Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Permanence of stability for a class of system of differential equations with two delays

The paper studies a class of a system of linear retarded differential difference equations with several parameters. It presents some sufficient conditions under which no stability changes for an equilibrium point occurs. Application of these results is given. (c) 2007 Elsevier Ltd. All rights reserved.

STABILITY FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential equations (GODEs). In this paper, some stability concepts for retarded functional differential equations are introduced and they are discussed using known stability results for GODEs. Then the equivalence of the different concepts of stabilities considered here are proved and converse Lyapunov theorems for a very wide class of retarded functional differential equations are obtained by means of the correspondence of this class of equations with GODEs.

Poisson stability for impulsive semidynamical systems

In this paper, the concept of Poisson stability is investigated for impulsive semidynamical systems. Recursive properties are also investigated. (C) 2009 Elsevier Ltd. All rights reserved.

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

Fibrinogen stability under surfactant interaction

Differential scanning calorimetry (DSC), circular dichroism (CD), difference spectroscopy (UV-vis), Raman spectroscopy, and small-angle X-ray scattering (SAXS) measurements have been performed in the present work to provide a quantitatively comprehensive physicochemical description of the complexation between bovine fibrinogen and the sodium perfluorooctanoate, sodium octanoate, and sodium dodecanoate in glycine buffer (pH 8.5). It has been found that sodium octanoate and dodecanoate act as fibrinogen destabilizer. Meanwhile, sodium perfluorooctanoate acts as a structure stabilizer at low molar concentration and as a destabilizer at high molar concentration. Fibrinogen`s secondary structure is affected by all three studied surfactants (decrease in alpha-helix and an increase in beta-sheet content) to a different extent. DSC and UV-vis revealed the existence of intermediate states in the thermal unfolding process of fibrinogen. In addition, SAXS data analysis showed that pure fibrinogen adopts a paired-dimer structure in solution. Such a structure is unaltered by sodium octanoate and perfluoroctanoate. However, interaction of sodium dodecanoate with the fibrinogen affects the protein conformation leading to a complex formation. Taken together, all results evidence that both surfactant hydrophobicity and tail length mediate the fibrinogen stability upon interaction. (C) 2011 Elsevier Inc. All rights reserved.

Stability of the curvature perturbation in dark sectors` mutual interacting models

We consider perturbations in a cosmological model with a small coupling between dark energy and dark matter. We prove that the stability of the curvature perturbation depends on the type of coupling between dark sectors. When the dark energy is of quintessence type, if the coupling is proportional to the dark matter energy density, it will drive the instability in the curvature perturbations: however if the coupling is proportional to the energy density of dark energy, there is room for the stability in the curvature perturbations. When the dark energy is of phantom type, the perturbations are always stable, no matter whether the coupling is proportional to the one or the other energy density. (C) 2008 Elsevier B.V. All rights reserved.

Stability and related properties of vacua and ground states

We consider the formal non-relativistic limit (nrl) of the : phi(4):(s+1) relativistic quantum field theory (rqft), where s is the space dimension. Following the work of R. Jackiw [R. Jackiw, in: A. Ali, P. Hood-bhoy (Eds.), Beg Memorial Volume, World Scientific, Singapore, 1991], we show that, for s = 2 and a given value of the ultraviolet cutoff K, there are two ways to perform the nrl: (i) fixing the renormalized mass m(2) equal to the bare mass m(0)(2); (ii) keeping the renormalized mass fixed and different from the bare mass mo. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as K -> infinity in case (i) and, in case (ii), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s = 1 by a rigorous stability/instability result of a different nature. (C) 2007 Elsevier Inc. All rights reserved.

Energetics and stability of vacancies in carbon nanotubes

In this work we present ab initio calculations of the formation energies and stability of different types of multi-vacancies in carbon nanotubes. We demonstrate that, as in the case of graphene, the reconstruction of the defects has drastic effects on the energetics of the tubes. In particular, the formation of pentagons eliminates the dangling bonds thus lowering the formation energy. This competition leads to vacancies having an even number of carbon atoms removed to be more stable. Finally the appearance of magic numbers indicating more stable defects can be represented by a model for the formation energies that is based on the number of dangling bonds of the unreconstructed system, the pentagons and the relaxation of the final form of the defect formed after the relaxation. (C) 2011 Elsevier Ltd. All rights reserved.

Stability and interface properties of thin cellulose ester films adsorbed from acetone and ethyl acetate solutions

Stability and interface properties of cellulose acetate propionate (CAP) and cellulose acetate butyrate (CAB) films adsorbed from acetone or ethyl acetate onto Si wafers have been investigated by means of contact angle measurements and atomic force microscopy (AFM). Surface energy (gamma(total)(S)) values determined for CAP adsorbed from acetone are larger than those from ethyl acetate. In the case of CAB films adsorbed from ethyl acetate and acetone were similar. Dewetting was observed by AFM only for CAP films prepared from ethyl acetate. Positive values of effective Hamaker constant (A(eff)) were found only for CAP prepared from ethyl acetate, corroborating with dewetting phenomena observed by AFM. Oil the contrary, negative values of A(eff) were determined for CAP and CAB prepared from acetone and for CAB prepared from ethyl acetate, Corroborating with experimental observations. Sum frequency generation (SFG) vibrational spectra indicated that CAP and CAB films prepared from ethyl acetate present more alkyl groups oriented perpendicularly to the polymer-air interface than those films prepared from acetone. Such preferential orientation corroborates with macroscopic contact angle measurements. Moreover, SFG spectra showed that acetone hinds strongly to Si wafers, creating a new surface for CAP and CAB films. (C) 2008 Elsevier Inc. All rights reserved.

