Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero

2000 Mathematics Subject Classification: 14B05, 32S25.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

Properties of the Bellman Gamma Distribution

2000 Mathematics Subject Classification: 62H10.

On Thom Polynomials for A4(−) via Schur Functions

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.

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

MSC 2010: 46F30, 46F10

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Weak Langmuir optical turbulence in a fiber cavity

We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave: an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Aside from nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integrodifferential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental setup in which the theoretical predictions can be observed and studied.

Predictors of developmental gains in children enrolled in an early intervention setting

The purpose of this research was to determine whether initial developmental delay, site of intervention, frequency of intervention, age of the child, socio-economic status (SES), gender and ethnicity significantly predict developmental gains in a group of children enrolled in an early intervention setting. The records of 134 children enrolled in an inner-city program in Miami, Florida were reviewed for inclusion in this study. ^ Demographic variables, site placement and treatment frequencies were collected during a retrospective chart review. Level of delay was expressed using the developmental quotient and developmental gain was calculated using the mean gain on age equivalent scores or developmental tests. A multiple regression analysis was performed to determine which of the above variables significantly predicted developmental gains. Multivariate analysis compared developmental gains for all the developmental domains based on intervention site (center versus home-based) while controlling for developmental delay. ^ Children made greater developmental gains if they had higher developmental quotients and if they were younger at the time services were initiated. Frequency of intervention significantly improved developmental outcomes in children attending center-based programs. Children attending center-based programs also made significantly greater gains in gross motor skills compared to children attending home-based programs. ^ These findings emphasize the importance of early screening and referral of children with developmental delay and adjusting intervention for the child's developmental quotient. Children should receive intense treatment to maximize results. Decisions regarding program placement should be individualized according to the child's unique developmental pattern. Policy and program decisions affecting the curriculum of a child in early intervention need to reflect these multivariate considerations. ^

The role of emotional intelligence in college students' success

The purpose of this study was to determine if higher academic performance was positively correlated to higher emotional intelligence among traditional age male and female college students enrolled in an Introduction to Business course at a large multi-campus state college in Florida. The Bar-On 2004 (Emotional Quotient Inventory) EQ-i 133-item inventory was used to assess students’ emotional intelligence. Within the scope of this ex-post facto study, a quasi-experimental design was included to further determine if emotional intelligence could be increased through the inclusion of a curricular component on emotional intelligence. Four groups of students (N=111) participated in the three-phase study over two semesters. The first phase (pre-intervention) was limited to students with an established GPA and an attempted-to-completed credit hour ratio within the institution (N=82). Results showed a slight positive correlation between the two factors and the students’ emotional intelligence pretest assessment scores. The second phase of the study involved establishing a control and an experimental group in each of two semesters to compare the attainment of overall emotional intelligence scores as measured by the EQ-i. The third phase of the study examined four measures of academic success (GPA, the attempted-to-completed credit hour ratio, grade in the business course, and persistence in college) to determine if these factors were positively correlated with the students’ posttest EQ-i scores. The study also included a research question to determine if significant differences in overall EQ-i scores existed between male and female students during the three phases. Findings from the study indicated that (a) there was a slight positive correlation in the pre-intervention stage between emotional intelligence and traditional measures of academic success specifically, GPA and the attempted-to-completed credit hour ratio; (b) curricular intervention made a significant difference at the p <.05 level, with an .5 effect size, in one semester but failed to meet that threshold in the following semester with the second pair of groups; (c) at the post-intervention phase, the four measures of traditional academic success yielded a low positive correlation with the students’ emotional intelligence assessment scores, and (d) female students showed significant gains in their overall EQ-i scores.

Comparison of snail density, standing stock, and body size between Caribbean karst wetlands and other freshwater ecosystems

Synthesizing data from multiple studies generates hypotheses about factors that affect the distribution and abundance of species among ecosystems. Snails are dominant herbivores in many freshwater ecosystems, but there is no comprehensive review of snail density, standing stock, or body size among freshwater ecosystems. We compile data on snail density and standing stock, estimate body size with their quotient, and discuss the major pattern that emerges. We report data from 215 freshwater ecosystems taken from 88 studies that we placed into nine categories. Sixty-five studies reported density, seven reported standing stock, and 16 reported both. Despite the breadth of studies, spatial and temporal sampling scales were limited. Researchers used 25 different sampling devices ranging in area from 0.0015 to 2.5 m2. Most ecosystem categories had similar snail densities, standing stocks, and body sizes suggesting snails shared a similar function among ecosystems. Caribbean karst wetlands were a striking exception with much lower density and standing stock, but large body size. Disparity in body size results from the presence of ampullariids in Caribbean karst wetlands suggesting that biogeography affects the distribution of taxa, and in this case size, among aquatic ecosystems. We propose that resource quality explains the disparity in density and standing stock between Caribbean karst wetlands and other categories. Periphyton in Caribbean karst wetlands has high carbon-to-phosphorous ratios and defensive characteristics that inhibit grazers. Unlike many freshwater ecosystems where snails are key grazers, we hypothesize that a microbial loop captures much of the primary production in Caribbean karst wetlands.

