Rationality of quotients by linear actions of affine groups

Let G be the (special) affine group, semidirect product of SL_n and C^n. In this paper we study the representation theory of G and in particular the question of rationality for V/G where V is a generically free G-representation. We show that the answer to this question is positive if the dimension of V is sufficiently large and V is indecomposable. We have a more precise theorem if V is a two-step extension 0 -> S -> V -> Q -> 0 with S, Q completely reducible.Comment: 18 pages; dedicated to Fabrizio Catanese on the occasion of his 60th birthda

Endomorphisms of abelian varieties, cyclotomic extensions and Lie algebras

We prove an analogue of the Tate conjecture on homomorphisms of abelian varieties over infinite cyclotomic extensions of finitely generated fields of characteristic zero.Comment: 9 page

Luttinger-liquid-like transport in long InSb nanowires

Long nanowires of degenerate semiconductor InSb in asbestos matrix (wire diameter is around 50 \AA, length 0.1 - 1 mm) were prepared. Electrical conduction of these nanowires is studied over a temperature range 1.5 - 350 K. It is found that a zero-field electrical conduction is a power function of the temperature $G\propto T^\alpha$ with the typical exponent $\alpha \approx 4$. Current-voltage characteristics of such nanowires are found to be nonlinear and at sufficiently low temperatures follows the power law $I\propto V^\beta$. It is shown that the electrical conduction of these nanowires cannot be accounted for in terms of ordinary single-electron theories and exhibits features expected for impure Luttinger liquid. For a simple approximation of impure LL as a pure one broken into drops by weak links, the estimated weak-link density is around $10^3-10^4$ per cm.Comment: 5 pages, 2 figure

A New Limit on the Antiproton Lifetime

Measurements of the cosmic ray pbar/p ratio are compared to predictions from an inhomogeneous disk-diffusion model of pbar production and propagation within the Galaxy, combined with a calculation of the modulation of the interstellar cosmic ray spectra as the particles propagate through the heliosphere to the Earth. The predictions agree with the observed pbar/p spectrum. Adding a finite pbar lifetime to the model, we obtain the limit tau_pbar > 0.8 Myr (90 % C.L.).Comment: 13 pages, 3 encapsulated Postscript figures, uses AASTeX; accepted by Astrophysical Journal; minor change

Modeling of high energy impact on ice in taking into account the temperature

In this paper, the problems deep penetration of compact impactors into the ice, taking into account different temperatures were solved. The behavior of ice is described by the basic system equations of continuum mechanics, i.e., the equations of continuity, momentum and energy in the lagrangian approach. Medium are compressible, isotropic, no mass forces, internal sources of heat and thermal conductivity. Medium also includethe shockwave phenomena, as well as formation “spall” and “shear” damage. The stress tensor is divided into deviatoric and spherical components. Equation of statewas chosen in the form of Walsh. The components of the stress tensor deviator located on the elasticplastic flow model based on the equations of Prandtl-Reis associated with von Mises yield criterion. Initial impactor velosity was varied atfrom 50 to 325 m/s. Numerical simulation results showed the influence of temperature of the ice to the depth of penetration of the impactors

Metallic Xenon, Molecular Condensates, and Superconductivity

A possibility of explaining the light absorption observed to occur under pressure-induced xenon metallization as due to the transition to the superconducting state is analyzed. The mechanism of the van der Waals bonding is discussed.Comment: LaTeX 2.09 (RevTeX), 4 pages, 4 PostScript figures included in tex

Holomorphic symplectic geometry: a problem list

A list of open problems on holomorphic symplectic, contact and Poisson manifolds

On the canonical degrees of curves in varieties of general type

A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples coming from the theory of Shimura varieties that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety. We also prove the desired inequality in the case of compact Shimura varieties.Comment: 10 pages, to appear in Geometric and Functional Analysi

Safe Reach Set Computation via Neural Barrier Certificates

\ua9 2024 The Authors. This is an open access article under the CC BY-NC-ND license. We present a novel technique for online safety verification of autonomous systems, which performs reachability analysis efficiently for both bounded and unbounded horizons by employing neural barrier certificates. Our approach uses barrier certificates given by parameterized neural networks that depend on a given initial set, unsafe sets, and time horizon. Such networks are trained efficiently offline using system simulations sampled from regions of the state space. We then employ a meta-neural network to generalize the barrier certificates to state-space regions that are outside the training set. These certificates are generated and validated online as sound over-approximations of the reachable states, thus either ensuring system safety or activating appropriate alternative actions in unsafe scenarios. We demonstrate our technique on case studies from linear models to nonlinear control-dependent models for online autonomous driving scenarios

Novel Single Photon Detectors for UV Imaging

There are several applications which require high position resolution UV imaging. For these applications we have developed and successfully tested a new version of a 2D UV single photon imaging detector based on a microgap RPC. The main features of such a detectors is the high position resolution - 30 micron in digital form and the high quantum efficiency (1-8% in the spectral interval of 220-140 nm). Additionally, they are spark- protected and can operate without any feedback problems at high gains, close to a streamer mode. In attempts to extend the sensitivity of RPCs to longer wavelengths we have successfully tested the operation of the first sealed parallel-plate gaseous detectors with CsTe photocathodes. Finally, the comparison with other types of photosensitive detectors is given and possible fields of applications are identified.Comment: Presented at the 5th International Workshop on RICH detectors Playa del Carmen, Mexico, November 200