Gravitational waves from coalescing neutron stars encode information about nuclear matter at extreme densities, inaccessible by laboratory experiments. The late inspiral is influenced by the presence of tides, which depend on the neutron star equation of state. Neutron star mergers are expected to often produce rapidly rotating remnant neutron stars that emit gravitational waves. These will provide clues to the extremely hot post-merger environment. This signature of nuclear matter in gravitational waves contains most information in the 2–4 kHz frequency band, which is outside of the most sensitive band of current detectors. We present the design concept and science case for a Neutron Star Extreme Matter Observatory (NEMO): a gravitational-wave interferometer optimised to study nuclear physics with merging neutron stars. The concept uses high-circulating laser power, quantum squeezing, and a detector topology specifically designed to achieve the high-frequency sensitivity necessary to probe nuclear matter using gravitational waves. Above 1 kHz, the proposed strain sensitivity is comparable to full third-generation detectors at a fraction of the cost. Such sensitivity changes expected event rates for detection of post-merger remnants from approximately one per few decades with two A+ detectors to a few per year and potentially allow for the first gravitational-wave observations of supernovae, isolated neutron stars, and other exotica.

We present motivations for and study feasibility of a small, rapid-optical/IR responsegamma-ray burst (GRB) space observatory. By analyzing existing GRB data, we give realisticdetection rates for X-ray and optical/IR instruments of modest size under actual flightconditions. Given new capabilities of fast optical/IR response (~1 s to target) andsimultaneous multi-band imaging, such an observatory can have a reasonable event rate,likely leading to new science. Requiring a Swift-like orbit, duty cycle,and observing constraints, a Swift-BAT scaled down to 190 cm2of detector area would still detect and locate about 25 GRB yr-1 for a triggerthreshold of 6.5σ. About 23% of X–ray located GRB would be detectedoptically for a 10 cm diameter instrument (~6 yr-1 for the6.5σ X-ray trigger).

We show that for every computable limit ordinal α, there is a computable structure that is categorical, but not relatively categorical (equivalently, it does not have a formally Scott family). We also show that for every computable limit ordinal α, there is a computable structure with an additional relation R that is intrinsically on , but not relatively intrinsically on (equivalently, it is not definable by a computable Σα formula with finitely many parameters). Earlier results in [7], [10], and [8] establish the same facts for computable successor ordinals α.

We describe the synthesis of nitrides of iridium and palladium using the laser-heated diamond anvil cell. We have used the in situ techniques of x-ray powder diffraction and Raman scattering to characterize these compounds and have compared our experimental findings where possible to the results of first-principles theoretical calculations. We suggest that palladium nitride is isostructural with pyrite, while iridium nitride has a monoclinic symmetry and is isostructural with baddeleyite.

We give a natural construction of framed mixed Tate motives unramified over $\mathbb{Z}$ whose periods are the multiple $\zeta$-values. Namely, for each convergent multiple $\zeta$-value we define two boundary divisors A and B in the moduli space $\overline{\mathcal{M}}_{0,n+3}$ of stable curves of genus zero. The corresponding multiple zeta-motive is the nth cohomology of the pair $(\overline{\mathcal{M}}_{0,n+3}-A,B)$.

In the previous works of the first author, two completely different constructions of single valued Grassmannian trilogarithms were given. One of the constructions, in Math. Res. Lett. 2 (1995), 99–114, is very simple and provides Grassmannian n-logarithms for all n. However its motivic nature is hidden. The other construction in Adv. in Math. 114 (1995), 197–318, is very explicit and motivic, but the generalization for n>4 is not known. In this paper we will compute explicitly the Grassmannian trilogarithm constructed in Math. Res. Lett. 2 (1995), 99–114 and prove that it differs from the motivic Grassmannian trilogarithm by an explicitly given product of logarithms. We also derive some general results about the Grassmannian polylogarithms.

We have developed multipurpose spectral technique for amplitude and phase measurements at frequencies 100–1000 GHz based on the use of backward wave oscillators (BWOs) as sources of probing radiation. It utilizes to the utmost all the remarkable advantages of BWOs such as high radiation intensity, monochromaticity, polarization, as well as high speed and wide range of frequency tuning. Extremely simple and flexible open-space measurement geometries are used. The developed technique seems to be the most appropriate and promising for the reliable, precise and mass characterization of materials and devices at millimeter-submillimeter waves.

The Zverev photographic vertical circle (PVC) of the Pulkovo observatory is in the process of modernization. The features of the vertical circle are:

1. a) Maksutov mirror-lens optical system with small aberrations and wide passband: aperture: 20 cm, focal length: 200 cm, focal scale: 103 arcsec/mm.

2. b) Very compact instrument: 140 cm total length, 60 cm — tube.

3. c) Wide field: 25 × 25 mm = 40′ × 40′. Wide-field imaging can be combined with meridian observations.

4. d) Easily-reversible instrument: reversing takes less than 30 seconds.

5. e) Two divided vertical circles of glass. Photoelectric circle reading microscopes.

6. f) Photographic micrometer in focal plane. This will be changed with a CCD micrometer.