Seed industry is an important basic industry in agricultural, an emerging industry as well. However, the new varieties are driving force and providing source for seed industry development. How extending the new varieties to the most appropriate place are important issues that seed industry needs to address. East of North China as an example, the county for the evaluation unit, on the basis of a...

Organic and low-input agriculture needs flexible varieties that can buffer environmental stress and adapt to the needs of farmers. We implemented an experiment to investigate the evolutionary capacities of a sample of spinach (Spinacia oleracea L.) population varieties for a number of phenotypic traits. Three farmers cultivated, selected and multiplied one or several populations over two years ...

Eilenberg’s variety theorem gives a bijective correspondence between varieties of languages and varieties of finite semigroups. The second author gave a similar relation between conjunctive varieties of languages and varieties of semiring homomorphisms. In this paper, we add a third component to this result by considering varieties of meet automata. We consider three significant classes of lang...

Secant Varieties of Segre-Veronese Varieties

This paper studies the dimension of secant varieties to Segre varieties. The problem is cast both in the setting of tensor algebra and in the setting of algebraic geometry. An inductive procedure is built around the ideas of successive specializations of points and projections. This reduces the calculation of the dimension of the secant variety in a high dimensional case to a sequence of calcul...

Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety Vσ of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varie...

Net Photosynthetic rate(Pn), relative electrical conductivity and MDA content of 11 fennel varieties were tested using LI6400 portable photosynthesis system. The results showed that Pn of XJ0710 has distinct difference with other varieties in which there is no obvious difference. But the relative electrical conductivity and MDA of the varieties have obvious difference. Under environmental stres...

The goal of these lectures is to explain speaker’s results on uniqueness properties of spherical varieties. By a uniqueness property we mean the following. Consider some special class of spherical varieties. Define some combinatorial invariants for spherical varieties from this class. The problem is to determine whether this set of invariants specifies a spherical variety in this class uniquely...

1. Congruence lattices. G. Birkhoff and O. Frink noted that the congruence lattice Con04) of an algebra A (with operations of finite rank) is algebraic or compactly generated. The celebrated Grätzer-Schmidt theorem states that, conversely, every algebraic lattice is isomorphic to Con(A) for some algebra A. The importance of this is obvious, for it shows that unless something more is known about...