Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

New integrable boundary conditions for the q-deformed supersymmetric U model and Bethe ansatz equations

New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Modified logit life table system: Principles, empirical validation, and application

Despite its widespread use, the Coale-Demeny model life table system does not capture the extensive variation in age-specific mortality patterns observed in contemporary populations, particularly those of the countries of Eastern Europe and populations affected by HIV/AIDS. Although relational mortality models, such as the Brass logit system, can identify these variations, these models show systematic bias in their predictive ability as mortality levels depart from the standard. We propose a modification of the two-parameter Brass relational model. The modified model incorporates two additional age-specific correction factors (gamma(x), and theta(x)) based on mortality levels among children and adults, relative to the standard. Tests of predictive validity show deviations in age-specific mortality rates predicted by the proposed system to be 30-50 per cent lower than those predicted by the Coale-Demeny system and 15-40 per cent lower than those predicted using the original Brass system. The modified logit system is a two-parameter system, parameterized using values of l(5) and l(60).

HIV/AIDS knowledge among men who have sex with men: applying the item response theory

OBJECTIVE To evaluate the level of HIV/AIDS knowledge among men who have sex with men in Brazil using the latent trait model estimated by Item Response Theory. METHODS Multicenter, cross-sectional study, carried out in ten Brazilian cities between 2008 and 2009. Adult men who have sex with men were recruited (n = 3,746) through Respondent Driven Sampling. HIV/AIDS knowledge was ascertained through ten statements by face-to-face interview and latent scores were obtained through two-parameter logistic modeling (difficulty and discrimination) using Item Response Theory. Differential item functioning was used to examine each item characteristic curve by age and schooling. RESULTS Overall, the HIV/AIDS knowledge scores using Item Response Theory did not exceed 6.0 (scale 0-10), with mean and median values of 5.0 (SD = 0.9) and 5.3, respectively, with 40.7% of the sample with knowledge levels below the average. Some beliefs still exist in this population regarding the transmission of the virus by insect bites, by using public restrooms, and by sharing utensils during meals. With regard to the difficulty and discrimination parameters, eight items were located below the mean of the scale and were considered very easy, and four items presented very low discrimination parameter (< 0.34). The absence of difficult items contributed to the inaccuracy of the measurement of knowledge among those with median level and above. CONCLUSIONS Item Response Theory analysis, which focuses on the individual properties of each item, allows measures to be obtained that do not vary or depend on the questionnaire, which provides better ascertainment and accuracy of knowledge scores. Valid and reliable scales are essential for monitoring HIV/AIDS knowledge among the men who have sex with men population over time and in different geographic regions, and this psychometric model brings this advantage.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

COI barcode versus morphological identification of Culex ( Culex ) (Diptera: Culicidae) species: a case study using samples from Argentina and Brazil

Sequences of the cytochrome c oxidase subunit I (COI) mitochondrial gene from adults of 22 Culex ( Culex ) species from Argentina and Brazil were employed to assess species identification and to test the usefulness of COI for barcoding using the best close match (BCM) algorithm. A pairwise Kimura two-parameter distance matrix including the mean intra and interspecific distances for 71 COI barcode sequences was constructed. Of the 12 COI lineages recovered in the Neighbour-joining topology, five confirmed recognised morphological species ( Cx. acharistus , Cx. chidesteri , Cx. dolosus , Cx. lygrus and Cx. saltanensis ) with intraspecific divergences lower than 1.75%. Cx. bilineatus is formally resurrected from the synonymy of Cx. dolosus . Cx. maxi , Cx. surinamensis and the Coronator group species included were clustered into an unresolved lineage. The intraspecific distance of Cx. pipiens (3%) was almost twice the interspecific between it and Cx. quinquefasciatus (1.6%). Regarding the BCM criteria, the COI barcode successfully identified 69% of all species. The rest of the sequences, approximately 10%, 18% and 3%, remained as ambiguously, mis and unidentified, respectively. The COI barcode does not contain enough information to distinguish Culex ( Cux. ) species.

The maritime shrew, Sorex maritimensis (Insectivora : Soricidae): a newly recognized Canadian endemic.

