Avoiding infeasibility in DEA models with weight restrictions

The flexibility of weights assigned to inputs and outputs is a key aspect of DEA modeling. However, excessive weight variability and implausible weight values have led to the development of DEA models that incorporate weight restrictions, reflecting expert judgment. This in turn has created problems of infeasibility of the corresponding linear programs. We provide an existence theorem that establishes feasibility conditions for DEA multiplier programs with weight restrictions. We then propose a linear model that tests for feasibility and a nonlinear model that provides minimally acceptable adjustments to the original restrictions that render the program feasible. The analysis can be applied to restrictions on weight ratios, or to restrictions on virtual inputs or outputs.     

Statistical Properties of Unimodal Maps

We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition into topological conjugacy classes, see [ALM]) is not transversely absolutely continuous. As an intermediate step in the proof of the formula, we show that the distribution of the critical orbit is described by the physical measure supported in the chaotic attractor.     

U and Th thin film neutron dosimetry for fission-track dating: application to the age standard Moldavite

Neutron dosimetry based on U and Th thin films was used for fission-track dating of the age standard Moldavite, the central European tektite, from the Middle Miocene deposit of Jankov (southern Bohemia, Czech Republic). Our fission-track age () agrees with a recent ⁴⁰Ar/³⁹Ar age, , based on several determinations on Moldavites from different sediments, including the Jankov deposit. This result indicates that the U and Th thin film neutron dosimetry represents a reliable alternative for an absolute approach in fission-track dating.     

Mode profiles in resonators with a near 90° roof-top mirror

The transverse modes of a laser resonator comprising a near 90° roof-top mirror and a feedback mirror are studied theoretically. We relate this configuration to an almost plane roof-top resonator and apply the Fox and Li technique to compute the lowest-order symmetric and antisymmetric modes. The effects of perturbations to the vertex angle of the roof-top mirror, misalignments of the feedback mirror and curved feedback mirrors are examined.     

Sufficient conditions for the Sal'nikov equation to have at least two limit cycles

We show that the Sal'nikov thermokinetic oscillator system has at least two limit cycles, an unstable one lying inside a stable one. The proof uses the elementary technique of Liénard's equation.     

Electro-optic properties of LiKSO4 and LiK1-xRbxSO4 crystals

1-x Rb_xSO₄ for x varying between 0 and 0.50 were investigated by an ac modulation method based upon the Sénarmont arrangement. The electro-optic coefficient r_c, and for the first time the coefficients r₄₁ and r₅₁ were determined with good accuracy in pure LiKSO₄ around room temperature at a wavelength of 633 nm. The frequency dependence of the electro-optic coefficient r_c was measured in the frequency range from 1 kHz up to 1 MHz. The values of the factor of merit n_e ³r_c of the mixed crystals LiK_1-xRb_xSO₄ were obtained for the first time, for the concentrations x=0.05, 0.10, 0.20, and 0.50. The electro-optic properties are shown to be affected by the random presence of the rubidium ions in this disordered system. Received: 16 March 1998/Revised version: 2 June 1998     

Mössbauer and infrared spectrometric studies of some iron(III) precipitates

The composition of iron(III) precipitates prepared by different methods was investigated by Mossbauer and infrared spectrometry. The principal constituents were identified as α-FeOOH, β-FeOOH, α-Fe₂O₃, and the van der Giessen precipitate, α-Fe₂O₃· nH₂O. Effects of chloride ion and formic acid on the products of precipitation were studied.     

Indirect interactions between localized magnetic moments in intrinsic semiconductors

The indirect interaction between localized magnetic moments in insulators and semiconductors is investigated at T = 0°K. This interaction arises from virtual excitations of the valence electrons to the conduction band and is oscillatory as a function of distance. The passage from the case of small gap semiconductors to insulators is studied in detail, as a function of the energy gap and the effective masses. The Bloembergen-Rowland interaction is derived as a limiting case for insulators. Possible applications are also discussed.     

Effect of high hydrostatic pressure on phenolic compounds,ascorbic acid and antioxidant activity in cashew apple juice

The cashew apple is native to Brazil, but there is insufficient information regarding the nutritional properties of this fruit. The objective of this study was to evaluate the impact of high pressure processing (HPP) at room temperature (25 °C) on phenolic compound and ascorbic acid contents and antioxidant capacity of cashew apple juice. This study showed that HPP at 250 or 400 MPa for 3, 5 and 7 min did not change pH, acidity, total soluble solids, ascorbic acid or hydrolysable polyphenol contents. However, juice pressurized for 3 and 5 min showed higher soluble polyphenol contents. Antioxidant capacity, measured by the ferric-reducing antioxidant power method, was not altered by HPP, but when treated at 250 MPa for 3 min, it resulted in an increased value when 2,2-diphenyl-1-picrylhydrazyl was used. These data demonstrate that HPP can be used in the food industry for the generation of products with higher nutritional quality.     

Influence of Diffusion Parameters on the Spectral Characteristics of Raman Modes of Titanium-Diffused Lithium Niobate Planar Waveguides

ABSTRACT

A systematic investigation on the influence of the diffusion parameters (time and temperature) and initial titanium film thickness on the spectral characteristics of the LiNbO₃ Raman modes is reported. Raman spectra are measured in the range 50–1000 cm^?1 ～2 µm below the surface of the crystals. Broadening of the Raman lines and, therefore, crystal lattice disorder induced by the titanium ions are found to depend on the fabrication parameters. The disorder associated with the titanium ions near the surface of LiNbO₃ is encoded in the broadening of the A₁(TO₁) Raman line. A linear relation between the A₁(TO₁) mode broadening and the Ti concentration is presented. The diffusion theory is used to explain the experimental data. Raman spectroscopy combined with diffusion theory can be used to estimate the evolution of the titanium surface concentration.