Tate (co)homology via pinched complexes

For complexes of modules we study two new constructions, which we call the pinched tensor product and the pinched Hom. They provide new methods for computing Tate homology and Tate cohomology, which lead to conceptual proofs of balancedness of Tate (co)homology for modules over associative rings. Another application we consider is in local algebra. Under conditions of vanishing of Tate (co)homology, the pinched tensor product of two minimal complete resolutions yields a minimal complete resolution.Comment: Final version; 23 pp. To appear in Trans. Amer. Math. So

On the Distribution of Random variables corresponding to Musielak-Orlicz norms

Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of the vector $(x_iX_i)_{i=1}^n$ is of the order $\| x \|_M$ (up to constants dependent on p only). In case $p=2$ we need the function $t\mapsto tM'(t) - M(t)$ to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into $L_1[0,1]$. We also provide a general result replacing the $\ell_p$-norm by an arbitrary $N$-norm. This complements some deep results obtained by Gordon, Litvak, Sch\"utt, and Werner. We also prove a result in the spirit of their work which is of a simpler form and easier to apply. All results are true in the more general setting of Musielak-Orlicz spaces

Isotropic magnetometry with simultaneous excitation of orientation and alignment CPT resonances

Atomic magnetometers have very high absolute precision and sensitivity to magnetic fields but suffer from a fundamental problem: the vectorial or tensorial interaction of light with atoms leads to "dead zones", certain orientations of magnetic field where the magnetometer loses its sensitivity. We demonstrate a simple polarization modulation scheme that simultaneously creates coherent population trapping (CPT) in orientation and alignment, thereby eliminating dead zones. Using $^{87}$Rb in a 10 Torr buffer gas cell we measure narrow, high-contrast CPT transparency peaks in all orientations and also show absence of systematic effects associated with non-linear Zeeman splitting.Comment: 4 pages, 4 figure

Optimization of graded multilayer designs for astronomical x-ray telescopes

We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-γ-ray telescopes based on the instrument’s bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si

Spectroscopy of a synthetic trapped ion qubit

$^{133}\text{Ba}^+$ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus and visible wavelength electronic transitions. Using a microgram source of radioactive material, we trap and laser-cool the synthetic $A$ = 133 radioisotope of barium II in a radio-frequency ion trap. Using the same, single trapped atom, we measure the isotope shifts and hyperfine structure of the $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $6^2 \text{S}_{1/2}$ and $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $5^2 \text{D}_{3/2}$ electronic transitions that are needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits. We also report the $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $5^2 \text{D}_{3/2}$ electronic transition isotope shift for the rare $A$ = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes

Archaeology of Atafu, Tokelau: Some initial results from 2008

Surface survey, shovel testing, and stratigraphic excavations were done on Atafu Atoll in Tokelau during August 2008. Initial results suggest that Fale Islet has the most potential for further archaeological research. Dense cultural deposits on this islet are >1 m (39 in.) deep. Cultural material recovered includes food bone, fire-affected volcanic rock, tool-grade basalt flakes and tool fragments, Tridacna shell adzes, and pearl-shell fishhook fragments. Dog bone occurs from the earliest deposits through to the late prehistoric, while pig bone is found only in historic contexts. Fish bone is common throughout, and, with the exception of Tridacna, there are few edible mollusk remains. Initial EDXRF (Energy Dispersive X-Ray Fluorescence) analyses have found the basalt to be consistent with documented sources on Tutuila, Samoa. Basal radiocarbon dates from two excavation units are 660-540 cal. BP and 500-310 cal. BP (at 2σ)

New Constraints on Quantum Gravity from X-ray and Gamma-Ray Observations

One aspect of the quantum nature of spacetime is its "foaminess" at very small scales. Many models for spacetime foam are defined by the accumulation power $\alpha$, which parameterizes the rate at which Planck-scale spatial uncertainties (and thephase shifts they produce) may accumulate over large path-lengths. Here $\alpha$ is defined by theexpression for the path-length fluctuations, $\delta \ell$, of a source at distance $\ell$, wherein $\delta \ell \simeq \ell^{1 - \alpha} \ell_P^{\alpha}$, with $\ell_P$ being the Planck length. We reassess previous proposals to use astronomical observations ofdistant quasars and AGN to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from {\em Chandra} to set the constraint $\alpha \gtrsim 0.58$, which rules out the random walk model (with $\alpha = 1/2$). Much firmer constraints canbe set utilizing detections of quasars at GeV energies with {\em Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $\alpha \gtrsim 0.67$ and $\alpha \gtrsim 0.72$, respectively. These limits on $\alpha$ seem to rule out $\alpha = 2/3$, the model of some physical interest.Comment: 11 pages, 9 figures, ApJ, in pres