A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.

A singular integro-differential equation model for dryout in LMFBR boiler tubes

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem Appropriate boundary conditions for the now are discussed The resulting non-lineal singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques) Predictions for the length to the dryout point from the entry of the annular regime are made The influence of both the traction tau provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter eta on the dryout length is investigated

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barabasi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks. Copyright (C) EPLA, 2009

Performance of balanced two-stage empirical predictors of realized cluster latent values from finite populations: A simulation study

Predictors of random effects are usually based on the popular mixed effects (ME) model developed under the assumption that the sample is obtained from a conceptual infinite population; such predictors are employed even when the actual population is finite. Two alternatives that incorporate the finite nature of the population are obtained from the superpopulation model proposed by Scott and Smith (1969. Estimation in multi-stage surveys. J. Amer. Statist. Assoc. 64, 830-840) or from the finite population mixed model recently proposed by Stanek and Singer (2004. Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 1119-1130). Predictors derived under the latter model with the additional assumptions that all variance components are known and that within-cluster variances are equal have smaller mean squared error (MSE) than the competitors based on either the ME or Scott and Smith`s models. As population variances are rarely known, we propose method of moment estimators to obtain empirical predictors and conduct a simulation study to evaluate their performance. The results suggest that the finite population mixed model empirical predictor is more stable than its competitors since, in terms of MSE, it is either the best or the second best and when second best, its performance lies within acceptable limits. When both cluster and unit intra-class correlation coefficients are very high (e.g., 0.95 or more), the performance of the empirical predictors derived under the three models is similar. (c) 2007 Elsevier B.V. All rights reserved.

ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

Prosodic Morphology : Gender in Arabic Perfect Active and Passive 3rd Person Singular Verbs

Prosodic /template Morphology, that "draws heavily on the theoretical apparatus and formalisms of the generative phonology model known as autosegmental phonology" (Katamba, F. 1993: 154), is the best analysis that can handle Arabic morphology. Verbs in Arabic are represented on three independent tiers: root tier, the skeletal tier and the vocalic melody tier (Katamba, F. 1993). Vowel morphemes, which are represented by diacritics, are inserted within the consonant morphemes, which are represented by primary symbols, to form words. The morpheme tier hypothesis paves the way to understand the nonconcatenative Arabic morphology. This paper analyzes gender in perfect active and passive 3rd person singular verbs on the basis of PM. The focus of the analysis shall be drawn heavily on the most common Arabic verbs; triconsonantal verbs, with brief introduction of the less common verbs; quadriconsonantal perfect active and passive masculine and feminine 3rd person singular verbs. I shall, too, cast the light on some vowel changes that some verbs undergo when voice changes.

Los errores más frecuentes en la conjugación del adjetivo en su forma singular entre un grupo de alumnos suecos que estudian español nivel 3

AbstractThe objective of the thesis is to find what kind of mistakes a certain group of Swedish students make when studying Spanish as a modern language, specifically when using qualitative adjectives in their singular form. The result is based on the cases of twelve students who study Spanish Level 3, institute level. Four of them were interviewed afterwards.The methods used in this report were the quantitative method which helped quantifying the incidence of these mistakes made by the students through a data sheet, and the qualitative method by analyzing each mistake and the results of the interviews.The conclusion shows that the errors in the use of qualitative adjectives in their singular form occur when the adjectives are feminine, with great higher frequency in feminine abstract adjectives.Key wordsAdjectives, quantitative method, qualitative method, interlanguage, errors and error analysis

Patriarchal values : girls are more apt to change

Patriarchal values: girls are more apt to change How has the family value system changed between generations, especially when taking into account the gender dimension? This article presents some results from a study carried outin 2007 in one village of the Gourani tribe where the people are followers of Ahle Hagh in Islamabad Gharb (west of Iran). The differences between generations (those born and raised before and after the Islamic Revolution) in patriarchal values in the family are statistically significant. The older generation opts for the man of the family to make most of the decisions; on children’s education, marriage, naming, the families expenditure, the place for residence, the social network of the family and even the number of children. The younger generation has a different value system and it has moved towards a more egalitarian type of family. With the gender variable included in the findings we see that although the values of the younger male population have evolved toward a less patriarchal decision making structure inthe family, the degree of changes among the young women is much higher. Looking into the preferences for male sex for the first child as well as a larger number of boys in the family, the difference between generations is significant. However data on the differences analyzed with the gender variable proves that the changes concerning the equality of sexes are mainly due to drastic changes in the young women’s value system. That is, the male population, young or old, still prefer to have a boy as their first born and to have more sons in the family. But the young female generation in the rural area sees less difference in having boys or girls in the family. It is concluded that reforms in the old value system is an evolving process of everyday life and that the girls are the main social force for change.

Torrenting values, feelings and thoughts : cyber nursing and virtual self care in a breast augmentation forum

Earlier research shows that breast augmentation is positively correlated with positive psychological states. The aim of this study was to explore the shared values, feelings, and thoughts within the culture of breast enlargement among women visiting Internet-based forums when considering and/or undergoing esthetic plastic surgery. The study used a netnographic method for gathering and analyzing data. The findings show that the women used the Internet forum to provide emotional support to other women. Through electronic postings, they cared for and nursed each others’ anxiety and feelings throughout the whole process. Apart from the process, another central issue was that the women's relationships were frequently discussed; specifically their relationship to themselves, their environment, and with the surgeons. The findings suggest that Internet forums represent a channel through which posters can share values, feelings, and thoughts from the position of an agent of action as well as from a position as the object of action. These dual positions and the medium endow the women with a virtual nursing competence that would otherwise be unavailable. By introducing the concept of torrenting as a means of sharing important self-care information, the authors provide a concept that can be further explored in relation to post modern self-care strategies within contemporary nursing theories and practice.