Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Nature, stability and bonding of the peroxy group in peroxy titanium compounds

Some physicochemical properties of peroxy titanium compounds are explained by assigning a strained triangular ring structure to the peroxy titanyl group, with a bent and reduced overlap of the O---O bonding orbitals. The stability of the peroxy group is found to depend on the stability of the other ligands. The decreasing order of stability of the peroxy group in the compounds is as: oxalato > meleato > malonato > sulphato > peroxide of titanium.

Force constants and thermodynamic functions of iodine heptafluoride

Normal coordinate analysis of a molecule of the type XY7 (point group D5h) has been carried out using Wilson's FG, matrix method and the results have been utilized to calculate the force constants of IF7 from the available Raman and infrared data. Some of the assignments made previously by Lord and others have been revised and with the revised assignments the thermodynamic quantities of IF7 have been computed from 300°K to 1000°K under rigid rotator and harmonic oscillator approximation.

Generalizations and Models in Ecology : Lawlikeness, Invariance, Stability, and Robustness

The question at issue in this dissertation is the epistemic role played by ecological generalizations and models. I investigate and analyze such properties of generalizations as lawlikeness, invariance, and stability, and I ask which of these properties are relevant in the context of scientific explanations. I will claim that there are generalizable and reliable causal explanations in ecology by generalizations, which are invariant and stable. An invariant generalization continues to hold or be valid under a special change called an intervention that changes the value of its variables. Whether a generalization remains invariant during its interventions is the criterion that determines whether it is explanatory. A generalization can be invariant and explanatory regardless of its lawlike status. Stability deals with a generality that has to do with holding of a generalization in possible background conditions. The more stable a generalization, the less dependent it is on background conditions to remain true. Although it is invariance rather than stability of generalizations that furnishes us with explanatory generalizations, there is an important function that stability has in this context of explanations, namely, stability furnishes us with extrapolability and reliability of scientific explanations. I also discuss non-empirical investigations of models that I call robustness and sensitivity analyses. I call sensitivity analyses investigations in which one model is studied with regard to its stability conditions by making changes and variations to the values of the model s parameters. As a general definition of robustness analyses I propose investigations of variations in modeling assumptions of different models of the same phenomenon in which the focus is on whether they produce similar or convergent results or not. Robustness and sensitivity analyses are powerful tools for studying the conditions and assumptions where models break down and they are especially powerful in pointing out reasons as to why they do this. They show which conditions or assumptions the results of models depend on. Key words: ecology, generalizations, invariance, lawlikeness, philosophy of science, robustness, explanation, models, stability

Role of entropy in the stability of cobalt titanates

The standard molar Gibbs free energy of formation of Co2TiO4, CoTiO3,and CoTi2O5 as a function of temperature over an extended range (900 to 1675) K was measured using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte, with CoO as reference electrode and appropriate working electrodes. For the formation of the three compounds from their component oxides CoO with rock-salt and TiO2 with rutile structure, the Gibbs free energy changes are given by:Delta(f)G degrees((ox))(Co2TiO4) +/- 104/(J . mol(-1)) = -18865 - 4.108 (T/K)Delta(f)G degrees((ox))(CoTiO3) +/- 56/(J . mol(-1)) = -19627 + 2.542 (T/K) Delta(f)G degrees((ox))(CoTi2O5) +/- 52/(J . mol(-1)) = -6223 - 6.933 (T/K) Accurate values for enthalpy and entropy of formation were derived. The compounds Co2TiO4 with spinel structure and CoTi2O5 with pseudo-brookite structure were found to be entropy stabilized. The relatively high entropy of these compounds arises from the mixing of cations on specific crystallographic sites. The stoichiometry of CoTiO3 was confirmed by inert gas fusion analysis for oxygen. Because of partial oxidation of cobalt in air, the composition corresponding to the compound Co2TiO4 falls inside a two-phase field containing the spinet solid solution Co2TiO4-Co3O4 and CoTiO3. The spinel solid solution becomes progressively enriched in Co3O4 with decreasing temperature. (c) 2010 Elsevier Ltd. All rights reserved.

Improved Conditions For L2-Stability Of Nonstationary Feedback-Systems

Concerning the L2-stability of feedback systems containing a linear time-varying operator, some of the stringent restrictions imposed on the multiplier as well as the linear part of the system, in the criteria presented earlier, are relaxed.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.

Structural stability of slender aerospace vehicles: Part I Mathematical modeling

A detailed mechanics based model is developed to analyze the problem of structural instability in slender aerospace vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic pressure and the propulsive thrust of the vehicle. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. Condition under which a flexible body with internal stress waves behaves like a perfect rigid body is derived. Two methods are developed for finite element discretization of the system: (1) A time-frequency Fourier spectral finite element method and (2) h-p finite element method. Numerical results using the above methods are presented in Part II of this paper. (C) 2010 Elsevier Ltd. All rights reserved.

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.

The Critical Role of N- and C-Terminal Contact in Protein Stability and Folding of a Family 10 Xylanase under Extreme Conditions

Background: Stabilization strategies adopted by proteins under extreme conditions are very complex and involve various kinds of interactions. Recent studies have shown that a large proportion of proteins have their N- and C-terminal elements in close contact and suggested they play a role in protein folding and stability. However, the biological significance of this contact remains elusive. Methodology: In the present study, we investigate the role of N- and C-terminal residue interaction using a family 10 xylanase (BSX) with a TIM-barrel structure that shows stability under high temperature,alkali pH, and protease and SDS treatment. Based on crystal structure,an aromatic cluster was identified that involves Phe4, Trp6 and Tyr343 holding the Nand C-terminus together; this is a unique and important feature of this protein that might be crucial for folding and stabilityunder poly-extreme conditions. Conclusion: A series of mutants was created to disrupt this aromatic cluster formation and study the loss of stability and function under given conditions. While the deletions of Phe4 resulted in loss of stability, removal of Trp6 and Tyr343 affected in vivo folding and activity. Alanine substitution with Phe4, Trp6 and Tyr343 drastically decreased stability under all parameters studied. Importantly,substitution of Phe4 with Trp increased stability in SDS treatment.Mass spectrometry results of limited proteolysis further demonstrated that the Arg344 residue is highly susceptible to trypsin digestion in sensitive mutants such as DF4, W6A and Y343A, suggesting again that disruption of the Phe4-Trp6-Tyr343 (F-W-Y) cluster destabilizes the N-and C-terminal interaction. Our results underscore the importance of N- and C-terminal contact through aromatic interactions in protein folding and stability under extreme conditions, and these results may be useful to improve the stability of other proteins under suboptimal conditions.