Spherical aberration and its correction using Lie algebraic methods

We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using Fermat's principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques. Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method. The result obtained with this approach is compared and found to agree with the exact result of the first method.

Non-interferometric methods of phase estimation for application in optical tomography

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.

Novel subspace methods for blind estimation of multiple CFOs in MIMO-OFDM systems

The problem of estimating multiple Carrier Frequency Offsets (CFOs) in the uplink of MIMO-OFDM systems with Co-Channel (CC) and OFDMA based carrier allocation is considered. The tri-linear data model for generalized, multiuser OFDM system is formulated. Novel blind subspace based estimation of multiple CFOs in the case of arbitrary carrier allocation scheme in OFDMA systems and CC users in OFDM systems based on the Khatri-Rao product is proposed. The method works where the conventional subspace method fails. The performance of the proposed methods is compared with pilot based Least-Squares method.

Chromatographic methods for determination of nimesulide and for stability studies

Simple and rapid HPLC, GC, and TLC procedures have been developed for detection and determination of nimesulide, a non-pharmacopeial drug, in preformulation and dosage form. Use of these techniques has enabled separation of impurities and the precursor in the bulk material and in formulations. Isocratic reversed-phase HPLC was performed on a C-18 column with methanol-water-acetic acid, 67:32:1 (v/v), as mobile phase and UV detection at 230 nm. Calibration curves were linear over the concentration range 100-1000 mug mL(-1) with a good correlation coefficient (0.9993) and a coefficient of variation of 1.5%. Gas chromatography was performed on an OV-17 packed column with temperature programming and flame-ionization detection. The lower limit of determination by HPLC and GC was 4 ppm. Thin-layer chromatography of nimesulide was performed on silica gel G with toluene-ethyl acetate, 8:2, as mobile phase. Stability testing of the drug was performed under different temperature, humidity, and UV-radiation conditions.

Improved preprocessing methods for modulo scheduling algorithms

Instruction scheduling with an automaton-based resource conflict model is well-established for normal scheduling. Such models have been generalized to software pipelining in the modulo-scheduling framework. One weakness with existing methods is that a distinct automaton must be constructed for each combination of a reservation table and initiation interval. In this work, we present a different approach to model conflicts. We construct one automaton for each reservation table which acts as a compact encoding of all the conflict automata for this table, which can be recovered for use in modulo-scheduling. The basic premise of the construction is to move away from the Proebsting-Fraser model of conflict automaton to the Muller model of automaton modelling issue sequences. The latter turns out to be useful and efficient in this situation. Having constructed this automaton, we show how to improve the estimate of resource constrained initiation interval. Such a bound is always better than the average-use estimate. We show that our bound is safe: it is always lower than the true initiation interval. This use of the automaton is orthogonal to its use in modulo-scheduling. Once we generate the required information during pre-processing, we can compute the lower bound for a program without any further reference to the automaton.

Methods for making prisms with submultiple or half angles: applications to the measurement of the angles of Pechan and Pellin-Broca prisms

A simple technique is devised for making prisms with submultiple or half angles. As an application of these prisms, methods are suggested to measure the angles of the Pechan and Pellin-Broca prisms without using expensive spectrometers, autocollimators, and angle gauges. (C) 2002 Society of Photo-Optical Instrumentation Engineers.

Optimum design of a helicopter rotor for low vibration using aeroelastic analysis and response surface methods

An aeroelastic analysis based on finite elements in space and time is used to model the helicopter rotor in forward flight. The rotor blade is represented as an elastic cantilever beam undergoing flap and lag bending, elastic torsion and axial deformations. The objective of the improved design is to reduce vibratory loads at the rotor hub that are the main source of helicopter vibration. Constraints are imposed on aeroelastic stability, and move limits are imposed on the blade elastic stiffness design variables. Using the aeroelastic analysis, response surface approximations are constructed for the objective function (vibratory hub loads). It is found that second order polynomial response surfaces constructed using the central composite design of the theory of design of experiments adequately represents the aeroelastic model in the vicinity of the baseline design. Optimization results show a reduction in the objective function of about 30 per cent. A key accomplishment of this paper is the decoupling of the analysis problem and the optimization problems using response surface methods, which should encourage the use of optimization methods by the helicopter industry. (C) 2002 Elsevier Science Ltd. All rights reserved.

Partial instantiation methods for inference in first-order logic

Satisfiability algorithms for propositional logic have improved enormously in recently years. This improvement increases the attractiveness of satisfiability methods for first-order logic that reduce the problem to a series of ground-level satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolution-based methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (3) simplifying it to obtain further speedup. We provide a similar development for a "dual" partial instantiation approach defined by Hooker and suggest a primal-dual strategy. We prove correctness of the primal and dual algorithms for full first-order logic with functions, as well as termination on unsatisfiable formulas. We also report some preliminary computational results.

Estimation of groundwater recharge of shallow aquifer on humid environment in Yaounde, Cameroon using hybrid water-fluctuation and hydrochemistry methods

A study of environmental chloride and groundwater balance has been carried out in order to estimate their relative value for measuring average groundwater recharge under a humid climatic environment with a relatively shallow water table. The hybrid water fluctuation method allowed the split of the hydrologic year into two seasons of recharge (wet season) and no recharge (dry season) to appraise specific yield during the dry season and, second, to estimate recharge from the water table rise during the wet season. This well elaborated and suitable method has then been used as a standard to assess the effectiveness of the chloride method under forest humid climatic environment. Effective specific yield of 0.08 was obtained for the study area. It reflects an effective basin-wide process and is insensitive to local heterogeneities in the aquifer system. The hybrid water fluctuation method gives an average recharge value of 87.14 mm/year at the basin scale, which represents 5.7% of the annual rainfall. Recharge value estimated based on the chloride method varies between 16.24 and 236.95 mm/year with an average value of 108.45 mm/year. It represents 7% of the mean annual precipitation. The discrepancy observed between recharge value estimated by the hybrid water fluctuation and the chloride mass balance methods appears to be very important, which could imply the ineffectiveness of the chloride mass balance method for this present humid environment.

{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation

In this paper, we develop and analyze C(0) penalty methods for the fully nonlinear Monge-Ampere equation det(D(2)u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well as quasi-optimal error estimates using the Banach fixed-point theorem as our main tool. Numerical experiments are presented which support the theoretical results.