Affine Manifolds and Zero Lyapunov Exponents in Genus 3

In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichm\"uller curve in genus three has two zero Lyapunov exponents in the Kontsevich-Zorich cocycle, then it lies in the principal stratum and has at most quadratic trace field. Moreover, there can be at most finitely many such Teichm\"uller curves.Comment: 40 pages, To appear in GAF

Progress Toward Classifying Teichmueller Disks with Completely Degenerate Kontsevich-Zorich Spectrum

We present results toward resolving a question posed by Eskin-Kontsevich-Zorich and Forni-Matheus-Zorich. They asked for a classification of all $\text{SL}_2(\mathbb{R})$-invariant ergodic probability measures with completely degenerate Kontsevich - Zorich spectrum. Let $\mathcal{D}_g(1)$ be the subset of the moduli space of Abelian differentials $mathcal{M}_g$ whose elements have period matrix derivative of rank one. There is an $\text{SL}_2(\mathbb{R})$-invariant ergodic probability measure $nu$ with completely degenerate Kontsevich-Zorich spectrum, i.e. $lambda_1 = 1 > lambda_2 = cdots = lambda_g = 0$, if and only if $nu$ has support contained in $\mathcal{D}_g(1)$. We approach this problem by studying Teichm"uller disks contained in $\mathcal{D}_g(1)$. We show that if $(X,omega)$ generates a Teichm"uller disk in $\mathcal{D}_g(1)$, then $(X,omega)$ is completely periodic. Furthermore, we show that there are no Teichm"uller disks in $\mathcal{D}_g(1)$, for $g = 2$, and the known example of a Teichm"uller disk in $mathcal{D}_3(1)$ is the only one. Finally, we present an idea that might be able to fully resolve the problem

The Curriculum Content of Master\u27s Level Fashion Merchandising Programs Throughout the United States

The following objectives were established to answer this problem: 1. Identify the schools offering master\u27s degrees in fashion merchandising; 2. Identify the courses offered within master\u27s programs at the different schools; 3. Identify the requirements needed for students to graduate from schools with fashion merchandising master\u27s programs; 4. Determine the mission of graduate programs in fashion merchandising; 5. Determine specific courses needed to be offered by Old Dominion University in order to produce a respected graduate fashion merchandising program

Vertex-to-Self Trajectories on the Platonic Solids

We consider the problem of walking in a straight line on the surface of a Platonic solid. While the tetrahedron, octahedron, cube, and icosahedron all exhibit the same behavior, we find a remarkable difference with the dodecahedron

Aplicación de índices de tolerancia a la salinidad en plántulas de maíz

Los objetivos de este trabajo fueron: estudiar la aplicación de diferentes índices de tolerancia en caracteres de plántulas de maíz y evaluar su posible utilidad en la identificación de genotipos tolerantes a la salinidad. Se probaron 68 accesiones en dos ambientes (0 y 100m MClNa). Se midieron: largo de raíz, vástago y 3ª hoja y peso seco de raíz y de parte aérea. Se incluyeron 6 índices de tolerancia: índice de susceptibilidad al estrés (SSI), índice de tolerancia al estrés (STI), tolerancia al estrés (TOL), media geométrica de la productividad (GMP), productividad media (MP) e índice de estabilidad del rendimiento (YSI). Debido a la variación espacial relacionada con la concentración de sal en ambientes salinos, sería importante identificar genotipos estables frente a una gama amplia de suelos salinos. El biplot agrupó las accesiones, caracteres medidos en ambientes con y sin estrés e índices de tolerancia a sal, y demostró que los índices GMP, MP y STI fueron los que permitieron identificar los accesiones estables que se caracterizan por tener una alta expresión de estos caracteres en ambos ambientes. La aplicación del método de Componentes Principales (CP) identificó a los caracteres peso seco aéreo y largo de raíz como los de mayor contribución y ambos estuvieron asociados con dichos indices de tolerancia a salinidad. De esta manera, en este estudio las accesiones 1, 7, 30, 33, 43 y 45 fueron los más estables para los caracteres peso seco aéreo y largo de raíz. Entre ellos las accesiones 30 y 33 fueron superiores (pertenecientes a genotipos del Grupo A) porque mostraron los escores más altos sobre el eje CP1 pero sus aportes al CP2 fueron bastantes pequeños, para la mayoría de las variables.The aims of this research were: to study the application of different tolerance Indices in traits measured in maize seedlings and to assess their possible use in the identification of genotypes tolerant to salinity. Sixty eight accessions were tested in two environments (0 and 100mM NaCl). We recorded length for radicle, shoot and third leaf and dry weight for root and shoot. Six stress tolerance indices were included: stress susceptibility (SSI), stress tolerance index (STI), stress tolerance (TOL), geometric mean productivity (GMP), mean productivity (MP) and yield stability index (YSI. Saline environments show a great spatial variation in relation to the salt concentration, for this reason it would be important to identify genotypes with stable behavior in a variety of saline soils. The biplot method allowed clustering accessions, traits measured in stress and non stress environment and salt tolerance Indexes in a same graphic, and showed that GMP, MP and STI indexes were the ones who helped identify the high yielding (group A genotype) and stable accessions, characterized by a high expression of these characters in both environments. Principal Component method showed that shoot dry weight and root length had the highest contribution and both were associated with these above indices in salinity. Therefore, in this study the accessions: 1, 7, 30, 33, 43 and 45 had stable values for the traits root length and shoot dry weight. Within this group the 30 and 33 entries were superior (bellowing to Group A genotypes) because they had the highest PC1 scores but its PC2 scores were rather small for the most of the variables.Fil: Collado, Mónica B.. Universidad Nacional de La Plata. Facultad de Ciencias Agrarias y Forestales. Instituto Fitotécnico de "Santa Catalina"; ArgentinaFil: Aulicino, Mónica Beatriz. Universidad Nacional de La Plata. Facultad de Ciencias Agrarias y Forestales. Instituto Fitotécnico de "Santa Catalina"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Arturi, Miguel Jacinto. Universidad Nacional de La Plata. Facultad de Ciencias Agrarias y Forestales. Instituto Fitotécnico de "Santa Catalina"; ArgentinaFil: Molina, María del Carmen. Universidad Nacional de La Plata. Facultad de Ciencias Agrarias y Forestales. Instituto Fitotécnico de "Santa Catalina"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin