This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert varieties in ordinary flag varieties. We give ...

We introduce a formal integral on the system of varieties mapping properly and birationally to a given one, with value in an associated Chow group. Applications include comparisons of Chern numbers of birational varieties, new birational invariants, ‘stringy’ Chern classes, and a ‘celestial’ zeta function specializing to the topological zeta function. In its simplest manifestation, the integral...

Bambara groundnut is an indigenous African vegetable grown mainly for human food and animal feed due to its high protein content. Different factors like varieties and origin can influence the chemical composition of Bambara groundnut cultivars. Therefore, the aims of this study are to produce defatted flour and protein concentrate from newly developed Bambara groundnut cultivars [Accessions No:...

New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry. Some old modules of equations (catalecticant minors) are revisited to determine when they are sufficient to give scheme-theoretic defining equations. An algorithm to decompose a general ternary quintic as the sum of seven fifth powers is given as an illustration o...

Chrysanthemum is one of the ornamental plants that cultivated widely in worldwide. This flower is one of the most important cut and pot flowers in the world due to its high diversity of colors and shapes. The creation of mutation is an important method for the production of new cultivars, and many cultivars have been produced through spontaneous and induced mutations. In this study, explants of...

We introduce a notion of integration on the category of proper birational maps to a given variety X, with value in an associated Chow group. Applications include new birational invariants; comparison results for Chern classes and numbers of nonsingular birational varieties; ‘stringy’ Chern classes of singular varieties; and a zeta function specializing to the topological zeta function. In its s...

Assessing the performance and the characteristics (e.g. yield, quality, disease resistance, abiotic stress tolerance) of new varieties is a key component of crop performance improvement. However, the variety testing process is presently exclusively based on experimental field approaches which inherently reduces the number and the diversity of experienced combinations of varieties x environmenta...