Reply to the Comment on¶Low temperature specific heat of blue bronze K0.30MoO3

Eur. Phys. J. B 24, 315 (2001) In our Reply to the Comment [#!1!#] we refute the “straightforward” interpretation of the excess low-temperature specific heat, C_p, contribution we have measured in our study of CDW systems K_0.3MoO₃ and (TaSe₄)₂I [#!2!#] as originating solely from normal phonon modes. The specific sensitivity of the bump in C _p / T ³ at low temperatures to the impurity content is consistent with the increased value of the phason pinning gap while the dispersion of normal phonons remains unaffected. We ascribe at least this part of the anomaly to the phason contribution. As stated in reference [3] that the phonon density of states extracted from neutron scattering measurements is the least reliable in this energy range (<0.5 meV), we conclude that C_p measurements are more accurate for detecting the phason contribution. Received 17 April 2002 Published online 19 July 2002     

Asymptotically minimax testing ofr>2 simple hypotheses

In this paper, we consider the problem of asymptotically minimax testing ofr≥2 simple hypotheses when a general stochastic process is observed. We establish general conditions for the exponential decrease of maximal probability errors of minimax tests as the number of observations increases. At the present time, similar results for testing several multinomial schemes were obtained by Salihov [8]. Similar results for testing two simple hypotheses were obtained in [5]. In the proofs of the main results, we use the theory of large deviations ([3], [2]). In Sec. 1, the main result is proved. In Secs. 2–4, we analyze the i.i.d. case, nonhomogeneous Poisson processes, and renewal processes as examples. Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 313–320, July–September, 2000.     

Development of special optical fibers for evanescent-wave chemical sensing

The paper summarizes results achieved in the Institute of Radio Engineering and Electronics in the field of investigation and fabrication of novel fiber-optic structures for evanescent-wave chemical sensing. Several approaches for increasing the evanescent-wave sensitivity of multimode silica optical fibers to gaseous and liquid chemicals are shown. These approaches make use of the decrease of the core diameter in sectorial and capillary sectorial fibers, modification of trajectories of optical rays in the cores of inverted-graded-index fibers, tailoring of the refractive index of porous layers applied on silica cores, an output mode filter preventing the detection of rays propagating at low axial angles or fibers bent in single or multiple turns. Presented at the 1st Czech-Chinese Workshop “Advanced Materials for Optoelectronics”, Prague, Czech Republic, June 13–17, 1998. This work was supported by the Grant Agency of the Czech Republic (projects No. 102/96/0939 and No. 102/98/1358) and by joint project No. 4104 of AS CR and CNRS, France.     

Coefficients for the determination of one-sided tolerance limits of normal distribution

A table of such coefficientsk is given that the interval (?∞, ¯x+ks) or (¯x?ks, +∞) covers with the probabilityP at least the ratioα of the normal population with unknown parameters.     

Magnetic anisotropy and low-frequency dielectric response of weak ferromagnetic phase in κ-(BEDT-TTF)2Cu[N(CN)2]Cl, where BEDT-TTF is Bis(ethylenedithio)tetrathiafulvalene

We report a detailed characterization of the magnetism and AC transport in single crystals of the organic conductor -(BEDT-TTF)₂Cu[N(CN)₂]Cl by means of magnetic anisotropy measurements and low-frequency dielectric spectroscopy. Magnetic anisotropy obeys Curie-Weiss law with negative Curie-Weiss temperature in the temperature range 300 K-70 K. An antiferromagnetic transition with concomitant canted antiferromagnetic state is established at 22 K. A large hysteresis in the spin-flop transition and magnetic field reversal of the weak ferromagnetic magnetization are documented for the first time. A broad dielectric relaxation mode of moderate strength () emerges at 32 K, and weakens with temperature. The mean relaxation time, much larger than that expected for single-particle excitations, is thermally activated in a manner similar to the DC conductivity and saturates below 22 K. These features suggest the origin of the broad relaxation as an intrinsic property of the weak ferromagnetic ground state. We propose a charged domain wall in a random ferromagnetic domain structure as the relaxation entity. We argue that the observed features might be well described if Dzyaloshinsky-Moriya interaction is taken into account. A Debye relaxation with similar temperature dependence was also observed and seems to be related to an additional ferromagnetic-like, most probably, field-induced phase. We tentatively associate this phase, whose tiny contribution was sample dependent, with a Cu²⁺ magnetic subsystem. Received 15 June 1998 and Received in final form 1 February 1999     

Homogenization approach for optimal design of perforated layer in acoustic wave propagation

Homogenization provides a reduced model of the acoustic wave propagation through a periodically perforated layer immersed in an inviscid fluid. The shape of the perforation influences some parameters of the non-local transmission condition. We developed and implemented numerically the sensitivity analysis for an optimal design of the perforation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the harmonic oscillator on the Lobachevsky plane

We introduce the harmonic oscillator on the Lobachevsky plane with the aid of the potential V (ϱ) = (a ² ω ²/4) sinh(ϱ/a)², where a is the curvature radius and ϱ is the geodesic distance from a chosen center. Thus, the potential is rotationally symmetric and unbounded, as in the Euclidean case. The eigenvalue equation leads to the differential equation of spheroidal functions. We provide a basic numerical analysis of eigenvalues and eigenfunctions provided that the value of the angular momentum, m, is equal to 0. Dedicated to the memory of V. A. Geyler     

Study of micro‐channel geometries for internally cooled Si monochromators

Rocking curves of micro‐channel (MC) water‐cooled monochromators are broadened by stresses introduced during fabrication and under X‐ray thermal load. This is a problem which will be even more serious with the rise of the fourth‐generation synchrotron sources, i.e. the free‐electron lasers. The X‐ray optics group at the Institute of Physics at the ASCR v.v.i. in Prague is designing, testing and, with company Polovodi?e a.s., fabricating novel internally water‐cooled Si monochromators. Here three new micro‐channel geometries are introduced which reduce rocking‐curve enlargement owing to the fabrication to less than 2.5 µrad (～0.5 arcsec). All three MC designs show less rocking‐curve enlargement and smoother topographic images. The designs also show better cooling efficiencies than the classical MC design in finite‐element analysis calculations.     

Application of very weak formulation on homogenization of boundary value problems in porous media

Czechoslovak Mathematical Journal - The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard...