The doodle of a finitely determined map germ from R(2) to R(3)

Let f : U subset of R(2) -> R(3) be a representative of a finitely determined map germ f : (R(2), 0) -> (R(3), 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R(3), call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.

Evaluation of simulated bone lesion in the head of the mandible by using multislice computed tomography

Conventional radiography has shown limitation in acquiring image of the ATM region, thus, computed tomography (CT) scanning has been the best option to the present date for diagnosis, surgical planning and treatment of bone lesions, owing to its specific properties. OBJECTIVE: The aim of the study was to evaluate images of simulated bone lesions at the head of the mandible by multislice CT. MATERIAL AND METHODS: Spherical lesions were made with dental spherical drills (sizes 1, 3, and 6) and were evaluated by using multislice CT (64 rows), by two observers in two different occasions, deploying two protocols: axial, coronal, and sagittal images, and parasagittal images for pole visualization (anterior, lateral, posterior, medial and superior). Acquired images were then compared with those lesions in the dry mandible (gold standard) to evaluate the specificity and sensibility of both protocols. Statistical methods included: Kappa statistics, validity test and chi-square test. Results demonstrated the advantage of associating axial, coronal, and sagittal slices with parasagittal slices for lesion detection at the head of the mandible. RESULTS: There was no statistically significant difference between the types of protocols regarding a particular localization of lesions at the poles. CONCLUSIONS: Protocols for the assessment of the head of the mandible were established to improve the visualization of alterations of each of the poles of the mandible's head. The anterior and posterior poles were better visualized in lateral-medial planes while lateral, medial and superior poles were better visualized in the anterior-posterior plane.

SOME PROPERTIES OF THE MULTIPLICITY SEQUENCE FOR ARBITRARY IDEALS

In this work we prove that the Achilles-Manaresi multiplicity sequence, like the classical Hilbert-Samuel multiplicity, is additive with respect to the exact sequence of modules. We also prove the associativity formula for his mulitplicity sequence. As a consequence, we give new proofs for two results already known. First, the Achilles-Manaresi multiplicity sequence is an invariant up to reduction, a result first proved by Ciuperca. Second, I subset of J is a reduction of (J,M) if and only if c(0)(I(p), M(p)) = c(0)(J(p), M(p)) for all p is an element of Spec(A), a result first proved by Flenner and Manaresi.

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Images of a `good nurse` presented by teaching staff

Nursing is at the same time a vocation, a profession and a job. By nature, nursing is a moral endeavor, and being a `good nurse` is an issue and an aspiration for professionals. The aim of our qualitative research project carried out with 18 nurse teachers at a university nursing school in Brazil was to identify the ethical image of nursing. In semistructured interviews the participants were asked to choose one of several pictures, to justify their choice and explain what they meant by an ethical nurse. Five different perspectives were revealed: good nurses fulfill their duties correctly; they are proactive patient advocates; they are prepared and available to welcome others as persons; they are talented, competent, and carry out professional duties excellently; and they combine authority with power sharing in patient care. The results point to a transition phase from a historical introjection of religious values of obedience and service to a new sense of a secular, proactive, scientific and professional identity.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Ultrastructural characterization of CD133(+) stem cells bound to superparamagnetic nanoparticles: possible biotechnological applications

CD133 antigen is an integral membrane glycoprotein that can bind with different cells. Originally, however. this cellular surface antigen was expressed in human stem cells and in various cellular progenitors of the haematopoietic system. Human cord blood has been described as an excellent source of CD133(+) haematopoietic progenitor cells with a large application potential. One of the main objectives of the present study is to describe for the first time the ultrastructural characteristics of CD133(+) stem cells using transmission electronic microscopy. Another objective of the manuscript is to demonstrate through transmission electronic microscopy the molecular image of magnetic nanoparticles connected to the stein cells of great biotechnological importance, as well as demonstrating the value of this finding for electronic paramagnetic resonance and its related nanobioscientific value. Ultrastructural results showed the monoclonal antibody anti-CD133 bound to the superparamagnetic nanoparticles by the presence of electrondense granules in cell membrane, as well as in the cytoplasm, revealing the ultrastructural characteristics of CD133(+) cells, exhibiting a round morphology with discrete cytoplasmic projections, having an active nucleus that follows this morphology. The cellular cytoplasm was filled up with mitochondrias, as well as microtubules and vesicles pinocitic. characterizing the process as being related to internalization of the magnetic nanoparticles that were endocyted by the cells in question. Electronic paramagnetic resonance analysis of the CD133(+) stem cells detected that the small (spectrum) generated by the labelled cells comes from the superparamagnetic nanoparticles that are bound to them. These results strongly suggest that these CD133(+) cells can be used in nanobiotechnology applications, with benefits in different biomedical areas.

Mango starch degradation. I. A microscopic view of the granule during ripening

The starch content of unripe mango Keitt is around 7% (FW), and it is converted to soluble sugars during the ripening of the detached fruit. Despite the importance of starch-to-soluble sugar metabolism for mango quality, little literature is found on this subject and none concerning the physical aspects of starch degradation. This manuscript presents some changes in the physical aspects of the starch granule during ripening, as analyzed by light microscopy, scanning electron microscopy (SEM), and atomic force microscopy (AFM). According to the analysis, unripe Keitt-mango-starch being spherical in shape and measuring around 15,mu m, has A-type X-ray diffraction pattern with a degree of crystallinity around 21% with slight changes after 8 days of ripening. AFM images of the surface of the granules showed ultra microstructures, which are in agreement with a blocklet-based organization of the granules. The AFM-contrast image of growing layers covering the granule showed fibril-like structures, having 20 nm in diameter, transversally connecting the layer to the granule. The appearance of the partially degraded granules and the pattern of degradation were similar to those observed as a result of amylase activity, suggesting a hydrolytic pathway for the degradation of starch from mango cultivar Keitt. These results provide clues to a better understanding of starch degradation in fruits.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

Strong surjectivity of maps from 2-complexes into the 2-sphere

Given a model 2-complex K(P) of a group presentation P, we associate to it an integer matrix Delta(P) and we prove that a cellular map f : K(P) -> S(2) is root free (is not strongly surjective) if and only if the diophantine linear system Delta(P) Y = (deg) over right arrow (f) has an integer solution, here (deg) over right arrow (f) is the so-called vector-degree of f

WHICH TOPOLOGIES HAVE IMMEDIATE PREDECESSORS IN THE POSET OF HAUSDORFF TOPOLOGIES?

We study which topology have an immediate predecessor in the poset of Sigma(2) of Hausdorff topologies on set X. We show that certain classes of H-closed topologies, do have predecessors. and we give examples of second countable H-closed topologies which are not upper Sigma(2.)

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

On the extent of star countable spaces

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y aS, X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelof spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelof. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense sigma-compact subspace can have arbitrary extent. It is proved that for any omega (1)-monolithic compact space X, if C (p) (X)is star countable then it is Lindelof.

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

Homogeneous polynomials of degree 2 on the complex Banach space c(0)(l(n)(2)) are shown to have unique norm-preserving extension to the bidual space. This is done by using M-projections and extends the analogous result for c(0) proved by P.-K. Lin.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.