For d 2:: 2, let Dd be the symmetric block design formed from the points and hyperplanes of the projective space PG(d, 2). Let 3d equal the number of blocks in a smallest defining set of Dd . The known results 32 = 3 and S3 = 9 are reviewed and it is shown that 34 = 24 and 52 :::; 35 :::; 55. If J-Ld = 3d/ (2d+ 1 1) is the proportion of blocks in a smallest defining set of Dd, then J-L2 = 3/7, ...

An analytic hypersurface of M is a subset V ⊂ M such that for each point x ∈ V there exists an open set Ux ⊂ M containing x and a holomorphic function fx defined on Ux such that V ⊂ Ux is the zero-set of fx. Such an fx is called a local defining function for V near x. The quotient of any two local defining functions around x is a non-vanishing holomorphic function around x. An analytic hypersur...

Supply Chain Operations Reference (SCOR) model is developed and maintained by the Supply Chain Council (SCC). The model is a reference model which can be utilized to map benchmark and improve the supply chain operations. SCOR model provides companies with a basic process modeling tool, an extensive benchmark database by defining a set of supply chain metrics. This paper explains the process and...

Let A be an algebra over a field K of characteristic zero, let δ1, . . . , δs ∈ DerK(A) be commuting locally nilpotent K-derivations such that δi(xj) = δij , the Kronecker delta, for some elements x1, . . . , xs ∈ A. A set of algebra generators for the algebra A := ∩i=1ker(δi) is found explicitly and a set of defining relations for the algebra A is described. Similarly, given a set σ1, . . . , ...

The rough set concept is a relatively new mathematical approach to vagueness and uncertainty in data. The rough set theory is a well-understood formal framework for building data mining models in the form of logic rules, on the basis of which it is possible to issue predictions that allow classifying new cases. The indiscernibility relation and approximations based on this relation form the mat...

Let D ⊆ R be closed and discrete and f : Dn → R be such that f(Dn) is somewhere dense. We show that (R,+, ·, f) defines Z. As an application, we get that for every α, β ∈ R with log α (β) / ∈ Q, the real field expanded by the two cyclic multiplicative subgroups generated by α and β defines Z.

Abstract We study defining inequalities of string cones via a potential function on reduced double Bruhat cell. give necessary criterion for the to provide minimal set tropicalization and conjecture an equivalence.