Continued fraction solution of Krein's inverse problem

The spectral data of a vibrating string are encoded in its so-called characteristic function. We consider the problem of recovering the distribution of mass along the string from its characteristic function. It is well-known that Stieltjes' continued fraction provides a solution of this inverse problem in the particular case where the distribution of mass is purely discrete. We show how to adapt Stieltjes' method to solve the inverse problem for a related class of strings. An application to the excursion theory of diffusion processes is presented.Comment: 18 pages, 2 figure

Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the corresponding Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of the result

Effect of high intratesticular estrogen on global gene expression and testicular cell number in rats

<p>Abstract</p> <p>Background</p> <p>The identification of estrogen receptors alpha and beta and aromatase in the testis has highlighted the important role of estrogens in regulating spermatogenesis. There is a wealth of information on the deleterious effects of fetal and neonatal exposure of estrogens and xenoestrogens in the testis, including spermiation failure and germ cell apoptosis. However, very little is known about gene transcripts affected by exogenous estradiol exposure in the testis. The objective of the present study was to unveil global gene expression profiles and testicular cell number changes in rats after estradiol treatment.</p> <p>Methods</p> <p>17beta-estradiol was administered to adult male rats at a dose of 100 micrograms/kg body weight in saline daily for 10 days; male rats receiving only saline were used as controls. Microarray analysis was performed to examine global gene expression profiles with or without estradiol treatment. Real time RT-PCR was conducted to verify the microarray data. In silico promoter and estrogen responsive elements (EREs) analysis was carried out for the differentially expressed genes in response to estradiol. Quantitation of testicular cell number based on ploidy was also performed using flow cytometry in rats with or without estradiol treatment.</p> <p>Results</p> <p>We found that 221 genes and expressed sequence tags (ESTs) were differentially expressed in rat testes treated with estradiol compared to the control; the microarray data were confirmed by real time RT-PCR. Gene Ontology analysis revealed that a number of the differentially expressed genes are involved in androgen and xenobiotic metabolism, maintenance of cell cytoskeleton, endocytosis, and germ cell apoptosis. A total of 33 up-regulated genes and 67 down-regulated genes showed the presence of EREs. Flow cytometry showed that estradiol induced a significant decrease in 2n cells (somatic and germ cells) and 4n cells (pachytene spermatocytes) and a marked increase in the number of elongated and elongating spermatids.</p> <p>Conclusions</p> <p>This study provides a novel insight into the molecular basis for spermiation failure and apoptosis caused by 17beta-estradiol and it also offers new mechanisms by which adult exposure to environmental estrogens can affect spermatogenesis and fertility.</p

Translation Representations and Scattering By Two Intervals

Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U (t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator, and scattering matrix. We illustrate our results in the Lax-Phillips model where (U (t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states

De Branges spaces and Krein's theory of entire operators

This work presents a contemporary treatment of Krein's entire operators with deficiency indices $(1,1)$ and de Branges' Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown mathematicians. Remarkably, entire operators and de Branges spaces are intimately connected and the interplay between them has had an impact in both spectral theory and the theory of functions. This work exhibits the interrelation between Krein's and de Branges' theories by means of a functional model and discusses recent developments, giving illustrations of the main objects and applications to the spectral theory of difference and differential operators.Comment: 37 pages, no figures. The abstract was extended. Typographical errors were corrected. The bibliography style was change

Forms of Science Capital Mobilized in Adolescents’ Engineering Projects

The purpose of this multiple case study was to identify the forms of science capital that six groups of adolescents mobilized toward the realization of their self-selected engineering projects during after-school meetings. Research participants were high school students who self-identified as Hispanic, Latina, or Latino; who had received English as a Second Language (ESL) services; and whose parents or guardians had immigrated to the United States and held working class jobs. The research team used categories from Bourdieusian theories of capital to identify the forms of science capital mobilized by the participants. Data sources included transcripts from monthly interviews and from bi-monthly group meetings during which the group members worked on their engineering projects. Data analysis indicated that the groups activated science capital in the following categories: embodied capital in the form of formal scientific knowledge, literacy practices, and experiences with solving everyday problems; social capital in the form of connections with authorities, experts, and peers; objectified capital in the form of information and communication technologies (ICTs) and measuring tools; and institutional capital in the form of awards and titles. The participants co-mobilized multiple forms of science capital to advance their engineering projects, and some instances of co-mobilization enabled the future activation of subsequent forms of science capital. Engineering, as a vehicle for learning science, provided the youth with opportunities to draw from diverse community resources and from multilingual literacy practices, recasting these resources and skills as forms of science capital, which were mobilized toward the attainment of other high-status forms of science capital

A linguistic approach to assess the dynamics of design team preference in concept selection

This paper addresses the problem of describing the decision-making process of a committee of engineers based upon their verbalized linguistic appraisals of alternatives. First, we show a way to model an individual’s evaluation of an alternative through natural language based on the Systemic-Functional Linguistics system of APPRAISAL. The linguistic model accounts for both the degree of intensity and the uncertainty of expressed evaluations. Second, this multi-dimensional linguistic model is converted into a scalar to represent the degree of intensity and a probability distribution function for the stated evaluation. Finally, we present a Markovian model to calculate the time-varying change in preferential probability, the probability that an alternative is the most preferred alternative. We further demonstrate how preferential probability toward attributes of alternatives correspond to preferential probability toward alternatives. We illustrate the method on two case studies to highlight the time-variant dynamics of preferences toward alternatives and attributes. This research contributes to process tracing in descriptive decision science to understand how engineers actually take decisions.National Science Foundation (U.S.) (Award CMMI-0900255

Defining the industrial and engineering management professional profile: a longitudinal study based on job advertisements

The engineering professional profiles have been discussed by several branches of the engineering field. On the one hand, this discussion helps to understand the professional practice and contributes to the specification of the competences that are suitable for each function and company culture. On the other hand, it is an essential starting point for the definition of curricula in engineering schools. Thus, this study aims to characterize, in an innovative way based on job advertisements, the demand for competences and areas of practice for Industrial Engineering and Management contributing for the definition of a professional profile. This characterization is based on the analysis of 1391 job advertisements, collected during seven years from a Portuguese newspaper. The data analysis takes into account the job description in which two categories were considered: areas of professional practice (e.g. project management) and transversal competences (e.g. teamwork). Considering the total number of job advertisements, it was possible to identify 1,962 cumulative references for 11 professional practice areas and 5,261 cumulative references for transversal competences. The contribution of this study lies on the identification of the main areas of practice and the main transversal competences demanded by employers.This work was partially funded by COMPETE-POCI-01-0145-FEDER-007043 and FCT-UID-CEC-00319-2013

Proliferation and renewal of spermatogonia following x-irradiation of the rat testis.

The behaviour of the two classes of spermatogonial stem cells (AO and A1-A4) was investigated following 300r of X-rays to rat testes. Radioautographs of cross sections and whole mounts of seminiferous tubules were prepared from animals injected with 3H-thymidine. In nonirradiated controls type AO spermatogonia were generally dormant, while type A1 spermatogonia periodically initiated a series of divisions resulting in the production of spermatocytes and new type A1 spermatogonia. [...