Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...

Lignin and cellulose represent the two main components of plant secondary walls and the most abundant polymers on Earth. Quantitatively one of the principal products of the phenylpropanoid pathway, lignin confers high mechanical strength and hydrophobicity to plant walls, thus enabling erect growth and high-pressure water transport in the vessels. Lignin is characterized by a high natural heter...

In this paper, we propose a new method of estimating pure spectra and the mixture ratio by applying the Independent Component Analysis (ICA) to the agricultural remote sensing images for recognizing fine structure vegetation change on farmland, where the covering plant is unknown. This technique enables to separate the change of vegetation into qualitative one due to ecological characteristics ...

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...

Horticulture is an important subsector of agriculture. The potential of horticultural crops has not yet been fully explored or exploited in Bangladesh. More than 90 vegetables and 60 fruits are grown in Bangladesh, with great regional variation in the extent of cultivation. The cultivated area given to fruits and vegetables is 0.52 million hectares, covering 3.7 percent of total cropped area. V...