Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm

2000 Mathematics Subject Classification: 17A50, 05C05.

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

Convexity around the Unit of a Banach Algebra

2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.

Effects of using manipulative materials to teach remedial algebra to community college students on achievement and attitudes towards mathematics

This dissertation derived hypotheses from the theories of Piaget, Bruner and Dienes regarding the effects of using Algebra Tiles and other manipulative materials to teach remedial algebra to community college students. The dependent variables measured were achievement and attitude towards mathematics. The Piagetian cognitive level of the students in the study was measured and used as a concomitant factor in the study.^ The population for the study was comprised of remedial algebra students at a large urban community college. The sample for the study consisted of 253 students enrolled in 10 sections of remedial algebra at three of the six campuses of the college. Pretests included administration of an achievement pre-measure, Aiken's Mathematics Attitude Inventory (MAI), and the Group Assessment of Logical Thinking (GALT). Posttest measures included a course final exam and a second administration of the MAI.^ The results of the GALT test revealed that 161 students (63.6%) were concrete operational, 65 (25.7%) were transitional, and 27 (10.7%) were formal operational. For the purpose of analyzing the data, the transitional and formal operational students were grouped together.^ Univariate factorial analyses of covariance ($\alpha$ =.05) were performed on the posttest of achievement (covariate = achievement pretest) and the MAI posttest (covariate = MAI pretest). The factors used in the analysis were method of teaching (manipulative vs. traditional) and cognitive level (concrete operational vs. transitional/formal operational).^ The analyses for achievement revealed a significant difference in favor of the manipulatives groups in the computations by campus. Significant differences were not noted in the analysis by individual instructors.^ The results for attitude towards mathematics showed a significant difference in favor of the manipulatives groups for the college-wide analysis and for one campus. The analysis by individual instructor was not significant. In addition, the college-wide analysis was significant in favor of the transitional/formal operational stage of cognitive development. However, support for this conclusion was not obtained in the analyses by campus or individual instructor. ^

Causal attributions for success or failure by passing and failing students in College Algebra

Success in mathematics has been identified as a predictor of baccalaureate degree completion. Within the coursework of college mathematics, College Algebra has been identified as a high-risk course due to its low success rates. ^ Research in the field of attribution theory and academic achievement suggests a relationship between a student's attributional style and achievement. Theorists and researchers contend that attributions influence individual reactions to success and failure. They also report that individuals use attributions to explain and justify their performance. Studies in mathematics education identify attribution theory as the theoretical orientation most suited to explain academic performance in mathematics. This study focused on the relationship among a high risk course, low success rates, and attribution by examining the difference in the attributions passing and failing students gave for their performance in College Algebra. ^ The methods for the study included a pilot administration of the Causal Dimension Scale (CDSII) which was used to conduct reliability and principal component analyses. Then, students (n = 410) self-reported their performance on an in-class test and attributed their performance along the dimensions of locus of causality, stability, personal controllability, and external controllability. They also provided open-ended attribution statements to explain the cause of their performance. The quantitative data compared the passing and failing groups and their attributions for performance on a test using One-Way ANOVA and Pearson chi square procedures. The open-ended attribution statements were coded in relation to ability, effort, task difficulty, and luck and compared using a Pearson chi square procedure. ^ The results of the quantitative data comparing passing and failing groups and their attributions along the dimensions measured by the CDSII indicated statistical significance in locus of causality, stability, and personal controllability. The results comparing the open-ended attribution statements indicated statistical significance in the categories of effort and task difficulty. ^

Algebra I and other predictors of high school dropout

This study investigated the relation of several predictors to high school dropout. The data, composed of records from a cohort of students ( N = 10,100) who entered ninth grade in 2001, were analyzed via logistic regression. The predictor variables were: (a) Algebra I grade, (b) Florida Comprehensive Assessment Test (FCAT) level, (c) language proficiency, (d) gender, (e) race/ethnicity, (f) Exceptional Student Education program membership, and (g) socio-economic status. The criterion was graduation status: graduated or dropped out. Algebra I grades were an important predictor of whether students drop out or graduate; students who failed this course were 4.1 times more likely to drop out than those who passed the course. Other significant predictors of high school dropout were language proficiency, Florida Comprehensive Assessment Test (FCAT) level, gender, and socio-economic status. The main focus of the study was on Algebra I as a predictor, but the study was not designed to discover the specific factors related to or underlying success in this course. Nevertheless, because Algebra I may be considered an important prerequisite for other major facets of the curriculum and because of its high relationship to high school dropout, a recommendation emerging from these findings is that districts address the issue of preventing failure in this course. Adequate support mechanisms for improving retention include addressing the students' readiness for enrolling in mathematics courses as well as curriculum improvements that enhance student readiness through such processes as remediation. Assuring that mathematics instruction is monitored and improved and that remedial programs are in place to facilitate content learning in all subjects for all students, but especially for those having limited English proficiency, are critical educational responsibilities.

Self-Identified Capabilities and Experiences with Mathematics of Adults Who Have Taken a Developmental Algebra Course

Some were born to do math, some persevered past fearful environments, while others withdrew. In this qualitative study, adults describe life with algebra and the meaning they sought. For all, pedagogy was critical, either positively or negatively; and all found salvation in intervention.

A retrospective-longitudinal examination of the relationship between apportionment of seat time in community-college algebra courses and student academic performance

During the past decade, there has been a dramatic increase by postsecondary institutions in providing academic programs and course offerings in a multitude of formats and venues (Biemiller, 2009; Kucsera & Zimmaro, 2010; Lang, 2009; Mangan, 2008). Strategies pertaining to reapportionment of course-delivery seat time have been a major facet of these institutional initiatives; most notably, within many open-door 2-year colleges. Often, these enrollment-management decisions are driven by the desire to increase market-share, optimize the usage of finite facility capacity, and contain costs, especially during these economically turbulent times. So, while enrollments have surged to the point where nearly one in three 18-to-24 year-old U.S. undergraduates are community college students (Pew Research Center, 2009), graduation rates, on average, still remain distressingly low (Complete College America, 2011). Among the learning-theory constructs related to seat-time reapportionment efforts is the cognitive phenomenon commonly referred to as the spacing effect, the degree to which learning is enhanced by a series of shorter, separated sessions as opposed to fewer, more massed episodes. This ex post facto study explored whether seat time in a postsecondary developmental-level algebra course is significantly related to: course success; course-enrollment persistence; and, longitudinally, the time to successfully complete a general-education-level mathematics course. Hierarchical logistic regression and discrete-time survival analysis were used to perform a multi-level, multivariable analysis of a student cohort (N = 3,284) enrolled at a large, multi-campus, urban community college. The subjects were retrospectively tracked over a 2-year longitudinal period. The study found that students in long seat-time classes tended to withdraw earlier and more often than did their peers in short seat-time classes (p < .05). Additionally, a model comprised of nine statistically significant covariates (all with p-values less than .01) was constructed. However, no longitudinal seat-time group differences were detected nor was there sufficient statistical evidence to conclude that seat time was predictive of developmental-level course success. A principal aim of this study was to demonstrate—to educational leaders, researchers, and institutional-research/business-intelligence professionals—the advantages and computational practicability of survival analysis, an underused but more powerful way to investigate changes in students over time.

Effects of worked examples and algebra problem -solving skill on error and cognitive load

This study determined the levels of algebra problem solving skill at which worked examples promoted learning of further problem solving skill and reduction of cognitive load in college developmental algebra students. Problem solving skill was objectively measured as error production; cognitive load was subjectively measured as perceived mental effort. ^ Sixty-three Ss were pretested, received homework of worked examples or mass problem solving, and posttested. Univarate ANCOVA (covariate = previous grade) were performed on the practice and posttest data. The factors used in the analysis were practice strategy (worked examples vs. mass problem solving) and algebra problem solving skill (low vs. moderate vs. high). Students in the practice phase who studied worked examples exhibited (a) fewer errors and reduced cognitive load, at moderate skill; (b) neither fewer errors nor reduced cognitive load, at low skill; and (c) only reduced cognitive load, at high skill. In the posttest, only cognitive load was reduced. ^ The results suggested that worked examples be emphasized for developmental students with moderate problem solving skill. Areas for further research were discussed. ^

