The Nature of the Peculiar Virgo Cluster Galaxies NGC 4064 and NGC 4424

We present a detailed study of the peculiar HI-deficient Virgo cluster spiral galaxies NGC 4064 and NGC 4424, using $^{12}$CO 1-0 interferometry, optical imaging and integral-field spectroscopic observations, in order to learn what type of environmental interactions have afected these galaxies. Optical imaging reveals that NGC 4424 has a strongly disturbed stellar disk, with banana-shaped isophotes and shells. NGC 4064, which lies in the cluster outskirts, possesses a relatively undisturbed outer stellar disk and a central bar. In both galaxies H-alpha emission is confined to the central kiloparsec. CO observations reveal bilobal molecular gas morphologies, with H-alpha emission peaking inside the CO lobes, implying a time sequence in the star formation process.Gas kinematics reveals strong bar-like non-circular motions in the molecular gas in both galaxies, suggesting that the material is radially infalling. In NGC 4064 the stellar kinematics reveal strong bar-like non-circular motions in the central 1 kpc. On the other hand, NGC 4424 has extremely modest stellar rotation velocities (Vmax ~ 30 km s-1), and stars are supported by random motions as far out as we can measure it. The observations suggest that the peculiarities of NGC 4424 are the result of an intermediate-mass merger plus ram pressure stripping. In the case of NGC 4064, the evidence suggests an already stripped "truncated/normal" galaxy that recently suffered a minor merger or tidal interaction with another galaxy. We propose that galaxies with "truncated/compact" H-alpha morphologies such as these are the result of the independent effects of ram pressure stripping, which removes gas from the outer disk, and gravitational interactions such as mergers, which heat stellar disks, drive gas to the central kpc and increase the central mass concentrations.Comment: 42 pages, 21 figure

Physical space description of decorated quasicrystals

In this paper the systematic method of dealing with the arbitrary decorations of quasicrystals is presented. The method is founded on the average unit cell formalism and operates in the physical space only, where each decorating atom manifests itself just by an additional component of the displacement density function in the average unit cell. Such approach allows us to use almost all classical crystallography algorithms for structure refining based on experimental data and may meaningly decrease the number of parameters which have to be fit. Further help for such analysis may be the use of proposed recently average Patterson function, here applied to decorated sets. As an example we present a description of a class of decorated quasicrystals based on Sturmian sequence of two interatomic spacings: we calculate explicitly structure factor, the shape of average Patterson function and give an algorithm for pattern analysis.Comment: 17 pages, 5 figure

The twisted fourth moment of the Riemann zeta function

We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length $T^{{1/11} - \epsilon}$Comment: 28 pages. v2: added reference

Prime numbers, quantum field theory and the Goldbach conjecture

Motivated by the Goldbach conjecture in Number Theory and the abelian bosonization mechanism on a cylindrical two-dimensional spacetime we study the reconstruction of a real scalar field as a product of two real fermion (so-called \textit{prime}) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators $b_{p}^{\dag}$ --labeled by prime numbers $p$-- acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allow us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.Comment: 20 pages in A4 format, 2 figure

Quantum Mechanical Interaction-Free Measurements

A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical applications for delicate quantum experiments.Comment: (revised file with no need for macro), 12, TAUP 1865-91

MACHO Mass Determination Based on Space Telescope Observation

We investigate the possibility of lens mass determination for a caustic crossing microlensing event based on a space telescope observation. We demonstrate that the parallax due to the orbital motion of a space telescope causes a periodic fluctuation of the light curve, from which the lens distance can be derived. Since the proper motion of the lens relative to the source is also measurable for a caustic crossing event, one can find a full solution for microlensing properties of the event, including the lens mass. To determine the lens mass with sufficient accuracy, the light curve near the caustic crossing should be observed within uncertainty of $\sim$ 1%. We argue that the Hubble Space Telescope observation of the caustic crossing supplied with ground-based observations of the full light curve will enable us to determine the mass of MACHOs, which is crucial for understanding the nature of MACHOs.Comment: 9 pages + 3 figures, accepted for publication in ApJ Letter

Pomeron loops in zero transverse dimensions

We analyze a toy model which has a structure similar to that of the recently found QCD evolution equations, but without transverse dimensions. We develop two different but equivalent methods in order to compute the leading-order and next-to-leading order Pomeron loop diagrams. In addition to the leading-order result which has been derived from Mueller's toy model~\cite% {Mueller:1994gb}, we can also calculate the next-to-leading order contribution which provides the $(\alpha_{s}^{2}\alpha Y)$ correction. We interpret this result and discuss its possible implications for the four-dimensional QCD evolution.Comment: 11 pages, 4 figure

Photoinduced Changes of Reflectivity in Single Crystals of YBa2Cu3O6.5 (Ortho II)

We report measurements of the photoinduced change in reflectivity of an untwinned single crystal of YBa2Cu3O6.5 in the ortho II structure. The decay rate of the transient change in reflectivity is found to decrease rapidly with decreasing temperature and, below Tc, with decreasing laser intensity. We interpret the decay as a process of thermalization of antinodal quasiparticles, whose rate is determined by an inelastic scattering rate of quasiparticle pairs.Comment: 4 pages, 4 figure

Analysis of survival following treatment of tumour-induced hypercalcaemia with intravenous pamidronate (APD).

The outcome of 114 patients with tumour-induced hypercalcaemia (TIH) treated between January 1992 and June 1993 with intravenous pamidronate (APD) was retrospectively analysed. The median overall survival was 55 days (range 3 days to > 21 months): 86 days if systemic anti-cancer therapy was available and only 35 days if not (P < 0.001). Survival was also significantly better for those who became normocalcaemic post APD (53 days vs 19 days, P < 0.001). There was no survival difference with respect to patient sex, age, tumour type, treatment of bone metastases with radiotherapy, initial calcium level, initial dose of APD or time from tumour diagnosis to first TIH. In those patients in whom systemic anti-cancer therapy is available, treatment with APD improves survival, but in all other patients the primary aim of treatment should be symptom control. This study confirms the dismal prognosis of TIH