A new stability indicating reverse phase high performance liquid chromatography method for the determination of enantiomeric purity of a DPP‐4 inhibitor drug linagliptin

A simple, sensitive, and stability indicating isocratic reverse phase high performance liquid chromatography method has been developed, optimized and validated for the separation and quantification of S‐enantiomer in linagliptin (R‐enantiomer) drug substance. Enantiomeric separation was achieved on a Cellulose tris(4‐chloro‐3‐methylphenylcarbamate) stationary phase. Mobile phase consists of aqueous diammonium hydrogen phosphate buffer and acetonitrile in the ratio of 35:65 v/v. Isocratic elution was performed at a flow rate of 1.0 mL/min, the column oven temperature was set at 40°C and detection was at 226 nm. The resolution between R and S enantiomers is found to be more than 4.0. The impact of mobile phase composition, pH of buffer and temperature on the resolution has been studied. The detector response is found to be linear over the concentration range of 0.17–1.7 μg/mL. LOD and LOQ levels of S‐enantiomer are found to be 0.057 and 0.172 μg/mL respectively. The recovery of S‐enantiomer is 99.8% w/w. The proposed method is validated for specificity, precision, linearity, accuracy and robustness.     

A scalable approach to combinatorial library design for drug discovery

In this paper, we propose an algorithm for the design of lead generation libraries required in combinatorial drug discovery. This algorithm addresses simultaneously the two key criteria of diversity and representativeness of compounds in the resulting library and is computationally efficient when applied to a large class of lead generation design problems. At the same time, additional constraints on experimental resources are also incorporated in the framework presented in this paper. A computationally efficient scalable algorithm is developed, where the ability of the deterministic annealing algorithm to identify clusters is exploited to truncate computations over the entire data set to computations over individual clusters. An analysis of this algorithm quantifies the tradeoff between the error due to truncation and computational effort. Results applied on test data sets corroborate the analysis and show improvement by factors as large as 10 or more, depending on the data sets.     

Melnikov-Based Dynamical Analysis of Microcantilevers in Scanning Probe Microscopy

We study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation. The interaction between the sample and the cantilever is modeled by a Lennard--Jones potential which consists of a short-range repulsive potential and a long-range van der Waals (vdW) attractive potential. We analyze the dynamics of the cantilever sample system when the cantilever is subjected to a sinusoidal forcing. Using the Melnikov method, the region in the space of physical parameters where chaotic motion is present is determined. In addition, using a proportional and derivative controller, we compute the Melnikov function in terms of the parameters of the controller. Using this relation, controllers can be designed to selectively change the regime of dynamical interaction.     

Analysis of a novel preconditioner for a class of p‐level lower rank extracted systems

This paper proposes and studies the performance of a preconditioner suitable for solving a class of symmetric positive definite systems, Âx=b, which we call p‐level lower rank extracted systems (p‐level LRES), by the preconditioned conjugate gradient method. The study of these systems is motivated by the numerical approximation of integral equations with convolution kernels defined on arbitrary p‐dimensional domains. This is in contrast to p‐level Toeplitz systems which only apply to rectangular domains. The coefficient matrix, Â, is a principal submatrix of a p‐level Toeplitz matrix, A, and the preconditioner for the preconditioned conjugate gradient algorithm is provided in terms of the inverse of a p‐level circulant matrix constructed from the elements of A. The preconditioner is shown to yield clustering in the spectrum of the preconditioned matrix which leads to a substantial reduction in the computational cost of solving LRE systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Controller design to optimize a composite performance measure

This paper studies a mixed objective problem of minimizing a composite measure of thel ₁, ₂, andl -norms together with thel -norm of the step response of the closed loop. This performance index can be used to generate Pareto-optimal solutions with respect to the individual measures. The problem is analyzed for discrete-time, single-input single-output (SISO), linear time-invariant systems. It is shown via Lagrange duality theory that the problem can be reduced to a convex optimization problem with a priori known dimension. In addition, continuity of the unique optimal solution with respect to changes in the coefficients of the linear combination that defines the performance measure is estabilished.This research was supported by the National Science Foundation under Grants No. ECS-92-04309, ECS-92-16690 and ECS-93-08481.     

Hysteresis models of dynamic mode atomic force microscopes: analysis and identification via harmonic balance

A new class of models based on hysteresis functions is developed to describe the operation of dynamic mode atomic force microscopy. Such models can account for dissipative phenomena affecting the interaction between the probe and the sample. The model analysis, which is developed using frequency domain techniques, provides a insights into experimentally observed behavior. Experimental data corroborates the models developed.     

On the Dynamics of a Harmonic Oscillator Undergoing Impacts with a Vibrating Platform

This paper deals with a model for repeated impacts of a massattached to a spring with a massive, sinusoidally vibrating table. Thismodel has been studied in an attempt to understand the cantilever-sampledynamics in atomic force microscopy. In this work, we have shown thatfor some values of the frequency of the vibrating table, there arecountably many orbits of arbitrarily long periods and the system issensitive to the initial conditions with which the experiments areconducted. We have also shown existence of complex dynamics in the caseswhen the natural frequency of the spring-mass system is very low; andwhen it is the same as the oscillating frequency of the table.     

Analysis of a circulant based preconditioner for a class of lower rank extracted systems

This paper proposes and studies the performance of a preconditioner suitable for solving a class of symmetric positive definite systems, A_px=b, which we call lower rank extracted systems (LRES), by the preconditioned conjugate gradient method. These systems correspond to integral equations with convolution kernels defined on a union of many line segments in contrast to only one line segment in the case of Toeplitz systems. The p × p matrix, A_p, is shown to be a principal submatrix of a larger N × N Toeplitz matrix, A_N. The preconditioner is provided in terms of the inverse of a 2N × 2N circulant matrix constructed from the elements of A_N. The preconditioner is shown to yield clustering in the spectrum of the preconditioned matrix similar to the clustering results for iterative algorithms used to solve Toeplitz systems. The analysis also demonstrates that the computational expense to solve LRE systems is reduced to O(N log N). Copyright © 2004 John Wiley & Sons, Ltd.