Esforços governamentais locais para o desenvolvimento: desenhos, tendências e limites dos Fundos de Desenvolvimento Industrial nos estados do Rio Grande do Norte, Maranhão e Ceará (1985-2010)

This research aimed to analyze the main government efforts to promote economic development in the Northeast, from 1985 to 2010, under the view that growth is crucial for increasing industrialization process and allows for more significant growth patterns. The analysis was the context in which state governments react to the abandonment of developmental line the federal level, in the 1980s, incorporating features of the actions called endogenous regional development and providing local players with greater responsibility in the development process. Justifies the need to analyze the following scenario: state governments in northeastern Brazil using relevant part of its resources to finance the installation and expansion of companies through tax incentives, with a view to generating income and employment, whilst waiting for an increase in output and a positive change in economic dynamism. In addition, it puts in question the fact that these policies receive such importance of state administrations for the purpose of achieving regional development. It was left to consider, therefore, the contents of the shares elected by state governments to examine the scope of these policies both in the pattern of growth, the transformation of the industrial sector and the development of the region attention to changes in state production structures. Due to limitations on the availability of data and time to carry out research, we were elected three states for the study: Rio Grande do Norte, Ceará and Maranhão. The study found that, despite the contribution of policies analyzed to economic growth, sub-national states are unable to compensate for the lack of development agencies structured at the federal level.

Dinâmica de expansão urbana de Ceará-Mirim-RN: aspectos locais e metropolitanos?

This study aims to understand the growth dynamics of Ceará-Mirim city considering the aspects that define its current urban sprawl. We chose to use as methodological approach the concept of space as a product and producer of social relations and the same constitutes by objects and actions that relate in a dialectical process over time. As a research tool, it took place bibliographical study that features the historical aspects of use and occupation, in order to evidence the regional ground agents that explain its current urban setting. Then, it was collected a secondary data of economic analysis activities from municipality and their impact on local social structure. Between these aspects, the sugar economy, even in decline, had appeared as defining the boundaries of urban growth. At the regional scale, other factors were discussed in a way of urban influence processes forming the Greater Natal (RMNatal), and Ceará-Mirim appears integrating into this scale in a very low level according to Metropolis Observatory (2012). However, we have pointed out that in recent years, especially in growth vector of BR 406, settled metropolitan scope equipment. These objects have been associating in a real estate sector's reasoning while the possible "metropolization" have been promoting as investments in the city's expansion area.

Inibição dos efeitos locais induzidos pelas peçonhas das serpentes Bothrops erythromelas e Bothrops jararaca pelo extrato aquoso das folhas de Jatropha mollissima (Pohl) Bail

