L_{2}- stability of a class of nonstationary feedback systems with dynamical nonlinear subsystems

A class of feedback systems, consisting of dynamical non-linear subsystems which arise in many diverse control applications, is analyzed for L2-stability. It is shown that, although a transformation of these systems to the familiar Lur'e configuration does not seem to be possible, a one-to-one correspondence may be effected between the stability properties of these and the Lur'e systems. Interesting stability criteria are developed by exploiting this characteristic.

An analytical approach to the study of a class of bi-state social interaction processes

Sufficient conditions for obtaining an equivalent linear model to classes of non-linear, bi-state, social interaction processes are derived. These parametric constraints, when satisfied, permit analytical determination of the dynamics of the non-linear process of social interaction.

Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

Conformationally Restricted Nucleocyclitols: a Study into their Conformational Preferences and Supramolecular Architecture in the Solid State

With the intent of probing the feasibility of employing annulation as a tactic to engender axial rich conformations in nucleoside analogues, two adenine-derived, ``conformationally restricted'' nucleocylitols, 9 and 10, have been conceptualized as representatives of a hitherto unexplored class of nucleic acid base-cyclitol hybrids. A general synthetic strategy, with an inherent scope for diversification, allowed rapid functionalization of indane and tetralin to furnish 9 and 10 respectively in fair yield. Single-crystal X-ray diffraction analysis revealed that the two nucleocyclitols under study, though homologous, present completely dissimilar modes of molecular packing, marked, in particular, by the nature of involvement of the adenynyl NH2 group in the supramolecular assembly. In addition, the crystal structures of 9 and 10 also exhibit two different conformations of the functionalized cyclohexane ring. Thus, while the six-membered carbocycle in cyclopenta-annulated 9 exists in the expected chair (C) conformation that in cyclohexaannulated 10, which crystallizes as a dihydrate, shows an unusual twist-boat (TB) conformation. From a close analysis of the (HNMR)-H-1 spectroscopic data recorded for 9 and 10 in CD3OD, it was possible to put forth a putative explanation for the uncanny conformational preferences of crystalline 9 and 10.

Structural studies of analgesics and their interactions. III. The crystal and molecular structure of amidopyrine

Amidopyrine (1-phenyl-2,3-dimethyl-4-dimethylaminopyrazolone), C13HzvN30, a dimethylamino derivative of antipyrine and an important analgesic and antipyretic agent, crystallizes in the triclinic space group P1 with four molecules in a unit cell of dimensions a= 7.458 (5), b = 10.744 (5), c= 17.486 (15)/~,, e=98.6 (2),/~= 85.6 (3), y= 108-6 (2) . The structure was solved by direct methods and refined to an R value of 0.055 for 3706 photographically observed reflexions. The dimensions of the two crystallographically independent molecules are very nearly the same. The pyrazolone moiety in the molecule has dimensions comparable to those in antipyrine. Unlike antipyrine, the molecular dimensions of amidopyrine in the free state (the present structure) are close to those found in some of its hydrogenbonded complexes. Thus it appears that the presence of the dimethylamino group makes the molecule more resistant to changes in its dimensions resulting from molecular association. An attempt has also been made to correlate the polar nature of the pyrazolone moiety and the hybridization state of the hetero nitrogen atoms in antipyrine, amidopyrine and their complexes.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Thermal decomposition of hydrazinium monoperchlorate in the molten state

The thermal decomposition of hydrazinium monoperchlorate (HP-1) in the molten state has been investigated using differential thermal analysis, thermogravimetric analysis, a constant volume manometric technique and mass-spectrometry. The stoichiometry of the reaction can be represented by the equation: 20 N2H5C1O4 13 NH4C1O4 + 3.5 Cl2 + 2 O2 + 13 N2 + 0.5 N2O + 0.5 H2 + + 23.5 H2O The data seem to indicate that the mechanism, which involves an associated complex, remains unchanged from 140 to 190°. Consequently, impurities capable of forming associated complexes with the hydrazinium or the perchlorate ion desensitize the thermal decomposition of HP-1, the extent of desensitization being determined by the size, the charge and the concentration of the impurity.

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

State Minimization of Incompletely Specified Sequential Machines

A simple procedure for the state minimization of an incompletely specified sequential machine whose number of internal states is not very large is presented. It introduces the concept of a compatibility graph from which the set of maximal compatibles of the machine can be very conveniently derived. Primary and secondary implication trees associated with each maximal compatible are then constructed. The minimal state machine covering the incompletely specified machine is then obtained from these implication trees.

Feedback-type inhibition of activity of 3-hydroxy-3-methylglutaryl coenzyme a reductase by ubiquinone

Accompanying the decrease in serum cholesterol and increase in concentration of ubiquinone in liver and its microsomes, the activity, but not the protein, of HMG-CoA reductase decreased in ubiquinone-supplemented rats. A soluble 58-kDa preparation of HMG-CoA reductase was partially inhibited on addition of ubiquinone indicating a possible feedback type of action.

Thermodynamic characterization of the reversible, two-state unfolding of maltose binding protein, a large two-domain protein

The folding and stability of maltose binding protein (MBP) have been investigated as a function of pH and temperature by intrinsic tryptophan fluorescence, far- and near-UV circular dichroism, and high-sensitivity differential scanning calorimetric measurements. MBP is a monomeric, two-domain protein containing 370 amino acids. The protein is stable in the pH range of 4-10.5 at 25 degrees C. The protein exhibits reversible, two-state, thermal and guanidine hydrochloride-mediated denaturation at neutral pH. The thermostability of MBP is maximal at pH 6, with a Tm of 64.9 degrees C and a deltaHm of 259.7 kcal mol(-1). The linear dependence of deltaHm on Tm was used to estimate a value of deltaCp of 7.9 kcal mol(-1) K(-1) or 21.3 cal (mol of residue)(-1) K(-1). These values are higher than the corresponding deltaCp's for most globular proteins studied to date. However, the extrapolated values of deltaH and deltaS (per mole of residue) at 110 degrees C are similar to those of other globular proteins. These data have been used to show that the temperature at which a protein undergoes cold denaturation depends primarily on the deltaCp (per mol of residue) and that this temperature increases with an increase in deltaCp. The predicted decrease in stability of MBP at low temperatures was experimentally confirmed by carrying out denaturant-mediated unfolding studies at neutral pH at 2 and 28 degrees C.