High peak power Nd:YAG laser pumped by 600-W diode laser stack

The Q-switched laser with triangle slab made of Nd:YAG crystal side pumped by 600-W quasi-cw diode laser stack has been designed. The multimode (M²≈2.6) output energy of about 42 mJ was demonstrated in free running mode for110-mJ pump energy. In Q-switch experiments, the KDDP Pockels cell was placed between the slab and rear mirror in plane-plane cavity with output coupler of 84% transmission. The energy of 8 mJ in 2.1-ns pulse duration was obtained for near TEM₀₀ output beam. For passive Q-switching by means of Cr:YAG crystal of 12.6% unsaturated transmission, the energy of 5.1 mJ in 2.5-ns pulse duration was obtained for output beam close to TEM₀₀ mode.     

Møller was right

Direct calculation proves that the total energy-momentum vector derived from the Møller energy-momentum complex from 1958 does not transform like a free 4-vector with respect to the Lorentz transformation. This conforms with the conclusion formulated by Møller himself, but it contradicts the result of the critical analysis of Kovacs. Defects in Kovacs argumentation are found.     

Theory of electronic transport in two-dimensional systems in the presence of magnetic fields

The paper of three parts is focused on the Landauer-Büttiker approach to the study of transport in two-dimensional electron systems, with particular attention to the influence of an external magnetic field. In the previous part the total conductance of such a system was shown to be proportional to the transmission current. In the present part we give a detailed proof, based on the linear response theory, to the last statement. The value of the magnetic field may be arbitrary and possible inhomogeneity of the electric field is also considered.The author wishes to thank to Professor P. Steda and Professor L. Smrka for discussions and encouragement.     

Polyèdre de Newton et distributionf + s . II

Sans résumé

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Graphs that are not complete pluripolar

Let be domains in . Under very mild conditions on we show that there exist holomorphic functions , defined on with the property that is nowhere extendible across , while the graph of over is not complete pluripolar in . This refutes a conjecture of Levenberg, Martin and Poletsky (1992).

     

Inversion and inversion-rotation spectrum of 14NH3 in the ν2 excited state

Using the vibration-inversion-rotation Hamiltonian for ammonia [V. ?pirko, J. M. R. Stone, and D. Papou?ek, J. Mol. Spectrosc.60, 159–178 (1976)], a modified theory is worked out for the Δk = ±3n interactions between the inversion-rotation energy levels of NH₃ which takes into account the large amplitude inversion motion. Eighty frequencies of inversion and inversion-rotation transitions and two perturbation-allowed transitions in the ν₂ state of ¹⁴NH₃ are measured in the far-infrared region around 1 THz (≈33 cm^?1), mostly with the microwave accuracy, by the radiofrequency spectrometer with acoustic detector. By a least-squares fit of these data and the data of the infrared-microwave two-photon and infrared heterodyne measurements of the ν₂ band, a set of molecular constants for the ν₂ state of ¹⁴NH₃ is obtained which reproduces the submillimeterwave data with the accuracy of the experiment.     

Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems

Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation is possible and can be done in different ways. Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002 RID="*" ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and NSF DMS-9802367 RID="**" ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated     

On the structure ofn-point sets

Letn be an integer greater than one. Our main result, called the “Structure Theorem” is that a set that containsn−1 disjoint continua that are cut by a single line cannot be ann-point set, that is, a set that meets every line in preciselyn points. This theorem unifies and significantly improves upon a number of known theorems. The second part of the paper is devoted to several theorems that address the question when a set that meets every line in at mostn points can be extended to ann-point set. These theorems also highlight the sharpness of the Structure Theorem.