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.     

On the invariant sets of a family of quadratic maps

The Julia setB for the mappingz (z–)² is considered, where is a complex parameter. For 2 a new upper bound for the Hausdorff dimension is given, and the monic polynomials orthogonal with respect to the equilibrium measure onB are introduced. A method for calculating all of the polynomials is provided, and certain identities which obtain among coefficients of the three-term recurrence relations are given. A unifying theme is the relationship betweenB and -chains ± (± (± ...), which is explored for –1/42 and for with ||1/4, with the aid of the Böttcher equation. ThenB is shown to be a Hölder continuous curve for ||<1/4.Supported by NSF Grant MCS-8104862Supported by NSF Grant MCS-8002731     

Experimental modelling of groove effect on finline transitions at Ka-Band

The mounting groove of finline circuits is always the area of research for low loss E-Plane components. The normal practice says, the groove depth should be kept /4 or /2 according to the termination at the top surface for electrical short inside the waveguide. Here we have investigated the effect experimentally at Ka-Band for short ended circuit grooves. It has been found that if the groove depth is kept /10, just adequate to hold the card vertical rigidly, considerable improvement has been observed in the Insertion Loss of the line. An improvement of 0.6 dB has been observed with /4 to /10 groove depth for short ended circuit for Symmetric unilateral finline.     

Geometry and combinatorics of Julia sets of real quadratic maps

For real a correspondence is made between the Julia setB forz(z–)², in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325.     

The ground state energy of Sdhrödinger operators

We studye()=inf spec(-+V) and examine whene()<0 for all 0. We prove thatc ²e()–d ² for suitableV and all small ||.Research partially funded under NSF grant number DMS-9101716.     

Hydromagnetic laminar flow of a conducting fluid in an annulus in presence of a radial magnetic field

The object of the present paper is to study the MHD effects on the laminar flow of a viscous, incompressible and conducting fluid in an annulus with arbitrary time-varying pressure gradient and arbitrary initial velocity in presence of a radial magnetic field. Using finite Hankel transform, solutions for both the unsteady and steady flows under different prescribed pressure gradients have been found out.Notation H a constant characterising the intensity of the magnetic field - p hydrostatic pressure - _e magnetic permeability - coefficient of viscosity - kinematic coefficient of voscosity - conductivity of the medium - density - a radius of the inner cylinder - b radius of the outer cylinder - parameter - s positive root - J (sr) Bessel's function of first kind of ordergl - Y (sr) Bessel's function of second kind of order     

Kac-Moody symmetry of generalized non-linear Schrödinger equations

The classical non-linear Schrödinger equation associated with a symmetric Lie algebra =km is known to possess a class of conserved quantities which from a realization of the algebrak []. The construction is now extended to provide a realization of the Kac-Moody algebrak[, ^–1] (with central extension). One can then define auxiliary quantities to obtain the full algebra [, ^–1]. This leads to the formal linearization of the system.     

Stimulated IR- and vacuum-UV emission following two-photon-excitation of molecular hydrogen using an ArF laser

Hydrogen molecules are excited by two 193 nm-photons [X¹ _g ⁺ E,F¹ _g ⁺ ;Q₀₂(1)] generated with a commerical oscillator-amplifier ArF laser. Stimulated emission is subsequently observed in the IR (=752.4 nm to 836.6 nm;E, FB) and in the VUV (=134.0 nm to 160.9 nm;BX) with a VUV conversion efficiency of 0.2%. The rotational fine-structure, the saturation behaviour, pump depletion as well as SRS-onset on and off two-photon resonance are investigated.     

К СПЕКТРУ ПОГЛОЩЕНИЯ АМОРФНОГО СЕЛЕНА В ИНФРАКРАСНОЙ ОБЛАС ТИ

0,6 25 . , , . , 13,4 20,4 , , , . . , . .

