The reassignment method for the wavelet transform is investigated. Particularly good results are obtained if the wavelet is an extremal for the uncertainty relation of the affine group.

Hans Martin Reimann

The MACHO Collaboration's search for baryonic dark matter via its gravitational microlensing signature has generated a massive database of time ordered photometry of millions of stars in the LMC and the bulge of the Milky Way. The search's experimental design and capabilities are reviewed and the dark matter results are briefly noted. Preliminary analysis of the approximately 39,000 variable stars discovered in the LMC database is presented and examples of periodic variables are shown. A class of aperiodically variable Be stars is described which is the closest background to microlensing which has been found. Plans for future work on variable stars using the MACHO data are described.

K. H. Cook C. Alcock R. A. Allsman T. S. Axelrod K. C. Freeman B. A. Peterson P. J. Quinn A. W. Rodgers D. P. Bennett J. Reimann K. Griest S. L. Marshall M. R. Pratt C. W. Stubbs W. Sutherland D. Welch

In this outline we recognize the idea of complexity factor for static anisotropic self-gravitating source with generalized $f(R)$ metric gravity theory. In present consideration, we express the Einstein field equations, hydrostatic equilibrium equation, the mass function and physical behavior of $f(R)$ model by using some observational data of well known compact stars like $4U~1820-30, SAX~J1808.4-3658$ and $Her~X-1$. We define the scalar functions through the orthogonal splitting of the Reimann-Christofell tensor and then find the vanishing complexity condition for self-gravitating system with the help of these scalars. It has been found that the vanishing condition for the complexity are pressure anisotropy and energy density inhomogeneity must cancel each other. Moreover, we study the momentous results of an astral object for the vanishing of complexity factor. Finally, these solutions reduced to previous investigation about complexity factor in General Relativity by taking $\lambda=0$.

G. Abbas H. Nazar

We investigated the magnetic properties of two isostructural Ni(II) metal complexes [Ni4Lb8] and [Ni4Lc8]. In each molecule the four Ni(II) centers form almost perfect regular squares. Magnetic coupling and anisotropy of single crystals were examined by magnetization measurements and in particular by high-field torque magnetometry at low temperatures. The data were analyzed in terms of an effective spin Hamiltonian appropriate for Ni(II) centers. For both compounds, we found a weak intramolecular ferromagnetic coupling of the four Ni(II) spins and sizable single-ion anisotropies of the easy-axis type. The coupling strengths are roughly identical for both compounds, whereas the zero-field-splitting parameters are significantly different. Possible reasons for this observation are discussed.

R. Koch O. Waldmann P. Mueller U. Reimann R. W. Saalfrank

The MAGIC 17m diameter Cherenkov telescope will be upgraded with a second telescope within the year 2007. The camera of MAGIC-II will include several new features compared to the MAGIC-I camera. Photomultipliers with the highest available photon collection efficiency have been selected. A modular design allows easier access and flexibility to test new photodetector technologies. The camera will be uniformly equipped with 0.1 degree diamter pixels, which allows the use of an increased trigger area. Finally, the overall signal chain features a large bandwidth to retain the shape of the very fast Cherenkov signals.

C. C. Hsu A. Dettlaff D. Fink F. Goebel W. Haberer J. Hose R. Maier R. Mirzoyan W. Pimpl O. Reimann A. Rudert P. Sawallisch J. Schlammer S. Schmidl A. Stipp M. Teshima

We experimentally demonstrate the occurrence of negative absolute resistance (NAR) up to about $-1\Omega$ in response to an externally applied dc current for a shunted Nb-Al/AlO$_x$-Nb Josephson junction, exposed to a microwave current at frequencies in the GHz range. The realization (or not) of NAR depends crucially on the amplitude of the applied microwave current. Theoretically, the system is described by means of the resistively and capacitively shunted junction model in terms of a moderately damped, classical Brownian particle dynamics in a one-dimensional potential. We find excellent agreement of the experimental results with numerical simulations of the model.

J. Nagel D. Speer T. Gaber A. Sterck R. Eichhorn P. Reimann K. Ilin M. Siegel D. Koelle R. Kleiner

MAGIC comprises two 17m diameter IACTs to be operated in stereo mode. Currently we are commissioning the second telescope, MAGIC II. The camera of the second telescope has been equipped with 1039 pixels of 0.1-degree diameter. Always seven pixels are grouped in a hexagonal configuration to form a cluster. This modular design allows easier control and maintenance of the camera. The pixel sensors are high quantum efficiency photomultiplier tubes (PMTs) from Hamamatsu (superbialkali type, QE ~ 32% at the peak wavelength) that we operate at rather low gain of 30 k. This allows us to also perform extended observations under moderate moonlight. The system of two MAGIC telescopes will at least double the sensitivity compared to MAGIC I and also will allow us to lower the energy threshold.Here we will report the performances of the Camera of the second MAGIC telescope.

D. Borla Tridon F. Goebel D. Fink W. Haberer J. Hose C. C. Hsu T. Jogler R. Mirzoyan R. Orito O. Reimann P. Sawallisch J. Schlammer T. Schweizer B. Steinke M. Teshima

MAGIC-II is the second imaging atmospheric Cherenkov telescope of the MAGIC observatory, which has recently been inaugurated on Canary island of La Palma. We are currently developing a new camera based on clusters of hybrid photon detectors (HPD) for the upgrade of MAGIC-II. The photon detectors feature a GaAsP photocathode and an avalanche diode as electron bombarded anodes with internal gain, and were supplied by Hamamatsu Photonics K.K. (R9792U-40). The HPD camera with high quantum efficiency will increase the MAGIC-II sensitivity and lower the energy threshold. The basic performance of the HPDs has been measured and a prototype of an HPD cluster has been developed to be mounted on MAGIC-II. Here we report on the status of the HPD cluster and the project of eventually using HPD clusters in the central area of the MAGIC-II camera.

R. Orito E. Bernardini D. Bose A. Dettlaff D. Fink V. Fonseca M. Hayashida J. Hose E. Lorenz K. Mannheim R. Mirzoyan O. Reimann T. Y. Saito T. Schweizer M. Shayduk M. Teshima

This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with $1$-dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in general, is generalized Roter type, $Ein(3)$ and has pseudosymmetric Weyl conformal tensor satisfying the pseudosymmetric type condition $R\cdot R-Q(S,R)=\mathcal L' Q(g,C)$. The condition for which it satisfies the Roter type condition has been obtained. It is interesting to note that Melvin magnetic metric is pseudosymmetric and pseudosymmetric due to conformal tensor. Moreover such metric is $2$-quasi-Einstien, its Ricci tensor is Reimann compatible and Weyl conformal $2$-forms are recurrent. The Maxwell tensor is also pseudosymmetric type.

Absos Ali Shaikh Akram Ali Ali H. Alkhaldi Dhyanesh Chakraborty

We show that a dilute harmonically trapped two-component gas of fermionic atoms with a weak repulsive interaction has a pronounced super-shell structure: the shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the ``magic numbers'' occurring between the beat nodes by half a period. The length and amplitude of this beating mode depend on the strength of the interaction. We give a simple interpretation of the beat structure in terms of a semiclassical trace formula for the symmetry breaking U(3) --> SO(3).

Y. Yu M. Ogren S. Aberg S. M. Reimann M. Brack