Minimax Results and Finite-Dimensional Separation

In this paper, we review and unify some classes of generalized convex functions introduced by different authors to prove minimax results in infinite-dimensional spaces and show the relations between these classes. We list also for the most general class already introduced by Jeyakumar (Ref. 1) an elementary proof of a minimax result. The proof of this result uses only a finite-dimensional separa- tion theorem; although this minimax result was already presented by Neumann (Ref. 2) and independently by Jeyakumar (Ref. 1), we believe that the present proof is shorter and more transparent.     

A new trigonometric method of summation and its application to the degree of approximation

The object of the present investigation is to introduce a new trigonometric method of summation which is both regular and Fourier effective and determine its status with reference to other methods of summation (see §2-§4) and also give an application of this method to determine the degree of approximation in a new Banach space of functions conceived as a generalized Holder metric (see §5).     

Bragg diffraction of light in a restricted homogeneous system of tunnel-coupled waveguides

A system of tunnel-coupled rectilinear waveguides is studied. The dependence of the number of modes in this system on the number of waveguides N, the distance between the waveguides, and the number of modes in a separate waveguide is considered. It is shown that the modes of the m = N and N + 1 orders in such a system are Bragg modes; i.e., the angle between the direction of their propagation and the system axis is close to the Bragg angle. The effective refractive indices n ^* of these modes change stepwise. The step size Δn ^* is found to be dependent on the distance s between the waveguides and on the number of modes in a separate waveguide. A system of single-mode waveguides with the number of guided modes M = 34 < N = 50 is studied experimentally. It is shown that the Bragg modes of the system lie among the leakage modes of the system and have rather low losses. It is demonstrated that the localization of the Bragg modes among the leakage modes may be favorable for their selection upon light generation.     

NMR protocol for on-line Brix determination

Water suppression by diffusive attenuation was used to measure Brix in intact cellular tissue of apple and strawberry. Given the signal-to-noise ratio, the correlation for apple was established without repeated acquisition, so this protocol should also be useful for rapid, on-line measurements at low spectrometer frequencies. Water suppression by theT ₁-Null method fails with cellular tissue because of the considerable variation in the longitudinal relaxation times of vacuolar and cytoplasmic water.     

Temperature dependence of interband transition energy in InGaAsN strain-compensated quantum-well and ridge-waveguide lasers fabricated with pulsed anodic oxidation

Ridge-waveguide InGaAsN triple-quantum-well strain-compensated lasers grown by metal organic chemical vapor deposition were fabricated with pulsed anodic oxidation. The laser’s output power reached 145 mW in continuous-wave mode at room temperature for a 4-?m -stripe-width laser. Continuous-wave single longitudinal mode operation was maintained at a high injection current level with a wavelength of 1287.3 nm at room temperature. Single longitudinal mode operation at 1317.2 nm was achieved at twice the threshold current at 100 °C. The band gap of InGaAsN in the quantum wells at different temperatures was calculated and compared to the measured temperature-dependent laser wavelength.     

Necessary and sufficient conditions in constrained optimization

Additional conditions are attached to the Kuhn-Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications. Necessary and sufficient conditions are also given for optimality of the dual problem. Duality and converse duality are treated accordingly.     

Frequency-domain design of optimal controllers

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 615–621, May, 1989.     

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.