The impact of Round II Urban Empowerment Zones on local communities

In the United States, the federal Empowerment Zone (EZ) program aimed to create and retain business investment in poor communities and to encourage local hiring through the use of special tax credits, relaxed regulations, social service grants, and other incentives. My dissertation explores whether the Round II Urban EZs had a beneficial impact on local communities and what factors influenced the implementation and performance of the EZs, using three modes of inquiry. First, linear regression models investigate whether the federal revitalization program had a statistically significant impact on the creation of new businesses and jobs in Round II Urban EZ communities. Second, location quotient and shift-share analysis are used to reveal the industry clusters in three EZ communities that experienced positive business and job growth. Third, qualitative analysis is employed to explore factors that influenced the implementation and performance of EZs in general, and in particular, Miami-Dade County, Florida. The results show an EZ's presence failed to have a significant influence on local business and job growth. In communities that experienced a beneficial impact from EZs, there has been a pattern of decline in manufacturing companies and increase in service-driven firms. The case study suggests that institutional factors, such as governance structure, leadership, administrative capacity, and community participation have affected the effectiveness of the program's implementation and performance.

Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.

Foundations of quantitative information flow: Channels, cascades, and the information order

Secrecy is fundamental to computer security, but real systems often cannot avoid leaking some secret information. For this reason, the past decade has seen growing interest in quantitative theories of information flow that allow us to quantify the information being leaked. Within these theories, the system is modeled as an information-theoretic channel that specifies the probability of each output, given each input. Given a prior distribution on those inputs, entropy-like measures quantify the amount of information leakage caused by the channel. ^ This thesis presents new results in the theory of min-entropy leakage. First, we study the perspective of secrecy as a resource that is gradually consumed by a system. We explore this intuition through various models of min-entropy consumption. Next, we consider several composition operators that allow smaller systems to be combined into larger systems, and explore the extent to which the leakage of a combined system is constrained by the leakage of its constituents. Most significantly, we prove upper bounds on the leakage of a cascade of two channels, where the output of the first channel is used as input to the second. In addition, we show how to decompose a channel into a cascade of channels. ^ We also establish fundamental new results about the recently-proposed g-leakage family of measures. These results further highlight the significance of channel cascading. We prove that whenever channel A is composition refined by channel B, that is, whenever A is the cascade of B and R for some channel R, the leakage of A never exceeds that of B, regardless of the prior distribution or leakage measure (Shannon leakage, guessing entropy leakage, min-entropy leakage, or g-leakage). Moreover, we show that composition refinement is a partial order if we quotient away channel structure that is redundant with respect to leakage alone. These results are strengthened by the proof that composition refinement is the only way for one channel to never leak more than another with respect to g-leakage. Therefore, composition refinement robustly answers the question of when a channel is always at least as secure as another from a leakage point of view.^

The relationships between elementary school principals' emotional intelligence, leadership style and school culture

The role of the principal in school settings and the principal's perceived effect on student achievement have frequently been considered vital factors in school reform. The relationships between emotional intelligence, leadership style and school culture have been widely studied. The literature reveals agreement among scholars regarding the principal's vital role in developing and fostering a positive school culture. The purpose of this study was to explore the relationships between elementary school principals' emotional intelligence, leadership style and school culture. ^ The researcher implemented a non-experimental ex post facto research design to investigate four specific research hypotheses. Utilizing the Qualtrics Survey Software, 57 elementary school principals within a large urban school district in southeast Florida completed the Emotional Quotient Inventory (EQ-i), and 850 of their faculty members completed the Multifactor Leadership Questionnaire (MLQ Form 5X). Faculty responses to the school district's School Climate Survey retrieved from the district's web site were used as the measure of school culture. ^ Linear regression analyses revealed significant positive associations between emotional intelligence and the following leadership measures: Idealized Influence-Attributes (β = .23, p = < .05), Idealized Influence-Behaviors (β = .34, p = < .01), Inspirational Motivation (β = .39, p = < .01) and Contingent Reward (β = .33, p = < .01). Hierarchical regression analyses revealed positive associations between school culture and both transformational and transactional leadership measures, and negative associations between school culture and passive-avoidant leadership measures. Significant positive associations were found between school culture and the principals' emotional intelligence over and above leadership style. Hierarchical linear regressions to test the statistical hypothesis developed to account for alternative explanations revealed significant associations between leadership style and school culture over and above school grade. ^ These results suggest that emotional intelligence merits consideration in the development of leadership theory. Practical implications include suggestions that principals employ both transformational and transactional leadership strategies, and focus on developing their level of emotional intelligence. The associations between emotional intelligence, transformational leadership, Contingent Reward and school culture found in this study validate the role of the principal as the leader of school reform.^