If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...

To investigate responses of Glycyrrhiza glabra var. glabra and G. glabra var. glandulifera to molybdenum and salicylic acid, we measured four stress biochemical parameters: anthocyanin, nitric acid, glycyrrhizic acid and peroxidase activity in callus tissues. Callus tissues obtained from seedlings root cultures were treated by 60 mg. l-1 molybdenum and 5 µM salicylic acid alone or together for...

Richardson varieties play an important role in intersection theory and in the geometric interpretation of the Littlewood-Richardson Rule for flag varieties. We discuss three natural generalizations of Richardson varieties which we call projection varieties, intersection varieties, and rank varieties. In many ways, these varieties are more fundamental than Richardson varieties and are more easil...

In the area of symbolic-numerical computation within computer algebra, an interesting question is how “close” a random input to “critical” ones. Examples are singular matrices in linear algebra or polynomials with multiple roots for Newton's root-finding method. Bounds, sometimes very precise, known volumes over R C such neighborhoods varieties inputs; see references below. This paper deals dis...

Proposing the similarity measures formula between Vague sets E and G. Concluding Vague resistance analysis. The concrete application steps were:1Establishing comprehensive characters set; 2Screening excellent varieties set; 3Extracting theory optimal varieties set; 4The single-value date transformed into Vague date, obtaining different varieties Vague sets; 5Vague resistance analysis 1,the simi...

We study a family of subvarieties of the flag variety defined by certain linear conditions, called Hessenberg varieties. We compare them to Schubert varieties. We prove that some Schubert varieties can be realized as Hessenberg varieties and vice versa. Our proof explicitly identifies these Schubert varieties by their permutation and computes their dimension. We use this to answer an open quest...

RESUMEN Lilian Harrison fue la primera persona en completar travesía del Río de Plata a nado, entre Colonia (Uruguay) y Punta Lara (Argentina) 1923. La prensa argentina época coronó victoria como un logro toda nación, despecho las apelaciones sexistas los reportajes. Este artículo pretende analizar discursos uruguaya sobre hazaña nadadora, utilizando principales publicaciones periódicas época. ...