On the number of singularities in generic deformations of map germs

Let f:C-n, 0 --> C-p, 0 be a K-finite map germ, and let i = (i(1),..., i(k)) be a Boardman symbol such that Sigma(i) has codimension n in the corresponding jet space J(k)(n, p). When its iterated successors have codimension larger than n, the paper gives a list of situations in which the number of Sigma(i) points that appear in a generic deformation of f can be computed algebraically by means of Jacobian ideals of f. This list can be summarised in the following way: f must have rank n - i(1) and, in addition, in the case p = 6, f must be a singularity of type Sigma(i2.i2).

Immersions in the metastable dimension range via the normal bordism approach

Let f : M --> N be a continuous map between two closed n-manifolds such that f(*): H-*(M, Z(2)) --> H-* (N, Z(2)) is an isomorphism. Suppose that M immerses in Rn+k for 5 less than or equal to n < 2k. Then N also immerses in Rn+k. We use techniques of normal bordism theory to prove this result and we show that for a large family of spaces we can replace the homolog condition by the corresponding one in homotopy. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Curves in homogeneous spaces and their contact with 1-dimensional orbits

Let alpha be a C(infinity) curve in a homogeneous space G/H. For each point x on the curve, we consider the subspace S(k)(alpha) of the Lie algebra G of G consisting of the vectors generating a one parameter subgroup whose orbit through x has contact of order k with alpha. In this paper, we give various important properties of the sequence of subspaces G superset of S(1)(alpha) superset of S(2)(alpha) superset of S(3)(alpha) superset of ... In particular, we give a stabilization property for certain well-behaved curves. We also describe its relationship to the isotropy subgroup with respect to the contact element of order k associated with alpha.

The valuable role of renucleation rate in ultrananocrystalline diamond growth

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Transmission network expansion planning in full open market considering security constraints

This paper presents a mathematical model and a methodology to solve the transmission network expansion planning problem with security constraints in full competitive market, assuming that all generation programming plans present in the system operation are known. The methodology let us find an optimal transmission network expansion plan that allows the power system to operate adequately in each one of the generation programming plans specified in the full competitive market case, including a single contingency situation with generation rescheduling using the security (n-1) criterion. In this context, the centralized expansion planning with security constraints and the expansion planning in full competitive market are subsets of the proposal presented in this paper. The model provides a solution using a genetic algorithm designed to efficiently solve the reliable expansion planning in full competitive market. The results obtained for several known systems from the literature show the excellent performance of the proposed methodology.

Linear codes over finite local rings in a chain

For a positive integer $t$, let \begin{equation*} \begin{array}{ccccccccc} (\mathcal{A}_{0},\mathcal{M}_{0}) & \subseteq & (\mathcal{A}_{1},\mathcal{M}_{1}) & \subseteq & & \subseteq & (\mathcal{A}_{t-1},\mathcal{M}_{t-1}) & \subseteq & (\mathcal{A},\mathcal{M}) \\ \cap & & \cap & & & & \cap & & \cap \\ (\mathcal{R}_{0},\mathcal{M}_{0}^{2}) & & (\mathcal{R}_{1},\mathcal{M}_{1}^{2}) & & & & (\mathcal{R}_{t-1},\mathcal{M}_{t-1}^{2}) & & (\mathcal{R},\mathcal{M}^{2}) \end{array} \end{equation*} be a chain of unitary local commutative rings $(\mathcal{A}_{i},\mathcal{M}_{i})$ with their corresponding Galois ring extensions $(\mathcal{R}_{i},\mathcal{M}_{i}^{2})$, for $i=0,1,\cdots,t$. In this paper, we have given a construction technique of the cyclic, BCH, alternant, Goppa and Srivastava codes over these rings. Though, initially in \cite{AP} it is for local ring $(\mathcal{A},\mathcal{M})$, in this paper, this new approach have given a choice in selection of most suitable code in error corrections and code rate perspectives.

Cyclic codes through B[X;(a/b)Z_0, with (a/b) in Q^{+} and b=a+1, and Encoding

Let B[X; S] be a monoid ring with any fixed finite unitary commutative ring B and is the monoid S such that b = a + 1, where a is any positive integer. In this paper we constructed cyclic codes, BCH codes, alternant codes, Goppa codes, Srivastava codes through monoid ring . For a = 1, almost all the results contained in [16] stands as a very particular case of this study.

A note on the integral trace form in cyclotomic fields

Let m >= 3 be an integer, zeta(m) is an element of C a primitive mth root of unity, and K-m the cyclotomic field Q(zeta(m)). An explicit description of the integral trace form Tr-Km/Q(x (x) over bar)vertical bar Z[zeta(m)] where (x) over bar is the complex conjugate of x is presented. In the case where m is prime, a procedure for finding the minimum of the form subject to x being a nonzero element of a certain Z- module in Z[zeta(m)] is presented.

Undergraduate Scholarship in the College of Arts and Sciences 2003 Book of Abstracts

On behalf of the faculty, staff, and students in the College of Arts and Sciences, I want to thank you for your interest in this collection of abstracts of undergraduate research for 2003. This collection is the first we have published, and we expect it to be number one in a long and increasingly impressive series. The importance of this collection is what it represents. These abstracts are the results of untold hours of hard work by students and faculty. Through that work, students have learned much about the research process, developed important critical and analytical thinking skills, improved writing abilities, and deepened relationships with faculty mentors. Many students have presented their research in classes, through seminars, and at professional meetings. In this work, faculty have been challenged to push students to do the best they can, to let them flounder as they struggle to solve the problems at hand, to hold them to deadlines, and to know how to encourage and when to scold. I know from personal experience that working together on meaningful research is a powerful way to build lasting relationships between students and faculty members.

