En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

Measurement of the refractive index and optical absorption spectra of epitaxial bismuth substituted yttrium iron garnet films at uv to near-ir wavelengths

Refractive-index and optical-absorption spectra of Bi-substituted yttrium iron garnet films, epitaxially grown by liquid-phase epitaxy, have been measured in the spectral regime 0.26 m1.9 m by thin-film interference for 0.52 m and by ellipsometry for0.52 m. The Y_3–x–y Bi _x Pb _y Fe_5–z Pt _z O₁₂ films contain bismuth in the range Ox 1.42, lead in the range 0.01 y0.08 and platinum in the range 0.005<=z0.03. There is satisfactory coincidence between the results from ellipsometry and thin-film interference in the overlapping wavelength region. The materials investigated are the same as reported earlier from this laboratory in ter mof their magnetic and magnetooptic properties.     

Determination of the Coefficient of Laser Radiation Reflection from Dielectric Targets in Vacuum

We present the results of experimental determination of the coefficients of laser radiation reflection (₁ 10.6 m and ₂ 1.06 m) from dielectric targets of complex chemical composition in vacuum with allowance for a regime of developed plasma formation.     

A DCN laser interferometer for electron density measurements of plasmas

The main characteristic of this interferometric system is such that the systems can be used for DCN laser (=195m, 190m) and also for HCN laser (=337m) by changing the work medium, regulating the temperature of tube wall and adjusting the optic path, without changing any optic element.     

A μSR study of spin density wave condensation in Cr85Mo15

Zero field SR spectra from Cr₈₅Mo₁₅ are well described by the sum of a lightly damped (0.02s^–1<₁<0.2s^–1) and a heavily damped (2s^–1<₂<15s^–1) exponential. The temperature dependence of these components is discussed in relation to the condensation of the incommensurate spin density wave and the onset of the antiferromagnetic state in this Cr-like alloy below T_N=120K. Evidence is presented for the nucleation of the spin density wave at temperatures greater than 1.5T_N.     

n-Dimensional representations of the unified field tensor* g λν

For the first time Hlavatý represented the tensor^*g^v, defined by (15a), in terms of the unified field tensorg in the space-timeX ₄. Recently, the representations of^* g ^v in terms ofg in two- and three-dimensional generalized Riemannian space were obtained by Chung. The purpose of the present paper is to obtain the generalized representations of^* g ^v in terms ofg in a generalizedn-dimensional Riemannian spaceX _n.     

Conversion to the second harmonic of high power iodine photodissociation laser system PERUN

The frequency doubling of the iodine laser PERUN is described. The maximum conversion efficiency of 55% is attained, the energy of the red (=0.657m) radiation is 20 J.     

Plasma diagnostic applications on the TEXT tokamak using a high power, twin frequency optically pumped far-infrared laser

A high-power, twin-frequency, optically-pumped, far-infrared (FIR) laser has been developed at UCLA for diagnostic application on the TEXT tokamak. The source is operated at 245 GHz (=1.22 mm) for heterodyne scattering measurements and 694 GHz (=432 m) for high resolution interferometry. Future plans include a 30 channel interferometer/polarimeter operating at 694 GHz to accurately determine current profiles.     

Modified London model for the determination of λ and ζ in a high κ superconductor

We present a modified London model suggested by Brandt [1–3] which introduces a finite vortex core size appropriate for isotropic superconductors in which the average internal field is less than approximately (1/4)H _c2. TheSR lineshape resulting from this model possesses a distinctive shape due to the magnetic penetration depth and the vortex core diameter (approximately equal to twice the coherence length ). However, for a given lineshape, there is a large range of values of and which produce nearly the same lineshape. Lineshape smearing caused by disorder in the vortex lattice increases uncertainty in values for and . If well-determined values of either (T) or (T) are not available from another technique, both of them can be determined bySR measurements alone if runs in more than one applied field at the same temperature are fit with and as shared parameters. We also present our method of estimating the degree of disorder in the vortex lattice.     

The lasing mechanism of nuclear-pumped IR lasers at krypton and argon atomic transitions

For studying the lasing mechanism of nuclear-pumped IR lasers at krypton and argon atomic transitions, the kinetics of the plasma process is considered and computations are made for the energy and threshold characteristics of He-Kr (=2.52 m) and He-Ar (=1.79 m) lasers excited by uranium fission fragments. The calculated optimal pressures, mixture compositions, laser output powers and threshold characteristics agree satisfactorily with the experimental ones.     

Loss in low-finesse Ti:LiNbO3 optical waveguide resonators

We propose to measure the contrast of Fabry-Perot resonances in low-finesse (end face polished) integrated optical resonators to determine an upper limit of the waveguide attenuation coefficient. The method is discussed; its absolute accuracy increases with decreasing loss. As example, experimental results are presented for 3 and 10 m wide Ti: LiNbO₃ strip guides; the attenuation coefficients are 0.46 dB/cm (EH₁₁) in the narrower guide at =0.63 m, respectively 0.19 dB/cm (EH₁₁) and 0.09 dB/cm (HE₁₁) in the 10 m wide guide at =1.15 m.     

