A theorem on supports of a convex functional in a realBanach space

Summary A theorem on supports of a convex functional in a realBanach space is proved which provides us with the principal tool to establish certain duality results for a non-linear programming problem in a realBanach space.

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Zusammenfassung Es wird ein Satz über die Stützhyperebenen eines konvexen Funktionals in einem reellenBanach-Raum bewiesen. Dieser ist ein wesentliches Hilfsmittel zur Herleitung von Dualitätssätzen für nichtlineare Programme inBanach-Räumen.

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Vorgel. v.:J. Nitsche.     

Principal component analysis combined with truncated-Newton minimization for dimensionality reduction of chemical databases

 The similarity and diversity sampling problems are two challenging optimization tasks that arise in the analysis of chemical databases. As a first step to their solution, we propose an efficient projection/ refinement protocol based on the principal component analysis (PCA) and the truncated-Newton minimization method implemented by our package TNPACK (PCA/TNPACK). We show that PCA can provide the same initial guess as the singular value decomposition (SVD) for the optimization task of solving the distance-geometry optimization problem if each column of a database matrix has a mean of zero. Hence, our PCA/TNPACK approach is analogous to the SVD/TNPACK projection/refinement protocol that we developed recently for visualizing large chemical databases. Using PCA/TNPACK and the Merck MDDR database (MDL Drug Data Report), we further investigate the projection/refinement procedure with regards to the preservation of the original clusters of chemical compounds, the accuracy of similarity and diversity sampling of chemical compounds, and the potential application in the study of structure activity relationships. We also explore by simple experiments accuracy and efficiency aspects of the PCA/TNPACK procedure compared to those of a global optimization algorithm (simulated annealing, as implemented by the program package SIMANN) in terms of producing the projection mapping of a database. Numerical results show that the 2D PCA/TNPACK mapping can preserve the distance relationships of the original database and is thus valuable as a first step in similarity and diversity applications. Of course, the generation of a global rather than local minimizer and its interpretation in terms of pharameceutical applications remains a challenge. Since all numerical tests are performed on the Merck MDDR database, results are representative of realistic cases encountered in the field of drug design, and may help analyze properties of medicinal compounds. Received: December 21, 2000 / Accepted: August 19, 2002 Published online: September 27, 2002 Mathematics Subject Classification (2000): 65K10, 62H25, 92C50     

Spectroscopy and laser operation of Nd:ZBAN glass

The results of a study of the spectroscopic and laser properties of a Nd³⁺ doped fluoride glass are presented. Threshold energies and slope efficiencies are reported along with the stimulated emission cross section for the laser transition. The effect of excited state absorption of pump photons on the slope efficiency is investigated     

Nework topology for maximizing the terminal reliability in a Computer Communication Network

In the design of a Computer Communication Network (CCN), the reliability between any pair of nodes and the maximum permissible installation cost are of great importance. These characteristics are largely dependant upon the topological layout of the links, their costs and reliabilities. Having the knowledge of the topological layout of the various computer centres (nodes) and maximum permissible cost of installing the various links at their pre-assigned positions; in this paper an algorithm for obtaining an optimal network topology which gives the maximum s?t reliability is presented. The developed method is general and is computerized. The proposed method has an additional advantage that the system is not to be redesigned, if at a later stage the permissible cost is enhanced by budgetary provisions. An example illustrates the algorithm.     

Investigation of anomalons in He fragments

We have studied the mean free path of He fragments from projectile beams of Ar, Fe and Kr of energy 1 ? E ?2A GeV at different distances $\text{(L ? 2.5}\text{cm}\text{)}$ from their production point and found that they are the same, independent of their (i) energy, (ii) target size, (iii) target excitation, (iv) He multiplicities and (v) production angles.     

Reliability estimation for probabilistic switching circuits

A simple technique for the reliability estimation of switching circuits is developed. A Table is prepared for reliability expressions of basic logic modules. These expressions are then used for the reliability evaluation of complex switching circuits.     

Diamagnetic and zeeman shifts of the ground state of arsenic donors in germanium

The technique of four-wave mixing spectroscopy has been utilized to study the magnetic field dependence of the valley-orbit splitting, 4△(B), of As donors in Ge at 1.8°K for ⊥ [111]. The upper ground level, ls(T₂), splits into two levels, one of “high” and the other of “low” diamagnetism. For donor concentration N_D ? 5 × 10¹⁵ cm^-3 we have measured the diamagnetism and g-factor for the high diamagnetism level (g ? 1.07) as a function of (< 7 T). Transitions originating from both spin-up and spin-down levels are observed, indicating that the spins are heated during the 100 n-sec laser pulse. Excellent agreement between measured and theoretical values of 4▽(B) is found (employing no adjustable parameters) if magnetic field compression of the wavefunction is taken into account.