Let F be a compact Hausdorff foliation on a compact manifold. Let E 2 = ⊕{E 2 : p > 0, q ≥ 0} be the subalgebra of cohomology classes with positive transverse degree in the E2 term of the spectral sequence of the foliation. We prove that the saturated transverse Lusternik-Schnirelmann category of F is bounded below by the length of the cup product in E 2 . Other cohomological bounds are discussed.

We prove a positivity property for the cup product in the T -equivariant cohomology of the flag variety. This was conjectured by D. Peterson and has as a consequence a conjecture of S. Billey. The result for the flag variety follows from a more general result about algebraic varieties with an action of a solvable linear algebraic group such that the unipotent radical acts with finitely many orb...

We give algorithms for the computation of the algebraic de Rham cohomology of open and closed algebraic sets inside projective space or other smooth complex toric varieties. The methods, which are based on Gröbner basis computations in rings of differential operators, can also be used to compute the cohomology of intersections of smooth closed and open subsets, and in certain situations the cup...

A cohomology ring algorithm in a dimension-independent framework of combinatorial cubical complexes is developed with the aim of applying it to the topological analysis of high-dimensional data. This approach is convenient in the cup-product computation and motivated, among others, by interpreting pixels or voxels in digital images as cubes. The S-complex theory and so called co-reductions are ...

There are mainly two methods of deep drawing analysis; experimental and analytical/numerical. Experimental analysis can be useful in analyzing the process to determine the process parameters that produce a defect free product, and the analytical/numerical modeling can be used to model and analyze the process through all stages of deformation. This approach is less time consuming and more econom...

A cohomology ring algorithm in a dimension-independent framework of combinatorial cubical complexes is developed with the aim of applying it to the topological analysis of high-dimensional data. This approach is convenient in the cup-product computation and motivated, among others, by interpreting pixels or voxels in digital images as cubes. The S-complex theory and so called co-reductions are ...

The goal of this work is to establish a new algorithm for computing the cohomology ring of cubical complexes. The cubical structure enables an explicit recurrence formula for the cup product. We derive this formula and, next, show how to extend the Mrozek and Batko [7] homology coreduction algorithm to the cohomology ring structure. The implementation of the algorithm is a work in progress. Thi...

For a $$2n+1$$ -dimensional compact Sasakian manifold, if $$n\ge 2$$ , we prove that the analytic germ of variety representations fundamental group at every semi-simple representation is quadratic. To this result, almost-formality de Rham complex manifold with values in flat vector bundle. By almost-formality, also vanishing theorem on cup product cohomology bundles over manifold.

INTRODUCTION Hearing protection devices are one of the primary noise reduction tools in developing countries. This study is intended to produce and apply acrylonitrile butadiene styrene (ABS)/clay nanocomposites to fabricate a laboratory single cup earmuffs and then compare it with double cup and single cup pure ABS earmuffs in terms of noise attenuation performance and comfort. In addition, th...

Starch Each serving equals 80 calories and 15 grams carbohydrate. Cereals/grains/ pasta Cooked cereals, 1⁄2 cup Grits (cooked), 1⁄2 cup Ready-to-eat unsweetened cereals, 3⁄4 cup Granola (lowfat), 1⁄4 cup Pasta (cooked), 1⁄3 cup Rice, white or brown (cooked), 1⁄3 cup Starchy vegetables Corn, 1⁄2 cup Corn on the cob, 1⁄2 cob (5oz.) Peas, (green), 1⁄2 cup Plantain, 1⁄2 cup Potato, baked, 1⁄4 large...