The Neumann series as a fundamental solution of the two-dimensional convection–diffusion equation with variable velocity

The fundamental solution of the two-dimensional convection–diffusion equation with variable coefficients and its adjoint equation are obtained in complex form in terms of the unknown density of two equivalent uniquely solvable Volterra integral equations of the second kind whose analytical solutions are given explicitly as convergent Neumann series. The Volterra integral equations are obtained by integrating the complex form of the original differential equations, without additional change of variables as proposed by previously authors. In the numerical examples, cases corresponding to non-self-adjoint operators are considered. As a validation, the proposed approach is used to derive the fundamental solution of the adjoint to the convection–diffusion equation with constant velocity. In this case, the series solution can be evaluated analytically. For more general velocity fields, the recursive terms of the series can be evaluated by symbolic computation or numerical integration.     

Computing failure probabilities. Applications to reliability analysis

The paper presents one method for calculating failure probabilities with applications to reliability analysis. The method is based on transforming the initial set of variables to a n-dimensional uniform random variable in the unit hypercube, together with the limit condition set and calculating the associated probability using a recursive method based on the Gauss–Legendre quadrature formulas to calculate the resulting multiple integrals. An example of application is used to illustrate the proposed method.     

Thermodynamic analysis of alpha-spectrin SH3 and two of its circular permutants with different loop lengths: discerning the reasons for rapid folding in proteins

The temperature dependences of the unfolding-refolding reaction of a shorter version of the alpha-spectrin SH3 domain (PWT) used as a reference and of two circular permutants (with different poly-Gly loop lengths at the newly created fused loop) have been measured by differential scanning microcalorimetry and stopped-flow kinetics, to characterize the thermodynamic nature of the transition and native states. Differential scanning calorimetry results show that all these species do not belong to the same temperature dependency of heat effect. The family of the N47-D48s circular permutant (with 0-6 Gly inserted at the fused-loop) shows a higher enthalpy as happens with the PWT domain. The wild type (WT) and the S19-P20s permutant family have a more similar behavior although the second is far less stable. The crystallographic structure of the PWT shows a hairpin formation in the region corresponding to the unstructured N-terminus tail of the WT, explaining the enthalpic difference. There is a very good correlation between the calorimetric changes and the structural differences between the WT, PWT, and two circular permutants that suggests that their unfolded state cannot be too different. Elongation of the fused loop in the two permutants, taking as a reference the protein with one inserted Gly, results in a small Gibbs energy change of entropic origin as theoretically expected. Eyring plots of the unfolding and refolding semireactions show different behaviors for PWT, S19-P20s, and N47-D48s in agreement with previous studies indicating that they have different transition states. The SH3 transition state is relatively close to the native state with regard to changes in heat capacity and entropy, indicating a high degree of compactness and order. Regarding the differences in thermodynamic parameters, it seems that rapid folding could be achieved in proteins by decreasing the entropic barrier.     

Impact of environment on adolescent mental health and behavior: structural equation modeling

This study uses structural equation models to describe how objective neighborhood, perceived neighborhood, and environmental support predict mental health; 792 adolescents responded to highly structured interviews. The effect of objective environment on mental health was mediated through its influence on perceived neighborhood. Environmental support mitigated negative perceptions of environment and the effect of perceived environment on mental health, while exposure to violence augmented the negative effect of perceived environment.     

Clinical and histological outcome after hepatitis B e antigen to antibody seroconversion in children with chronic hepatitis B

Data regarding the outcome of children with chronic hepatitis B after seroconversion are scarce. We describe the long-term evolution of these patients. One hundred and three children with antibody against hepatitis B e antigen and normal alanine aminotransferase (ALT) levels were followed for 0.6 to 12.5 years (mean, 6.3 years). Paired liver biopsies (before and after seroconversion) were available in 83 cases. Final biopsies were obtained 0.5 to 12.5 years (mean, 4.5 years) after seroconversion. ALT levels remained normal in most of the children (79%) throughout the follow-up. All children, except five who lost hepatitis B surface antigen, had serum viral DNA detected by polymerase chain reaction. When comparing baseline and final liver biopsies, a significant improvement (P <.001) was found in the histological activity index and in the necrosis, cytolysis, inflammation, and fibrosis scores. The histological diagnosis improvement in the final biopsy was significantly related (P <.001) to the time from seroconversion to the biopsy performance. All children had viral DNA on their final liver biopsy. In summary, seroconversion and ALT normalization are quite stable findings in children, and no differences in the long-term outcome between treated and untreated children were found. In light of the histological outcome, it seems unnecessary to perform a follow-up liver biopsy in these cases.     

Optimal constrained adjustments for quality control

This paper considers the optimal adjustment of a production process under fixed adjustment and quadratic off-target quality costs, when the magnitude of the adjustment is constrained to lie within certain upper bound. The process model is that of the Box and Jenkins' 'machine tool' problem. Formulas for both end of run and long-run adjustment limits are presented. It is shown that unless the adjustment is severely constrained, in most cases the unconstrained limits are nearly as good as the considered optimal limits. Cases when the constrained solution is more economical are discussed. This includes applications in semiconductor manufacturing. An example from a chemical-mechanical wafer polishing process illustrates the use of the constrained optimal adjustment limits.     

ANALYSIS OF FREE-EDGE STRESS AND DISPLACEMENT FIELDS IN SCARF JOINTS SUBJECTED TO A UNIFORM CHANGE IN TEMPERATURE

The role of free-edge stresses in controlling the initiation of failure from the interface corner of a scarf joint subjected to a uniform change in temperature is examined. In general, the stress field can be expressed by σ _ij = Hr ^{λ −1} + σ _{ij 0} , where r is the radial distance from the interface corner, λ − 1 is the order of the stress singularity, H is the intensity of the singularity, and σ _{ij 0} is a non-singular constant stress. A combination of the finite element method and a path-independent integral is used to evaluate the magnitude of H for two joint configurations: (i) a scarf joint between two long bi-material strips; and (ii) a scarf joint consisting of a thin elastic layer sandwiched between two substrates. The magnitude of H is linearly dependent on a non-dimensional constant function a; the magnitude of a decreases with increasing level of mismatch in the elastic properties of the bonded materials. A comparison between the values of H evaluated by the path-independent integral method and the commonly used extrapolation method indicate that the extrapolation method could be in error by as much as 25%.     

Nanoparticles of antimony sulfide by pulsed laser ablation in liquid media

In the present article, antimony sulfide nanoparticles have been synthesized by pulsed laser ablation of an antimony sulfide pellet in distilled water and isopropyl alcohol. The target was irradiated by 1064 and 532 nm from a pulsed Nd:YAG laser operated at 10 Hz and pulse width of 10 ns at room temperature. Analysis of the morphology, crystalline phase and elemental composition were done using transmission electron microscopy (TEM), energy dispersive X-ray analysis (EDX), X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The optical band gap energies of these colloidal nanoparticles were evaluated from UV–Visible absorption spectra. It was observed that the morphology, size, and optical properties of the antimony sulfide nanoparticles depend on the wavelength of the laser and the liquid media.     

A statistical fatigue model covering the tension and compression Wöhler fields

A statistical fatigue model to predict the Wöhler field for any combination of _σmin${\sigma }_{min}$, _σmax${\sigma }_{max}$ or R=_σmin/_σmax$R={\sigma }_{min}/{\sigma }_{max}$ is presented. The model extends an existing model to the case of _σmax${\sigma }_{max}$ being tension and _σmin${\sigma }_{min}$ being tension or compression, and is derived based on physical, statistical and compatibility conditions, thus, eliminating the selection of arbitrary functions. The main tool to derive the model is a functional equation, which allows obtaining the most general model satisfying all the stated conditions. In particular, the regression formula for the _σmax${\sigma }_{max}$–logN$logN$ field for fixed R$R$ values is analyzed. A particular and powerful model is selected and its main properties are derived. This model is applied to some real data to illustrate its applicability to practical problems. The results seem to be very promising, especially because the model, due to its physical and statistical constraints, appears to be very robust and with a high capacity to detect outliers.