We study equivariant embeddings with small boundary of a given homogeneous space G/H, where G is a connected linear algebraic group with trivial Picard group and only trivial characters, and H ⊂ G is an extension of a connected Grosshans subgroup by a torus. Under certain maximality conditions, like completeness, we obtain finiteness of the number of isomorphism classes of such embeddings, and ...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Restriction Site Mapping is one of the interesting tasks in Computational Biology. A DNA strand can be thought of as a string on the letters A, T, C, and G. When a particular restriction enzyme is added to a DNA solution, the DNA is cut at particular restriction sites. The goal of the restriction site mapping is to determine the location of every site for a given enzyme. In partial digest metho...

y=1 φ(y) = 0, θ ∈ {1, 2, . . .}, i.e., φ(y) = 0, y ∈ {1, 2 . . .}. Consequently, if g : IR → IR is an unbiased estimator of θ on the basis of Y , it is “essentially unique”: if g̃ : IR → IR is another unbiased estimator, then it must hold by the completeness of {U(1, . . . , θ), θ ∈ {1, 2 . . .}} that g̃(Y ) = g(Y ) Pθ-a.s. θ ∈ {1, 2, . . .}, whence g̃(y) = g(y), y ∈ {1, 2, . . .}. Next, Eθ[g(Y )]...

In this work we investigate bounded Lukasiewicz logics, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, . . . , n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus G LBn for each bounded Lukasiewicz logic, obtained by adding a single rule to G L, a hypersequent calcu...