A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

On Excess-time Correlated Cumulative Processes

In this paper a class of correlated cumulative processes, B _s (t) = ∑^N(t)_i=1 H _s (X _i )X _i , is studied with excess level increments X _i ?s, where {N(t), t ?0} is the counting process generated by the renewal sequence T _n , T _n and X _n are correlated for given n, H _s (t) is the Heaviside function and s?0 is a given constant. Several useful results, for the distributions of B _s (t), and that of the number of excess (non-excess) increments on (0, t) and the corresponding means, are derived. First passage time problems are also discussed and various asymptotic properties of the processes are obtained. Transform results, by applying a flexible form for the joint distribution of correlated pairs (T _n , X _n ) are derived and inverted. The case of non-excess level increments, X _i < s, is also considered. Finally, applications to known stochastic shock and pro-rata warranty models are given.     

PRODEN: A new program for calculating integrated projected populations

Two new computational methods for the evaluation and partitioning of projected, planar, and averaged slab electron densities, implemented in the program PRODEN, are presented. The new algorithms for the projection, demarcation, and integration of electron densities are described and evaluated in terms of speed and numerical accuracy. Integrated Projected Populations are analyzed and some of the advantages and limitations of the methods are discussed.     

Multiobjective optimization of combinatorial libraries

Combinatorial chemistry and high-throughput screening have caused afundamental shift in the way chemists contemplate experiments.Designing a combinatorial library is a controversial art thatinvolves a heterogeneous mix of chemistry, mathematics, economics,experience, and intuition. Although there seems to be little agreementas to what constitutes an ideal library, one thing is certain: onlyone property or measure seldom defines the quality of the design. Inmost real-world applications, a good experiment requires the simultaneousoptimization of several, often conflicting, design objectives, some ofwhich may be vague and uncertain. In this paper, we discuss a class ofalgorithms for subset selection rooted in the principles of multiobjectiveoptimization. Our approach is to employ an objective function that encodesall of the desired selection criteria, and then use a simulated annealingor evolutionary approach to identify the optimal (or a nearly optimal)subset from among the vast number of possibilities. Many design criteriacan be accommodated, including diversity, similarity to known actives,predicted activity and/or selectivity determined by quantitativestructure-activity relationship (QSAR) models or receptor binding models,enforcement of certain property distributions, reagent costand availability, and many others. The method is robust, convergent,and extensible, offers the user full control over the relativesignificance of the various objectives in the final design, andpermits the simultaneous selection of compounds from multiple librariesin full- or sparse-array format.     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Excess-time Renewal Theory with Applications

In this paper, the renewal theory is investigated from the point of view of the excess-time (non-excess-time) renewal intervals. Useful results are derived, and applications to several renewal models are given.     

A self-organizing algorithm for molecular alignment and pharmacophore development

We present a method for simultaneous three-dimensional (3D) structure generation and pharmacophore-based alignment using a self-organizing algorithm called Stochastic Proximity Embedding (SPE). Current flexible molecular alignment methods either start from a single low-energy structure for each molecule and tweak bonds or torsion angles, or choose from multiple conformations of each molecule. Methods that generate structures and align them iteratively (e.g., genetic algorithms) are often slow. In earlier work, we used SPE to generate good-quality 3D conformations by iteratively adjusting pairwise distances between atoms based on a set of geometric rules, and showed that it samples conformational space better and runs faster than earlier programs. In this work, we run SPE on the entire ensemble of molecules to be aligned. Additional information about which atoms or groups of atoms in each molecule correspond to points in the pharmacophore can come from an automatically generated hypothesis or be specified manually. We add distance terms to SPE to bring pharmacophore points from different molecules closer in space, and also to line up normal/direction vectors associated with these points. We also permit pharmacophore points to be constrained to lie near external coordinates from a binding site. The aligned 3D molecular structures are nearly correct if the pharmacophore hypothesis is chemically feasible; postprocessing by minimization of suitable distance and energy functions further improves the structures and weeds out infeasible hypotheses. The method can be used to test 3D pharmacophores for a diverse set of active ligands, starting from only a hypothesis about corresponding atoms or groups.     

Radial clustergrams: visualizing the aggregate properties of hierarchical clusters

A new radial space-filling method for visualizing cluster hierarchies is presented. The method, referred to as a radial clustergram, arranges the clusters into a series of layers, each representing a different level of the tree. It uses adjacency of nodes instead of links to represent parent-child relationships and allocates sufficient screen real estate to each node to allow effective visualization of cluster properties through color-coding. Radial clustergrams combine the most appealing features of other cluster visualization techniques but avoid their pitfalls. Compared to classical dendrograms and hyperbolic trees, they make much more efficient use of space; compared to treemaps, they are more effective in conveying hierarchical structure and displaying properties of nodes higher in the tree. A fisheye lens is used to focus on areas of interest, without losing sight of the global context. The utility of the method is demonstrated using examples from the fields of molecular diversity and conformational analysis.