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A contribution to the absorption spectrum of amorphous selenium in the infra-red region

The absorption spectrum of amorphous selenium was measured in the region of 0·6 to 25 on samples of high purity and homogeneity. The absorption bands of amorphous and liquid sulphur were also measured in the same wave-length region. The measurements showed that the absorption bands 13·4 and 20·4 , appearing in the spectrum of amorphous selenium, are its intrinsic absorption bands and are not caused by impurities, as some authors think. The similarity between the infra-red spectra of selenium and sulphur is shown.

     

Compact recording of information by the holographic method

Conclusions For holography using a convergent subject beam arrangement, the effect associated with increased extrafocal information density is most pronounced when the parameter 2ac/F is small. This relationship between the object parameters (a and c) and the characteristics of the holographic system (, F) is encountered most frequently in problems of microfilming (ac) and radar imaging (ac,a ²/F is small). It is only in the case 2acF99 with an accuracy of not worse than 1%, that we can assert that the sizes of the minimal Fourier holograms will coincide.Gorkii State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 22, No. 4, pp. 449–457, April, 1979.     

Determination op energy gap width in some semi-conductors

The formula derived by the author for the width of the energy gap is compared with experiment for GaSb, InAs, InSb, and InSb. GaSb semi-conductors. The agreement is good.

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GaSb, InAs, InSb, InSb. GaSb. o.

     

Borel summability of the perturbation series in a hierarchical λ(▽φ)4 model

We prove Borel summability of the perturbation series for the dielectric constant and the free energy density for the hierarchical ()⁴ lattice model. Our methods are based on nonperturbative renormalization group analysis of the model.On leave from the Department of Mathematical Methods of Physics, Warsaw University, Poland.Supported in part by the Center for Interdisciplinary Research, Bielefeld University, Germany.     

Perturbation about the mean field critical point

We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4⁴ — /2² perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice ^d has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or ²) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920     

Influence of linear elastic stresses on dynamic magnetostriction of cold-rolled transformer steel

The anisotropy of dynamic magnetostriction is investigated without external stresses, in extension, and in compression. Results are obtained expressing the (B) dependence for constant elastic stresses and also — () for certain induction values. Oscillograph traces are taken of the (H) and B(H) hysteresis loops with the specimens under investigation in extension and compression.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 110–115, May, 1977.     

Determination of the scattering amplitude

The problem to determine the elastic scattering amplitude from the differential cross-section by the unitarity equation is reexamined. We prove that the solution is unique and can be determined by a convergent iteration if the parameter =sin of Newton and Martin is bounded by <₂0.86. The method is based on a fixed point theorem for holomorphic mappings in a complex Banach space.     

The propagation of excitation energy in perturbed crystals

The process of the propagation of excitation energy in perturbed dielectric crystals with a weak bond between the atoms having zero permanent dipole moment is studied. It is shown that on certain assumptions this process of propagation can be regarded as the motion of a Frenkel exciton in the electrostatic field of the defect. Frenkel's exciton can be characterized in this case as a neutral polarizable particle having induced dipole moment equal to the change in the induced dipole moment of the crystal during the excitation of one of its atoms.

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, . , . .

     

Existence of three phases for aP(ϕ)2 model of quantum field

In the two-dimensional model of the quantum field theory with lagrangean density :()²–(–)^{21/2 4}–⁶: there exist (at least) three different phases for small and some ().     

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 S-matrix for abstract scattering systems

Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()- _HS ² d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation.     

Gelation and Cluster Growth with Cluster-Wall Interactions

Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side reactions of metal atoms with the polymer matrix: where > 0 and where c _k denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the polymer matrix for reaction with metallic atoms. The initial conditions are required to be non-negative and satisfy and p(0) = p ₀. We assume that for 01, which encompasses both bond linking kernels (R _jk = j k ) and surface reaction kernels (R _jk = j + k ). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in others. We provide numerical evidence that gelation occurs for the classical coagulation equations ( = 0) with the bond linking kernel (d ) for 1/2<1. We examine the relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on ^–1 in the limiting case R _{= jk} , p ₀=1.