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.

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.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

Skipping of exon 30 in C5 gene results in complete human C5 deficiency and demonstrates the importance of C5d and CUB domains for stability

The deficiency of complement C5 is rare and frequently associated with severe and recurrent infections, especially caused by Neisseria spp. We observed the absence of component C5 in the serum of 3 siblings from a Brazilian family with history of consanguinity. The patients had suffered from recurrent episodes of meningitis and other less severe infections. Sera from these patients were unable to mediate hemolytic activity either by the classical or alternative pathways and presented extremely low levels of C5 protein (13, 0.9 and 1.0 mu g/ml-normal range: 45-190 mu g/ml). Hemolytic activity could be restored by the addition of purified C5 to deficient serum. Sequencing of sibling C5 cDNA revealed a homozygous 153 bp deletion that corresponds precisely to exon 30. The parents carried the same deletion but only in one allele. Sequencing of the corresponding region in the genomic DNA revealed a C to C substitution within intron 30 and, most significantly, the substitution of GAG(4028) for GAA(4028) at the 3` end of exon 30 which is most likely responsible for skipping of exon 30. The resulting in-frame deletion in the C5 mRNA codes for a mutant C5 protein lacking residues 1289-1339. These residues map to the CUB and C5d domains of the C5 alpha chain. This deletion is expected to produce a non-functional and unstable C5 protein which is more susceptible to degradation. (C) 2009 Published by Elsevier Ltd.

A Prospective Follow-up Study of 44 Mandibular Immediately Loaded Implants Using Resonance Frequency Analysis: Preliminary 1-Year Results

Purpose: This clinical study aimed to evaluate initial, 4-months, and 1-year stability of immediately loaded dental implants inserted according to a protocol of lower rehabilitation with prefabricated bars. Materials and Methods: The sample was composed of 11 edentulous patients. In each patient, 4 interforaminal implants were inserted. Immediately after implant installation, resonance frequency analysis (RFA) for each fixation was registered as well as after 4 months and 1 year with the prosthetic bar removed as it is a screwed system. Results: The clinical implant survival rate was 100%. The RFA showed an increase in stability after 4 months from 64.09 +/- 648 to 64.31 +/- 4.96 and I year, 67.11 +/- 4.37. The analysis of variance showed a statistically significant result (P = 0.015) among implant stability quotient values for the different periods evaluated. Tukey test results showed statistically significant differences between 1-year results and the initial periods but there was no statistically significant difference between initial and 4-month results (P > 0.05). Conclusion: These preliminary 1-year results indicate that immediate loading of mandibular dental implants using the studied prefabricated bars protocol is a reliable treatment as it is in accordance with the results described in the literature for other similar techniques. (Implant Dent 2009; 18:530-538)

COLOR STABILITY OF DENTAL CERAMICS SUBMITTED TO ARTIFICIAL ACCELERATED AGING AFTER REPEATED FIRINGS

Statement of problem. Color stability is an important factor to ensure the long-term clinical success of ceramic restorations. There is a lack of information on how color is affected by fabrication procedures, such as the number of firings. Purpose. The purpose of this study was to evaluate the effects that the number of firings and type of substrate have on the color stability of dental ceramic submitted to artificial accelerated aging. Material and methods. Sixty specimens were fabricated: 30 metal ceramic (Verabond II + IPS d.SIGN) and 30 all-ceramic (IPS d.SIGN). Specimens were divided into 3 groups (n=10), and submitted to 2, 3, or 4 firings (+/- 900 degrees C), respectively, according to the manufacturer`s instructions. Color readings were obtained with a spectro photometer before and after artificial accelerated aging, and L*, a*, and b* coordinates and total color variation (Delta E) were analyzed (2-way ANOVA, Bonferroni, (alpha=05). Results. For metal ceramic specimens, differences for the L* coordinates were significant (P<.05) only for the group submitted to 3 firings. With respect to the all-ceramic specimens, smaller L* coordinates were obtained for greater a* and b* coordinates, indicating that the greater the number of firings, the darker and more reddish/yellowish the specimen. All Delta E values, for all groups, were below 1.0. All-ceramic specimens submitted to 3 and 4 firings presented Delta E means differing statistically (P<.05) from those of the metal ceramic group. Conclusions. The type of substrate and number of firings affected the color stability of the ceramic material tested. Artificial accelerated aging did not produce perceptible color stability changes (Delta E<1.0). (J Prosthet Dent 2009-101:13-18)

Stability of the pstS transcript of Escherichia coli

The pst operon of Escherichia coli is composed of five genes that encode a high-affinity phosphate transport system. As a member of the PHO regulon, pst transcription is activated under phosphate shortage conditions. Under phosphate-replete conditions, the pst operon also functions as a negative regulator of the PHO genes. Transcription of pst is initiated at the promoter located upstream to the first gene, pstS. Immediately after its synthesis, the primary transcript of pst is cleaved into shorter mRNA molecules. The transcription unit corresponding to pstS is significantly more abundant than the transcripts of the other pst genes due to stabilisation of pstS mRNA by a repetitive extragenic palindrome (REP) structure downstream to the pstS locus. The presence of the REP sequence also results in an increased level of PstS proteins. However, the surplus level of PstS proteins produced in the presence of REP does not contribute to the repressive role of Pst in PHO expression.

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.

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.

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.

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.

A Single Mutation at the Sheet Switch Region Results in Conformational Changes Favoring lambda 6 Light-Chain Fibrillogenesis

Systemic amyloid light-chain (LC) amyloidosis is a disease process characterized by the pathological deposition of monoclonal LCs in tissue. All LC subtypes are capable of fibril formation although lambda chains, particularly those belonging to the lambda 6 type, are overrepresented. Here, we report the thermodynamic and in vitro fibrillogenic properties of several mutants of the lambda 6 protein 6aJL2 in which Pro7 and/or His8 was substituted by Ser or Pro. The H8P and H8S mutants were almost as stable as the wildtype protein and were poorly fibrillogenic. In contrast, the P7S mutation decreased the thermodynamic stability of 6aJL2 and greatly enhanced its capacity to form amyloid-like fibrils in vitro. The crystal structure of the P7S mutant showed that the substitution induced both local and long-distance effects, such as the rearrangement of the V(L) (variable region of the light chain)-V(L) interface. This mutant crystallized in two orthorhombic polymorphs, P2(1)2(1)2(1) and C222(1). In the latter, a monomer that was not arranged in the typical Bence-Jones dimer was observed for the first time. Crystal-packing analysis of the C222(1) lattice showed the establishment of intermolecular beta-beta interactions that involved the N-terminus and beta-strand B and that these could be relevant in the mechanism of LC fibril formation. Our results strongly suggest that Pro7 is a key residue in the conformation of the N-terminal sheet switch motif and, through long-distance interactions, is also critically involved in the contacts that stabilized the V(L) interface in lambda 6 LCs. (C) 2009 Elsevier Ltd. 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.