Let (X, d) a metric space and BX = X × R denote the partially ordered set of (generalized) formal balls in X. We investigate the topological structures of BX, in particular the relations between the Lawson topology and the product topology. We show that the Lawson topology coincides with the product topology if (X, d) is a totally bounded metric space, and show examples of spaces for which the ...

In 1957, N. G. de Bruijn showed that the symmetric group Sym(Ω) on an infinite set Ω contains a free subgroup on 2 generators, and proved a more general statement, a sample consequence of which is that for any group A of cardinality ≤ card(Ω), the group Sym(Ω) contains a coproduct of 2 copies of A, not only in the variety of all groups, but in any variety of groups to which A belongs. His key l...

Multivariate Process Capability Indices (MPCI) show how well a manufacturing process can meet specifica-tion limits when quality characteristics enclose a relative correlation. Process capability is an important and commonly used metric for assessing and improving the quality of a production process. When quality charac-teristics of a product are correlated then an attractive comes close to MPC...

We present SUSY LATTICE a C++ program that can be used to simulate certain classes of supersymmetric Yang–Mills (SYM) theories, including the well known N = 4 SYM in four dimensions, on a flat Euclidean space-time lattice. Discretization of SYM theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topolog...

We consider N = 4 supersymmetric Yang-Mills theory formulated in terms of N = 2 superfields in harmonic superspace. Using the background field method we define manifestly gauge invariant and N = 2 supersymmetric effective action depending on N = 2 strength superfields and develop a general procedure for its calculation in one-loop approximation. Explicit form for this effective action is found ...

multivariate process capability indices (mpci) show how well a manufacturing process can meet specifica-tion limits when quality characteristics enclose a relative correlation. process capability is an important and commonly used metric for assessing and improving the quality of a production process. when quality charac-teristics of a product are correlated then an attractive comes close to mpc...

The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existe...

We study Maldacena’s conjecture and the AdS/SYM correspondence on the Coulomb branch. Several interesting aspects of this conjectured AdS/SYM correspondence on the Coulomb branch are pointed out and clarified.

We prove that mcf < cf(Sym(ω))) and mcf > cf(Sym(ω)) = b are both consistent relative to ZFC. This answers a question by Banakh, Repovš and Zdomskyy and a question from [12].

The changeability, a sub-characteristic of maintainability, refers to the level of effort which is required to do modifications to a software product line (SPL) application component. Assuming dependencies between SPL application components and reference architecture implementation (a platform), this paper empirically investigates the relationship between 7 design metrics and changeability of 4...