Never Let a Crisis Go to Waste

The phrase, “never let a crisis go to waste” may take frugality to a whole new level! That’s the sentiment of Lynda Applegate, Professor of Business Administration at the Harvard Business School, in a recent on-line article, Building Businesses in Turbulent Times.

THE ROLE OF INDUSTRY IN DEVELOPING NEW MATERIALS FOR VERTEBRATE PEST CONTROL

In the first paper presented to you today by Dr. Spencer, an expert in the Animal Biology field and an official authority at the same time, you heard about the requirements imposed on a chemical in order to pass the different official hurdles before it ever will be accepted as a proven tool in wildlife management. Many characteristics have to be known and highly sophisticated tests have to be run. In many instances the governmental agency maintains its own screening, testing or analytical programs according to standard procedures. It would be impossible, however, for economic and time reasons to work out all the data necessary for themselves. They, therefore, depend largely on the information furnished by the individual industry which naturally has to be established as conscientiously as possible. This, among other things, Dr. Spencer has made very clear; and this is also what makes quite a few headaches for the individual industry, but I am certainly not speaking only for myself in saying that Industry fully realizes this important role in developing materials for vertebrate control and the responsibilities lying in this. This type of work - better to say cooperative work with the official institutions - is, however, only one part and for the most of it, the smallest part of work which Industry pays to the development of compounds for pest control. It actually refers only to those very few compounds which are known to be effective. But how to get to know about their properties in the first place? How does Industry make the selection from the many thousands of compounds synthesized each year? This, by far, creates the biggest problems, at least from the scientific and technical standpoint. Let us rest here for a short while and think about the possible ways of screening and selecting effective compounds. Basically there are two different ways. One is the empirical way of screening as big a number of compounds as possible under the supposition that with the number of incidences the chances for a "hit" increase, too. You can also call this type of approach the statistical or the analytical one, the mass screening of new, mostly unknown candidate materials. This type of testing can only be performed by a producer of many new materials,that means by big industries. It requires a tremendous investment in personnel, time and equipment and is based on highly simplified but indicative test methods, the results of which would have to be reliable and representative for practical purposes. The other extreme is the intellectual way of theorizing effective chemical configurations. Defenders of this method claim to now or later be able to predict biological effectiveness on the basis of the chemical structure or certain groups in it. Certain pre-experience should be necessary, that means knowledge of the importance of certain molecular requirements, then the detection of new and effective complete molecules is a matter of coordination to be performed by smart people or computers. You can also call this method the synthetical or coordinative method.

FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

MicroRNAs miR-146-5p and let-7f as prognostic tools for aggressive papillary thyroid carcinoma: a case report

Papillary thyroid cancer (PTC) is the most incident histotype of thyroid cancer. A certain fraction of PTC cases (5%) are irresponsive to conventional treatment, and refractory to radioiodine therapy. The current prognostic factors for aggressiveness are mainly based on tumor size, the presence of lymph node metastasis, extrathyroidal invasion and, more recently, the presence of the BRAFT(1799A) mutation. MicroRNAs (miRNAs) have been described as promising molecular markers for cancer as their deregulation is observed in a wide range of tumors. Recent studies indicate that the over-expression of miR-146b-5p is associated with aggressiveness and BRAFT(1799A) mutation. Furthermore, down-regulation of let-7f is observed in several types of tumors, including PTC. In this study, we evaluated the miR146b-5p and let-7f status in a young male patient with aggressive, BRAFT(1799A)-positive papillary thyroid carcinoma, with extensive lymph node metastases and short-time recurrence. The analysis of miR-146b-5p and let-7f expression revealed a distinct pattern from a cohort of PTC patients, suggesting caution in evaluating miRNA expression data as molecular markers of PTC diagnosis and prognosis. Arq Bras Endocrinol Metab. 2012;56(8):552-7

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

Introducing education for sustainable development in the undergraduate laboratory: quantitative analysis of bioethanol fuel and its blends with gasoline by using solvatochromic dyes

The concept of Education for Sustainable Development, ESD, has been introduced in a period where chemistry education is undergoing a major change, both in emphasis and methods of teaching. Studying an everyday problem, with an important socio-economic impact in the laboratory is a part of this approach. Presently, the students in many countries go to school in vehicles that run, at least partially, on biofuels; it is high time to let them test these fuels. The use of renewable fuels is not new: since 1931 the gasoline sold in Brazil contains 20 to 25 vol-% of bioethanol; this composition is being continually monitored. With ESD in mind, we have employed a constructivist approach in an undergraduate course, where UV-vis spectroscopy has been employed for the determination of the composition of two fuel blends, namely, bioethanol/water, and bioethanol/gasoline. The activities started by giving a three-part quiz. The first and second ones introduced the students to historical and practical aspects of the theme (biofuels). In the third part, we asked them to develop a UV-vis experiment for the determination of the composition of fuel blends. They have tested two approaches: (i) use of a solvatochromic dye, followed by determination of fuel composition from plots of the empirical fuel polarity versus its composition; (ii) use of an ethanol-soluble dye, followed by determination of the blend composition from a Beer's law plot; the former proved to be much more convenient. Their evaluation of the experiment was highly positive, because of the relevance of the problem; the (constructivist) approach employed, and the bright colors that the solvatochromic dye acquire in these fuel blends. Thus ESD can be fruitfully employed in order to motivate the students; make the laboratory "fun", and teach them theory (solvation). The experiments reported here can also be given to undergraduate students whose major is not chemistry (engineering, pharmacy, biology, etc.). They are low-cost and safe to be introduced at high-school level.