The lateral photovoltaic effect in CdS-Cu2S heterojunction solar cell

The lateral photovoltaic effect has been observed in CdS-Cu₂S thin-film solar cells. The effect is more pronounced on the CdS side than on the Cu₂S side of the cells. On the CdS side, where the contacts were formed by soldering Cu wire by indium and then applying Ag paint, the photovoltage developed were found to increase as the point of illumination was moved towards the contact. The spectral response of photovoltage for coevaporated cells shows a peak at=0.5m (2.45 eV). But for topotaxial cells two peaks, one at=0.5m and the other at=0.65m (1.89eV) were observed. A band model has been proposed for the heat-treated optimized cells.     

Strong far-infrared laser action in carbonyl fluoride and vinyl fluoride

Intense far-infrared laser action is reported for carbonyl fluoride and vinyl fluoride. Eleven new lines with wavelengths between 339 m538 m were obtained by optically pumping carbonyl fluoride with numerous lines of the 10.4 m band of a cw CO₂ laser. Twenty-three lines with wavelengths in the range 172 m783 m were detected when pumping the recently discovered efficient FIR laser molecule vinyl fluoride. In addition, three very weak new lines were found using 1.1-difluoroethylen.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Focussing of submillimeter radiation guided by a dielectric sheet

Guided submillimeter radiation (=118.8 m) has been focussed by inserting a cylinder lens into the freely propagating beam in front of the incoupling prism. The beam profile at the focal spot has been determined experimentally, the results agree with theoretical predictions. The optical quality of the focus is good.     

Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

Energy level crossings in quantum mechanics

From the eigenvalue equationH \ _n () =E _n ()\ _n () withH H ₀ +V one can derive an autonomous system of first order differential equations for the eigenvaluesE _n () and the matrix elementsV _mn () where is the independent variable. To solve the dynamical system we need the initial valuesE _n ( = 0) and \ _n ( = 0). Thus one finds the motion of the energy levelsE _n (). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH =H ₀ +V ₁ + ² V ₂ and give an application to a supersymmetric Hamiltonian.     

A characterization of carter's separable space-times

In a space-time admitting a two-parameter Abelian isometry group, and a quadratic Killing tensor with the eigenvalues (, , , ) and vanishing Lie derivatives with respect to the Killing vectors, we construct a canonical coordinate system. The isometry group acts orthogonally transitively. The Hamilton-Jacobi equation is separable. We give a necessary and sufficient condition for the separability of the Klein-Gordon equation. We obtain Carter's space-times with completely separable Klein-Gordon equation.     

Tunable UV radiation at short wavelengths (188–240 nm) generated by sum-frequency mixing in lithium borate

Sum-frequency mixing (₃=₁+₂) of UV laser radiation (₁=266 nm and 213 nm) and tunable coherent infrared light (₂=1.2–2.6 m) in lithium borate (LBO) generates radiation at short wavelengths (₃=188–242 nm). The UV radiation at ₁ is produced by the fourth and fifth harmonic of a pulsed Nd-YAG laser. The infrared light is generated with an optical parametric oscillator of beta barium borate. The phase-matching angle is measured as function of ₃ and compared with calculated values. For UV laser radiation at shorter wavelengths (173 nm₁213 nm) the calculations predict an extension of the tuning range of the sum-frequency generated at ₃ to wavelengths as short as the LBO transmission cutoff at 160 nm.     

Width reduction of laser microdrillings by subsequent mechanically induced plastic deformation

This work reports a novel process combination, which is capable of forming large hole matrices (100 pores/mm²) in thin stainless steel foils (10 mfoil<300 m) maintaining high processing rates and pore widths smaller than 5 m. This technique perforates stainless steel foils with high-speed on-the-fly laser perforation (60000 drillings/min) followed by a cold-roll forming of the laser-treated foil. The cold-roll forming leads to a pore-size reduction (in one dimension) perpendicular to the rolling direction. For the laser processing a diode-pumped, q-switched and frequency-tripled Nd:YAG laser (=355 nm, =30 ns), and a flashlamp-pumped Nd:YAG laser (=1064 nm, =57 s) were applied. Using this process combination, minimum pore sizes of 3.5 m have been achieved. At present, the processing efficiency of cold-rolled percussion drillings inserted with nanosecond pulse durations is lower in comparison with single-pulse on-the-fly perforation, but in terms of quality (straight pore channel, low standard deviation of pore widths and pore widths smaller than 5 m) well suited for various fields in filtration (e.g. particle removal) . PACS  81.20.Hy; 42.62.Cf; 81.40.Ef