On bilinear invariant differential operators acting on tensor fields on the symplectic manifold

Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$, in other words, $T(V)$ is the space of tensor fields of type $V$ on $M$ on which the group \Diff (M) of diffeomorphisms of $M$ naturally acts. Elsewhere, the author classified the \Diff (M)-invariant differential operators $D: T(V_{1})\otimes T(V_{2})\longrightarrow T(V_{3})$ for irreducible fibers with lowest weight. Here the result is generalized to bilinear operators invariant with respect to the group \Diff_{\omega}(M) of symplectomorphisms of the symplectic manifold $(M, \omega)$. We classify all first order invariant operators; the list of other operators is conjectural. Among the new operators we mention a 2nd order one which determins an ``algebra'' structure on the space of metrics (symmetric forms) on $M$

Mirror instability in a plasma with cold gyrating dust particles

In this work linear stability analysis of a magnetized dusty plasma with an anisotropic dust component having transversal motions much stronger than motions parallel to the external magnetic field, and isotropic light plasma components is described. Such a situation presumably establishes in a shock compressed space dusty plasma downstream the shock front. Oblique low-frequency magneto-hydrodynamic waves ($\omega\ll \omega_{cd}$, $\omega_{cd}$ being the dust cyclotron frequency) are shown to be undergone to the mirror instability. Consequences for nonthermal dust destruction behind shock fronts in the interstellar medium are discussed.Comment: 13 pages, 5 figs, accepted to Phys. Pasma

X-RAY DIAGNOSTICS OF PATHOLOGY OF MUSCULOSKELETAL SYSTEM USING DX-D FULL LEG FULL SPINE SYSTEM

Применение системы DX-D Full Leg Full Spine относится к современным технологиям рентгенологического исследования, позволяющего получить высокое качество рентгенограммы при минимальной лучевой нагрузке. Система DX-D Full Leg Full Spine обеспечивает технологический процесс получения изображений для диагностики ортопедической патологии в положении стоя. Основная функция данной системы - автоматический технологический процесс, позволяющий на основе индивидуальных анатомических особенностей пациента за короткий промежуток времени и с высокой степенью точности подобрать необходимую металлоконструкцию, соответствующую объему оперативного вмешательства. В описанном клиническом наблюдении показано выполнение исследования нижних конечностей на рентгенологическом аппарате DX-D 300 с использованием системы DX-D Full Leg Full Spine с определением укорочения ротационной деформации правой нижней конечности, оценки структуры костей, соотношения суставных поверхностей в тазобедренных и коленных суставах

Clinical use of Ortho-SUV transosseous hexapod in treatment of lower limb false joints

We studied the use of Ortho-SUV hexapod in the treatment of 15 patients with lower limb false joints. All patients were at active working age - from 22 to 50 years. 1n 12 patients, the period from the moment of trauma was 1 to 3 years, in 3 patients - 3 to 6 years. 5 patients had femoral false joints, 10 patients - shin false joints. 1n 98 % of cases, the formation of false joints was caused by inadequate treatment of initial trauma. 1n 100 % of cases, false joint localized at diaphyseal level and was accompanied with shortening of injured segment for 2.5 ± 1.0 cm in 13 patients, and for 0.5 and 0.8 cm in 2 cases. We also registered recurvatum and valgus deformity in 5 patients, recurvatum and varus deformity in 8 patients, and antecurvatum and varus deformity in 2 patients. Combined contracture in knee and ankle joint was found in 90 % of patients. Using combined transosseous osteosynthesis along with Ortho-SUV hexapod allowed us to correct hip deformity for 35 ± 10 days and ankle deformity - for 20 ± 5 days on the average. When shortening of femoral bone for more than 5.0 cm, the deformity was corrected in two stages. At the first stage, we reconstructed the length of a segment using methods of transosseous osteosynthesis at discrete-continuum distraction. At the second stage, we corrected deformity using Ortho-SUV hexapod within specified time limits. Duration of femoral and shin false joint consolidation was 194 ± 16 days. We registered inflammatory complications in the areas of transosseous elements contacting soft tissues in 3 (0.2 %) patients. These complications didn't have an effect on the treatment results

Restricted infinitesimal deformations of restricted simple Lie algebras

We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic different from 2 and 3.Comment: 15 pages; final version, to appear in Journal of Algebra and Its Application

An Antenna with a Feeder for a Superconducting Terahertz Josephson Oscillator with Phase Locking

A principal layout of a Josephson terahertz radiation oscillator integrated with a transmitting antenna-lens system and a harmonic mixer (HM) for phase locking of radiation has been proposed and was successfully implemented. Two antenna-feeder systems designed for the central frequencies of 0.3 and 0.6 THz and located on the same chip with the oscillator are numerically simulated and fabricated. A microstrip transmission line between the oscillator and the antenna is used as the feeder. A study was carried out on matching the oscillator power and HM for two designs; the frequency range of pumping HM was 0.25-0.45 and 0.5-0.68 THz for the designs at 0.3 and 0.6 THz, respectively. Good agreement was obtained between experimental results and numerical simulations. A study of the spectral characteristics of the radiation of the oscillator into the external space for the 0.6 THz design using a superconducting integrated spectrometer was carried out. The linewidth of an emission line in free-running regime was of the order of several megahertz; in the phase locking regime down to tens of kilohertz with a signal-to-noise ratio of more than 20 dB was obtained

Planet Packing Revisited

Ross Eckler discusses a problem in his article Planet Packing in the May 2001 Word Ways: given a list of words, such as the names of the planets, how efficiently can they be packed into a single string of characters so that each word on the list can be read off left to right (but not necessarily contiguously)? He hypothesizes there is no guarantee that any algorithm will end up with a minimum string. Since the design and analysis of algorithms has been my area of research for some 25 years, this caught my attention. Informally, an algorithm is a terminating procedure that could be coded as a computer program. (However, the procedure in the Planet Packing article does not contain enough tie-breaking rules to qualify as an algorithm)

Low-Noise Sis Receivers for New Radio-Astronomy Projects

We have developed, manufactured, and tested a waveguide mixer in the range 211-275 GHz on the basis of the superconductor-insulator-superconductor (SIS) tunnel structures. The methods of manufacturing high-quality tunnel structures on quartz substrates have been worked out. To extend the receiver band, the Nb/AlOx/Nb and Nb/AlN/NbN tunnel junctions with a high current density of up to 20 kA/cm2 are employed. The dependence of the characteristics of the receiving elements on the signal frequency is simulated for the intermediate-frequency band 4-12 GHz. The measurements demonstrate a good agreement of the input band of the receiving structures with the calculated results. The uncorrected noise temperature of the receiver amounts to 24 K at a frequency of 265 GHz, which is only two times higher than the quantum limit. The receivers under development are intended for a number of newly-built ground-based radio telescopes ("Suffa" and LLAMA), as well as for the "Millimetron" space program