion itself. On the other hand, it is also a restriction on the allowed variations when using D'Alembert's Principle to derive the equations of motion. We will show that many systems of physical interest where D'Alembert's Principle does not apply can be conveniently modeled within the general idea of the Principle of Virtual Work by the introduction of both kinematic constraints and variational constraints as being independent entities. This includes, for example, elastic rolling bodies and pneumatic tires. Also, D'Alembert's Principle and Chetaev's Principle fall into this scheme. We emphasize the geometric point of view, avoiding the use of local coordinates, which is the appropriate setting for dealing with questions of global nature, like reduction.Comment: 27 pages. Journal of Mathematical Physics (to zappear

A massive Feynman integral and some reduction relations for Appell functions

New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses $m_1^2$ and $m_2^2$ in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with respect to the masses $m_i^2$. Equating our expressions with previously known results in terms of Gauss hypergeometric functions yields reduction relations for the involved Appell functions that are apparently new mathematical results.Comment: 19 pages. To appear in Journal of Mathematical Physic

Analytical and numerical methods for massive two-loop self-energy diagrams

Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and especially four dimensions.This is done in three respects firstly results in terms of generalized, multivariable hypergeometric functions are presented giving explicit series for small and large momenta. Secondly the imaginary parts of these integrals are expressed as complete elliptic integrals.Finally one-dimensional integral representations with elementary functions are derived.They are very well suited for the numerical evaluations.Comment: 24 page

Multi-Dimensional Hermite Polynomials in Quantum Optics

We study a class of optical circuits with vacuum input states consisting of Gaussian sources without coherent displacements such as down-converters and squeezers, together with detectors and passive interferometry (beam-splitters, polarisation rotations, phase-shifters etc.). We show that the outgoing state leaving the optical circuit can be expressed in terms of so-called multi-dimensional Hermite polynomials and give their recursion and orthogonality relations. We show how quantum teleportation of photon polarisation can be modelled using this description.Comment: 10 pages, submitted to J. Phys. A, removed spurious fil

A Contingency Theory Approach to the Deployment of Lean Principles: The Case of Advanced Research and Complex Product Development Environments.

The introduction of lean principles is a common approach for organizations seeking to improve quality, lower cost, and shorten time to market. Many companies have applied lean to manufacturing, but a smaller number have brought it upstream to product development. This research focuses on how organizations can begin the transformation to lean product development through three essays. The first study is a comparative case analysis comparing approaches based on “rational planning” and “disciplined problem solving” to identify their relative advantages and disadvantages and organizational characteristics that enable successful deployment. The comparison shows that in the case of non-routine processes like product development the disciplined problem solving approach is more effective, while the rational planning approach can be effective for highly routine aspects of the job. The second study is an in-depth case study of how value stream mapping and obeya, two common lean product development tools, if used properly, can help cross-functional development teams achieve coordination and integration as well as team member engagement. This facilitates the learning of lean as a socio-technical system with a culture of problem solving and people development through the effective development of a product. The third study looks at how standardization can be used to establish an enabling bureaucracy with structures and standards effectively supporting people’s work. A common misunderstanding is that standardization kills creativity. It can be used to create predictability while maintaining flexibility and enabling innovation. Coercive bureaucracies result when formalization is used to control employees or when there is a misalignment between task requirements and the standards and/or organizational design. Having the people doing the work develop, maintain, continuously improve, and adapt the standards is an effective way to create an enabling bureaucracy. The insights from this study help to understand the challenges of lean deployment and characteristics that enable success in lean transformations. This can serve as an example to aid in the transformation to lean systems in other complex environments.Ph.D.Industrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89773/1/appell_1.pd

On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere

Producción CientíficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context

Integral representations of q-analogues of the Hurwitz zeta function

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this q-analogue. All the discussion developed here is entirely different from the previous work in [4]Comment: 14 page