Previous morphological and cytological analyses have suggested that the arctic shrew (Sorex arcticus) as currently recognized may be two distinct species. Specifically, those studies demonstrated considerable differentiation between the putative subspecies S. a. maritimensis and one or both of the other two subspecies, S. a. arcticus and S. a. laricorum. Phylogenetic analysis of 546 base pairs of cytochrome b sequence data from 10 arctic shrews from across Canada indicates that maritimensis is the sister-group to arcticus + laricorum. Furthermore, there is considerable genetic divergence between maritimensis and the other two putative subspecies (similar to8-9%; Kimura's two-parameter distance). Given that maritimensis and arcticus + laricorum appear to be reciprocally monophyletic clades with considerable genetic divergence (i.e., greater than that between other recognized pairs of sister-species within the S. araneus-arcticus group), we propose that S. maritimensis be recognized as a distinct species. The proportion of third-position transversion substitutions between S. arcticus and S. maritimensis suggests that these two species shared a common ancestor approximately 2.4 million years ago.

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Calculation of Activity Coefficients of Uni-Univalent Electrolytes by Equations Containing No Adjustable Parameters in Aqueous Solutions at 298.15 K

Normally either the Güntelberg or Davies equation is used to predict activity coefficients of electrolytes in dilute solutions when no better equation is available. The validity of these equations and, additionally, of the parameter-free equations used in the Bates-Guggenheim convention and in the Pitzerformalism for activity coefficients were tested with experimentally determined activity coefficients of HCl, HBr, HI, LiCl, NaCl, KCl, RbCl, CsCl, NH4Cl, LiBr,NaBr and KBr in aqueous solutions at 298.15 K. The experimental activity coefficients of these electrolytes can be usually reproduced within experimental errorby means of a two-parameter equation of the Hückel type. The best Hückel equations were also determined for all electrolytes considered. The data used in the calculations of this study cover almost all reliable galvanic cell results available in the literature for the electrolytes considered. The results of the calculations reveal that the parameter-free activity coefficient equations can only beused for very dilute electrolyte solutions in thermodynamic studies.

Calculation of Activity Coefficients of Electrolytes of Other Charge Types than 1-1 by Equations Containing No Adjustable Parameters in Aqueous Solutions at 25 0C

Normally either the Güntelberg or Davies equation is used to predict activity coefficients of electrolytes in dilute solutions when no betterequation is available. The validity of these equations and, additionally, of the parameter-free equation used in the Bates-Guggenheim convention for activity coefficients were tested with experimentally determined activity coefficients of LaCl3, CaCl2, SrCl2 and BaCl2 in aqueous solutions at 298.15 K. The experimentalactivity coefficients of these electrolytes can be usually reproduced within experimental error by means of a two-parameter equation of the Hückel type. The best Hückel equations were also determined for all electrolytes considered. The data used in the calculations of this study cover almost all reliable galvanic cell results available in the literature for the electrolytes considered. The results of the calculations reveal that the parameter-free activity coefficient equations can only be used for very dilute electrolyte solutions in thermodynamic studies

Analysis of bulk and surface contributions in the neutron skin of nuclei

The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy and has multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult to obtain. The analysis of the experimental data may imply some assumptions about the bulk or surface nature of the formation of the neutron skin. Here we study the bulk or surface character of neutron skins of nuclei following from calculations with Gogny, Skyrme, and covariant nuclear mean-field interactions. These interactions are successful in describing nuclear charge radii and binding energies but predict different values for neutron skins. We perform the study by fitting two-parameter Fermi distributions to the calculated self-consistent neutron and proton densities. We note that the equivalent sharp radius is a more suitable reference quantity than the half-density radius parameter of the Fermi distributions to discern between the bulk and surface contributions in neutron skins. We present calculations for nuclei in the stability valley and for the isotopic chains of Sn and Pb.