Snakebites are a serious public health problem in tropical and subtropical countries and Bothrops genus is responsible for the accidents in Brazil and throughout Latin America (90% of cases). The local effects (pain, edema, hemorrhage and myonecrosis) and systemic (cardiovascular alterations, shock and blood clotting disorders) caused by the venom of Bothrops are due to the numerous protein and non-protein components, which are part of the constitution of the poison. The only form of therapy is scientifically validated antivenom serum therapy which, however, is not effective with respect to local effects produced, risk of immunological reactions, high cost and difficult access in some regions. Thus, the search for new alternatives to serum therapy becomes important, and in this context, many medicinal plants have been highlighted by the popular use as antiophidic. Among these plants, we can mention the species Jatropha mollissima (Euphorbiaceae) which has popular use in traditional medicine as antiophidic, anti-inflammatory, antimicrobial and antipyretic. Therefore, this study aims to evaluate the neutralizing potential of local effects induced by the venom of Bothrops erythromelas and Bothrops jararaca with the aqueous extract of the leaves of J. mollissima. The leaf extracts were prepared by decoction, fractionated (by liquid-liquid partition) and characterized by thin layer chromatography (TLC) and High Performance Liquid Chromatography (HPLC). Antiophidic activity of the extract was evaluated in model of paw edema, peritonitis, bleeding and myotoxicity induced by venoms of B. jararaca and B. erythromelas. In all models, the extract was evaluated by intraperitoneal route at the doses of 50, 100 and 200 mg/kg, administered 30 minutes prior to injection of the venom (pretreatment protocol). Stains suggestive of the presence of flavonoids: apigenin, luteolin, orientin, isoorientin, vitexin and vitexin-2-O-rhamnoside were detected in the extract by co-CCD. By means of HPLC were identified isoorientin, orientin, vitexin and isovitexin. All tested doses of J. mollissima extract reduced the paw edema induced by the venom with intensity similar to dexamethasone. The aqueous extract of J. mollissima leaves on all evaluated doses, inhibited cell migration induced by B. jararaca and B. erythromelas promoting inhibition of recruitment of mononuclear cells and the polymorphonuclear cells. Local bleeding induced by B. jararaca venom was significantly inhibited by the extract. Both venoms were inhibited by the extract in myotoxic activity. These results indicate that the aqueous extract of J. mollissima leaves have snakebite potential, particularly with respect to local effects, which may justify the use of this plant in traditional medicine and complementary therapy as anti-venom serum.

Inibição dos efeitos locais induzidos pelas peçonhas das serpentes Bothrops erythromelas e Bothrops jararaca pelo extrato aquoso das folhas de Jatropha mollissima (Pohl) Bail

Snakebites are a serious public health problem in tropical and subtropical countries and Bothrops genus is responsible for the accidents in Brazil and throughout Latin America (90% of cases). The local effects (pain, edema, hemorrhage and myonecrosis) and systemic (cardiovascular alterations, shock and blood clotting disorders) caused by the venom of Bothrops are due to the numerous protein and non-protein components, which are part of the constitution of the poison. The only form of therapy is scientifically validated antivenom serum therapy which, however, is not effective with respect to local effects produced, risk of immunological reactions, high cost and difficult access in some regions. Thus, the search for new alternatives to serum therapy becomes important, and in this context, many medicinal plants have been highlighted by the popular use as antiophidic. Among these plants, we can mention the species Jatropha mollissima (Euphorbiaceae) which has popular use in traditional medicine as antiophidic, anti-inflammatory, antimicrobial and antipyretic. Therefore, this study aims to evaluate the neutralizing potential of local effects induced by the venom of Bothrops erythromelas and Bothrops jararaca with the aqueous extract of the leaves of J. mollissima. The leaf extracts were prepared by decoction, fractionated (by liquid-liquid partition) and characterized by thin layer chromatography (TLC) and High Performance Liquid Chromatography (HPLC). Antiophidic activity of the extract was evaluated in model of paw edema, peritonitis, bleeding and myotoxicity induced by venoms of B. jararaca and B. erythromelas. In all models, the extract was evaluated by intraperitoneal route at the doses of 50, 100 and 200 mg/kg, administered 30 minutes prior to injection of the venom (pretreatment protocol). Stains suggestive of the presence of flavonoids: apigenin, luteolin, orientin, isoorientin, vitexin and vitexin-2-O-rhamnoside were detected in the extract by co-CCD. By means of HPLC were identified isoorientin, orientin, vitexin and isovitexin. All tested doses of J. mollissima extract reduced the paw edema induced by the venom with intensity similar to dexamethasone. The aqueous extract of J. mollissima leaves on all evaluated doses, inhibited cell migration induced by B. jararaca and B. erythromelas promoting inhibition of recruitment of mononuclear cells and the polymorphonuclear cells. Local bleeding induced by B. jararaca venom was significantly inhibited by the extract. Both venoms were inhibited by the extract in myotoxic activity. These results indicate that the aqueous extract of J. mollissima leaves have snakebite potential, particularly with respect to local effects, which may justify the use of this plant in traditional medicine and complementary therapy as anti-venom serum.