Spatial amplification of a laser wave and the transverse spread of electrons in an undulator with a noncollinear configuration

The spatial amplification of a wave in a magnetostatic undulator with noncollinear electron and laser beams is studied in the framework of the dispersion relation for single-frequency and collective regimes. The dependence of the gain on the electron beam width is estimated with regard to the spatial boundedness of the beams. The laser power threshold at which the selection with respect to the transverse velocity is possible is obtained for a free-electron laser without inversion.     

On the torsion of Jacobians of principal modular curves of level 3<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3ⁿ) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the second uses the moduli interpretation. Received: 30 September 2005     

Regular variation of order 1 nonlinear AR-ARCH models

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain.     

An asymptotic approach to the problem of the free oscillations of a beam

Equations describing the free small longitudinal and transverse oscillations of a straight elastic beam of rectangular cross section are obtained using the plane linear theory of elasticity and the method of integrodifferential relations. The initial system of partial differential equations is reduced to a system of ordinary linear differential equations with constant coefficients. The effect of the geometrical and elastic characteristics of the beam on the frequency and form of the natural oscillations is investigated. For longitudinal motions it is shown that different types of natural displacements and internal stresses of the beam exist. For transverse oscillations, it is found that there are frequency zones corresponding to different forms of the solutions of the characteristic equation obtained using the proposed model.     

Comment on breakup densities of hot nuclei

In [V.E. Viola et al., Phys. Rev. Lett. 93 (2004) 132701, D.S. Bracken et al., Phys. Rev. C 69 (2004) 034612] the observed decrease in spectral peak energies of IMFs emitted from hot nuclei was interpreted in terms of a breakup density that decreased with increasing excitation energy. Subsequently, Raduta et al. [Ad. Raduta et al., Phys. Lett. B 623 (2005) 43] performed MMM simulations that showed decreasing spectral peaks could be obtained at constant density. In this Letter we point out that this apparent inconsistency is due to a selective comparison of theory and data that overlooks the evolution of the fragment multiplicities as a function of excitation energy.     

On a Polynomial Fractional Formulation for Independence Number of a Graph

In this paper we characterize the local maxima of a continuous global optimization formulation for finding the independence number of a graph. Classical Karush-Kuhn-Tucker conditions and simple combinatorial arguments are found sufficient to deduce several interesting properties of the local and global maxima. These properties can be utilized in developing new approaches to the maximum independent set problem.     

The structure of monolayer SiO2 on Mo(1 1 2): A 2-D [Si-O-Si] network or isolated [SiO4] units?

In this letter, atomically resolved scanning tunneling microscopic (STM) images obtained from monolayer SiO₂/Mo(1 1 2) are presented. The results are consistent with a previously proposed structural model of isolated [SiO₄] units based on vibrational features observed by high-resolution electron energy loss spectroscopy (HREELS) and infrared reflection-absorption spectroscopy (IRAS), and oxygen species identified by ultra-violet photoemission spectroscopy (UPS). These results are inconsistent with a structural model that assumes a two-dimensional (2-D) [Si-O-Si] network. These data illustrate that a metal substrate, although coated with an oxide thin layer, can be directly imaged at the atomic-scale with STM.     

Lines Tangent to Four Triangles in Three-Dimensional Space

We investigate the lines tangent to four triangles in R³. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.     

A topological aspect of Sobolev mappings

Let be a connected open set, . We give a sufficient condition for a mapping , , to have the property that sgn is almost everywhere of one sign. Following the work of Müller, Spector, and Tang [MST], we give an application of our results to the theory of non-linear elasticity. Received: 13 October 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001     

Aliasing Effects and Sampling Theorems of Spherical Random Fields when Sampled on a Finite Grid

Aliasing effects are investigated for spherical random fields sampled on a finite grid. Using the spherical harmonics expansion, it is shown that for a band-limited spherical random field its trend and spectrum can be uniquely reconstructed from the sampled field if the sampling points are judiciously designed. Analytical expressions are also obtained for aliasing errors in the trend and the spectrum when the field is not band-limited.