Student's t-statistic is a data-based linear transformation of an average. This paper proposes an extension i) to more general estimates including m.l.e.'s and M-estimates, and ii) to nonlinear transformations, so that the variance of the estimate is approximately constant. The expansion of the statistic and its properties are derived using basic procedures for the symbolic computation of asymp...

We develop a tight-binding model description of semi-Dirac electronic spectra, with highly anisotropic dispersion around point Fermi surfaces, recently discovered in electronic structure calculations of VO2-TiO2 nanoheterostructures. We contrast their spectral properties with the well-known Dirac points on the honeycomb lattice relevant to graphene layers and the spectra of bands touching each ...

In this article, we study an inverse boundary value problem for a Dirac-type equation. Let V be a bundle with a base manifold M which has a Dirac structure with a chirality operator F . We assume that we can observe on the lateral boundary ∂M ×R+ the boundary values of solutions of the Dirac-type equation in M × R+. When the coefficients of the Dirac-type equation are time-independent, i.e. we ...

We introduce a variational principle for field theories, referred to as the HamiltonPontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then d...

Anderson’s theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. γ-matrices are the only absolute objects of the Dirac equation. There are two ways of the γmatrices transformation: (1) γi is a 4-vector and ψ is a scalar, (2) γi are scalars and ψ is a spinor. ...

Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from t...

Statistical Rate Monotonic Scheduling (SRMS) is a generalization of the classical RMS results of Liu and Layland [LL73] for periodic tasks with highly variable execution times and statistical QoS requirements. The main tenet of SRMS is that the variability in task resource requirements could be smoothed through aggregation to yield guaranteed QoS. This aggregation is done over time for a given ...

The authors’ recent paper in Reports in Mathematical Physics develops Dirac reduction for cotangent bundles of Lie groups, which is called Lie– Dirac reduction. This procedure simultaneously includes Lagrangian, Hamiltonian, and a variational view of reduction. The goal of the present paper is to generalize Lie–Dirac reduction to the case of a general configuration manifold; we refer to this as...