Polymeric scaffolds for enhanced stability of melanin incorporated in liposomes

The use of melanin in bioinspired applications is mostly limited by its poor stability in solid films. This problem has been addressed here by incorporating melanin into dipalmitoyl phosphatidyl glycerol (DPPG) liposomes, which were then immobilized onto a solid substrate as an LbL film. Results from steady-state and time-resolved fluorescence indicated an increased stability for melanin incorporated into DPPG liposomes. If not protected by liposomes, melanin looses completely its fluorescence properties in LbL films. The thickness of the liposome-melanin layer obtained from neutron reflectivity data was 4.1 +/- 0.2 nm, consistent with the value estimated for the phospholipid bilayer of the liposomes, an evidence of the collapse of most liposomes. On the other hand, the final roughness indicated that some of the liposomes had their structure preserved. In summary, liposomes were proven excellent for encapsulation, thus providing a suitable environment, closer to the physiological conditions without using organic solvents or high pHs. (C) 2010 Elsevier Inc. All rights reserved.

Thermodynamic characterization of the palm tree Roystonea regia peroxidase stability

The structural stability of a peroxidase, a dimeric protein from royal palm tree (Roystonea regia) leaves, has been characterized by high-sensitivity differential scanning calorimetry, circular dichroism, steady-state tryptophan fluorescence and analytical ultracentifugation under different solvent conditions. It is shown that the thermal and chemical (using guanidine hydrochloride (Gdn-HCl)) folding/unfolding of royal palm tree peroxidase (RPTP) at pH 7 is a reversible process involving a highly cooperative transition between the folded dimer and unfolded monomers, with a free stabilization energy of about 23 kcal per mol of monomer at 25 degrees C. The structural stability of RPTP is pH-dependent. At pH 3, where ion pairs have disappeared due to protonation, the thermally induced denaturation of RPTP is irreversible and strongly dependent upon the scan rate, suggesting that this process is under kinetic control. Moreover, thermally induced transitions at this pH value are dependent on the protein concentration, allowing it to be concluded that in solution RPTP behaves as dimer, which undergoes thermal denaturation coupled with dissociation. Analysis of the kinetic parameters of RPTP denaturation at pH 3 was accomplished on the basis of the simple kinetic scheme N ->(k) D, where k is a first-order kinetic constant that changes with temperature, as given by the Arrhenius equation; N is the native state, and D is the denatured state, and thermodynamic information was obtained by extrapolation of the kinetic transition parameters to an infinite heating rate. Obtained in this way, the value of RPTP stability at 25 degrees C is ca. 8 kcal per mole of monomer lower than at pH 7. In all probability, this quantity reflects the contribution of ion pair interactions to the structural stability of RPTP. From a comparison of the stability of RPTP with other plant peroxidases it is proposed that one of the main factors responsible for the unusually high stability of RPTP which enhances its potential use for biotechnological purposes, is its dimerization. (c) 2008 Elsevier Masson SAS. All rights reserved.

Structural stability and reversible unfolding of recombinant porcine S100A12

Porcine S100A12 is a member of the S100 proteins, family of small acidic calcium-binding proteins characterized by the presence of two EF-hand motifs. These proteins are involved in many cellular events such as the regulation of protein phosphorylation, enzymatic activity, protein-protein interaction, Ca(2+) homeostasis, inflammatory processes and intermediate filament polymerization. In addition, members of this family bind Zn(2+) or Ca(2+) with cooperative effect on binding. In this study, the gene sequence encoding porcine S100A12 was obtained by the synthetic gene approach using E. coli codon bias. Additionally, we report a thermodynamic study of the recombinant S100A12 using circular dichroism, fluorescence and isothermal titration calorimetry. The results of urea and temperature induced unfolding and refolding processes indicated a reversible two-state process. Also, the ANS fluorescence studies showed that in presence of divalent ions the protein exposes hydrophobic sites which could facilitate the interaction with other proteins and trigger the physiological responses. (c) 2008 Elsevier B.V. All rights reserved.

The stability and aggregation properties of the GTPase domain from human SEPT4

The septins are a family of conserved proteins involved in cytokinesis and cortical organization. An increasing amount of data implicates different septins in diverse pathological conditions including neurodegenerative disorders, neoplasia and infections. Human SEPT4 is a member of this family and its tissue-specific ectopic expression profile in colorectal and urologic cancer makes it a useful diagnostic biomarker. Thermal unfolding of the GTPase domain of SEPT4 (SEPT4-G) revealed an unfolding intermediate which rapidly aggregates into amyloid-like fibers under physiological conditions. In this study, we examined the effects of protein concentration, pH and metals ions on the aggregation process of recombinant SEPT4-G using a series of biophysical techniques, which were also employed to study chemical unfolding and stability. Divalent metal ions caused significant acceleration to the rate of SEPT4-G aggregation. Urea induced unfolding was shown to proceed via the formation of a partially unfolded intermediate state which unfolds further at higher urea concentrations. The intermediate is a compact dimer which is unable to bind GTR At 1 M urea concentration, the intermediate state was plagued by irreversible aggregation at temperatures above 30 degrees C. However, higher urea concentration resulted in a marked decay of the aggregation, indicating that the partially folded structures may be necessary for the formation of these aggregates. The results presented here are consistent with the recently determined crystal structure of human septins and shed light on the aggregation properties of SEPT4 pertinent to its involvement in neurodegenerative disease. (C) 2008 Elsevier B.V. All rights reserved.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.