On the Application of Beam on Elastic Foundation Theory to the Analysis of Stiffened Plate Strips

The main objective of this thesis is to show that plate strips subjected to transverse line loads can be analysed by using the beam on elastic foundation (BEF) approach. It is shown that the elastic behaviour of both the centre line section of a semi infinite plate supported along two edges, and the free edge of a cantilever plate strip can be accurately predicted by calculations based on the two parameter BEF theory. The transverse bending stiffness of the plate strip forms the foundation. The foundation modulus is shown, mathematically and physically, to be the zero order term of the fourth order differential equation governing the behaviour of BEF, whereas the torsion rigidity of the plate acts like pre tension in the second order term. Direct equivalence is obtained for harmonic line loading by comparing the differential equations of Levy's method (a simply supported plate) with the BEF method. By equating the second and zero order terms of the semi infinite BEF model for each harmonic component, two parameters are obtained for a simply supported plate of width B: the characteristic length, 1/ λ, and the normalized sum, n, being the effect of axial loading and stiffening resulting from the torsion stiffness, nlin. This procedure gives the following result for the first mode when a uniaxial stress field was assumed (ν = 0): 1/λ = √2B/π and nlin = 1. For constant line loading, which is the superimposition of harmonic components, slightly differing foundation parameters are obtained when the maximum deflection and bending moment values of the theoretical plate, with v = 0, and BEF analysis solutions are equated: 1 /λ= 1.47B/π and nlin. = 0.59 for a simply supported plate; and 1/λ = 0.99B/π and nlin = 0.25 for a fixed plate. The BEF parameters of the plate strip with a free edge are determined based solely on finite element analysis (FEA) results: 1/λ = 1.29B/π and nlin. = 0.65, where B is the double width of the cantilever plate strip. The stress biaxial, v > 0, is shown not to affect the values of the BEF parameters significantly the result of the geometric nonlinearity caused by in plane, axial and biaxial loading is studied theoretically by comparing the differential equations of Levy's method with the BEF approach. The BEF model is generalised to take into account the elastic rotation stiffness of the longitudinal edges. Finally, formulae are presented that take into account the effect of Poisson's ratio, and geometric non linearity, on bending behaviour resulting from axial and transverse inplane loading. It is also shown that the BEF parameters of the semi infinite model are valid for linear elastic analysis of a plate strip of finite length. The BEF model was verified by applying it to the analysis of bending stresses caused by misalignments in a laboratory test panel. In summary, it can be concluded that the advantages of the BEF theory are that it is a simple tool, and that it is accurate enough for specific stress analysis of semi infinite and finite plate bending problems.

Thermodynamic properties of dilute HBr(aq) and HI(aq)

The theory of electrolyte solutions was described by explaining Debye–Hückel theory and deriving the Debye–Hückel equation for the mean activity coefficient. Simple two-parameter Hückel equation was used for the calculation of the activity coefficients of aqueous hydrobromic and hydriodic acids up to 0.5 mol/kg at temperatures from (0 to 60) °C and from (0 to 50) °C, respectively. The parameters were observed to be independent of the temperature. The Hückel equation for the osmotic coefficients of water in the studied solutions was compared to that of Pitzer model by predicting the vapor pressures up to 1 mol/kg at 25 °C. The experimental vapor pressures over the reference electrolyte solutions were calculated with the Pitzer equation for the osmotic coefficients for isopiestic data in this comparison. The simple Hückel model was found to be equally good as the Pitzer model for both hydrobromic and hydriodic acids up to 0.5 mol/kg at 25 °C but applies also to other temperatures studied.

Mathematical modelling of the osmotic dehydration of cherry tomato (Lycopersicon esculentum var. cerasiforme)

Osmotic dehydration of cherry tomato as influenced by osmotic agent (sodium chloride and a mixed sodium chloride and sucrose solutions) and solution concentration (10 and 25% w/w) at room temperature (25°C) was studied. Kinetics of water loss and solids uptake were determined by a two parameter model, based on Fick's second law and applied to spherical geometry. The water apparent diffusivity coefficients obtained ranged from 2.17x10-10 to 11.69x10-10 m²/s.

Elliptical orbital studies of H21 and H2 molecules /|nS. K. Gupta. -- 260 St. Catharines, Ont. : [s. n.],

Calculations are performed on the \S <:Jd ground states of d ' + the H and HC) molecules using a basis set of non-integral ~ ~ I elliptical orbitals. Different variational wavefunctions constructed i- for H~ involved one parameter to three par~~eter variation. In order to l"'educe the ntunber of parameters in most commonly 0- used basis orbitals set, the importance of the term (,+~) Y\ over the term ;u 'Where n is a variational pararneter and the value of cr may be given by boundary condition or cusp condition is outlined in Chapters II and III. It is found that the two parameter -+ two electron problem, the variational energy is computed for the H~ molecule from unrestricted two parameter closed shell wavefunctions including the term U+ft)