Resonance energies of meta-stable dtµ*

Using the coupled rearrangement channel method, we have calculated resonance energies for meta-stable states of the molecular ion dtµ^* associated with the adiabatic 3 potential. The vacuum polarization effect was taken into account by direct inclusion of the Uehling potential in our three-body Hamiltonian. Comparing with the solution of the pure Coulombic Schrödinger equation a shift of approximately +0.1 eV is found. Thus the infinite series of states of the Coulombic Schrödinger equation becomes truncated. Eleven states remain semi-bound, five of them with binding energy smaller than the dissociation energy of the D₂ molecule, facilitating formation of dtµ^* in tµ(2s)-D₂ scattering by means of the Vesman-mechanism.     

A Big Horizontal Solar Telescope of the Main Astronomical Observatory of the Ukrainian National Academy of Sciences in the caucasus

This paper presents the Big Horizonal Solar Telescope of the Main Astronomical Observatory of the Ukrainian National Academy of Sciences installed at the Peak Terskol high-altitude station near Elbrus (the main mirror diameter is 650 mm and the focal length is 17.5 m). The telescope is equipped with a five-camera spectrograph intended for photographic spectral observations of active regions in the solar atmosphere and photoelectric measurements of the solar spectra with high spectral and spatial resolution. The observation procedure is described, and the results of the quality analysis of the recorded spectra and of the early measurements are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 10, pp. 1326–1333, October, 1996.The authors wish to express their gratitude to C.I.Gandzha, V.V.Kul'beda, and Yu. M. Gavrilyuk from the Solar Physics Department of the PAO of the Ukrainian NAS and to the Board of Directors of the Observatory and of the High-Altitude Station for help in the development of the instrument.This paper is dedicated to the memory of E. A. Gurtovenko, D.Sc. in Phys. and Math., who initiated the installation of the telescope at Peak Terskol and who was the leader, an executor, and an observer in this project.     

The overlay of lower envelopes and its applications

Let and be two collections of a total ofn (possibly partially defined) bivariate, algebraic functions of constant maximum degree. The minimization diagrams of are the planar maps obtained by the xy-projections of the lower envelopes of , respectively. We show that the combinatiorial complexity of the overlay of the minimization diagrams of and of is O(n^2+ɛ), for any ɛ>0. This result has several applications: (i) a near-quadratic upper bound on the complexity of the region in 3-space enclosed between the lower envelope of one such collection of functions and the upper envelope of another collection; (ii) an efficient and simple divide-and-conquer algorithm for constructing lower envelopes in three dimensions; and (iii) a near-quadratic upper bound on the complexity of the space of all plane transversals of a collection of simply shaped convex sets in three dimensions. Work on this paper by the first author was supported by National Science Foundation Grant CCR-93-01259 and an NYI award. Work on this paper by the second author was supported by the Netherlands’ Organization for Scientific Research (NWO) and partially supported by ESPRIT Basic Research Action No. 6546 (project PROMotion). His current address is Department of Computer Science, Postech, San 31, Hyoja-Dong, Pohang, Kyungbuk 790–784, South Korea. Email: otfried@vision.postech.ac.kr. Work on this paper by the third author was supported by NSF Grant CCR-91-22103, by a Max-Planck Research Award, and by grants from the U.S.-Israeli Binational Science Foundation the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

Analysis and design of highly broad-band,planar evanescent couplers

It is shown that by taking advantage of the maximum in the spectral dependence of the coupling coefficient, very broad-band symmetric and asymmetric single-mode planar couplers can be designed. The symmetric coupler allows at least 95.6% coupling between the two cores over the wavelength range 1.3–1.58 m, while the asymmetric coupler can act as a 3 dB splitter with only ±1.6% variation in the splitting ratio over the wavelength range 1.3–1.67 m. In both cases, the design includes the curved input-output arms, and the estimated bend loss is approximately 0.1 dB.     

Separation of polycyclic aromatic hydrocarbons by micellar electrokinetic chromatography with aqueous short-chain alcohol solvent

Micellar electrokinetic capillary chromatography (MEKC) with aqueous organic solvent has been developed to separate polycyclic aromatic hydrocarbons (PAHs). Methanol, ethanol or propanol as an organic modifier was added to sodium dodecyl sulfate (SDS) micellar solution in order to increase the solubility of very hydrophobic solutes in mobile phase. Both methanol and ethanol can be used as co-solvents for the separation of PAHs. Use of ethanol resulted in a shorter analysis time than use of methanol. The separations of some PAHs were unsatisfactory using propanol although the analysis time was much shorter than with ethanol. The influence of ethanol content, SDS concentration and temperature on the separations was studied. Benzene and nine polycyclic aromatic hydrocarbons were successfully separated using 50 mM SDS-20 mM phosphate-5 mM borate, containing 40% (v/v) ethanol at 35 degrees C. The relative standard deviation (R.S.D.) of t(R) ranged from 0.5 to 1.5% for six repeat injections.