Semidefinite Representation of the kk-Ellipse

The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if $k$ is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted $k$-ellipses and $k$-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure

Classes of exact wavefunctions for general time-dependent Dirac Hamiltonians in 1+1 dimensions

In this work we construct two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in 1+1 dimensions. Some problems regarding to some formal solutions in the literature are discussed. Finally the existence of a generalized Lewis-Riesenfeld invariant connected with such solutions is discussed

A new method of angular correlation measurements

A new type of angular correlation apparatus is described, and a mathematical model of its statistics is given. The angular correlation of coincident nuclear radiations can be measured by detecting intensity correlations in the output of two counters. For prompt coincidences, the detector currents are mixed in a broadband circuit whose output is the product of the two inputs. The time-average output of the mixer is shown to be proportional to the rate of true coincidences, and therefore to the angular correlation function. Furthermore, the fluctuation of this output has the same ratio to the average current as the rate of random to true coincidences both for weak and strong sources. For delayed coincidences, other circuits give the time spectrum and the frequency spectrum of the perturbed correlation function. Possible applications are mentioned, and the relation to the Brown-Twiss interferometer is clarified.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32868/1/0000246.pd

Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited

We show the David-Jerison construction of big pieces of Lipschitz graphs inside a corkscrew domain does not require its surface measure be upper Ahlfors regular. Thus we can study absolute continuity of harmonic measure and surface measure on NTA domains of locally finite perimeter using Lipschitz approximations. A partial analogue of the F. and M. Riesz Theorem for simply connected planar domains is obtained for NTA domains in space. As a consequence every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure

Has the evolution of complexity in the amphibian papilla influenced anuran speciation rates?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72375/1/j.1420-9101.2006.01079.x.pd

Spatial Periodicity of Galaxy Number Counts, CMB Anisotropy, and SNIa Hubble Diagram Based on the Universe Accompanied by a Non-Minimally Coupled Scalar Field

We have succeeded in establishing a cosmological model with a non-minimally coupled scalar field $\phi$ that can account not only for the spatial periodicity or the {\it picket-fence structure} exhibited by the galaxy $N$-$z$ relation of the 2dF survey but also for the spatial power spectrum of the cosmic microwave background radiation (CMB) temperature anisotropy observed by the WMAP satellite. The Hubble diagram of our model also compares well with the observation of Type Ia supernovae. The scalar field of our model universe starts from an extremely small value at around the nucleosynthesis epoch, remains in that state for sufficiently long periods, allowing sufficient time for the CMB temperature anisotropy to form, and then starts to grow in magnitude at the redshift $z$ of $\sim 1$, followed by a damping oscillation which is required to reproduce the observed picket-fence structure of the $N$-$z$ relation. To realize such behavior of the scalar field, we have found it necessary to introduce a new form of potential $V(\phi)\propto \phi^2\exp(-q\phi^2)$, with $q$ being a constant. Through this parameter $q$, we can control the epoch at which the scalar field starts growing.Comment: 19 pages, 18 figures, Accepted for publication in Astrophysics & Space Scienc

M-theory on a Time-dependent Plane-wave

We propose a matrix model on a homogeneous plane-wave background with 20 supersymmetries. This background is anti-Mach type and is equivalent to the time-dependent background. We study supersymmetries in this theory and calculate the superalgebra. The vacuum energy of the abelian part is also calculated. In addition we find classical solutions such as graviton solution, fuzzy sphere and hyperboloid.Comment: 19pages, no figures, LaTeX, JHEP3.cl

Constraining the MSSM with universal gaugino masses and implication for searches at the LHC

Using a Markov chain Monte Carlo approach, we find the allowed parameter space of a MSSM model with seven free parameters. In this model universality conditions at the GUT scale are imposed on the gaugino sector. We require in particular that the relic density of dark matter saturates the value extracted from cosmological measurements assuming a standard cosmological scenario. We characterize the parameter space of the model that satisfies experimental constraints and illustrate the complementarity of the LHC searches, B-physics observables and direct dark matter searches for further probing the parameter space of the model. We also explore the different decay chains expected for the coloured particles that would be produced at LHC.Comment: 29 pages, 11 figure

Constraints on early dark energy from CMB lensing and weak lensing tomography

Dark energy can be studied by its influence on the expansion of the Universe as well as on the growth history of the large-scale structure. In this paper, we follow the growth of the cosmic density field in early dark energy cosmologies by combining observations of the primary CMB temperature and polarisation power spectra at high redshift, of the CMB lensing deflection field at intermediate redshift and of weak cosmic shear at low redshifts for constraining the allowed amount of early dark energy. We present these forecasts using the Fisher-matrix formalism and consider the combination of Planck-data with the weak lensing survey of Euclid. We find that combining these data sets gives powerful constraints on early dark energy and is able to break degeneracies in the parameter set inherent to the various observational channels. The derived statistical 1-sigma-bound on the early dark energy density parameter is sigma(Omega_d^e)=0.0022 which suggests that early dark energy models can be well examined in our approach. In addition, we derive the dark energy figure of merit for the considered dark energy parameterisation and comment on the applicability of the growth index to early dark energy cosmologies.Comment: 25 pages, 14 figures, 3 tables; v2: very minor additions, updated to match version to be published in JCA