Non-regular two-level fractional factorial designs, such as Plackett–Burman designs, are becoming popular choices in many areas of scientific investigation due to their run size economy and flexibility. The run size of nonregular two-level factorial designs is a multiple of 4. They fill the gaps left by the regular twolevel fractional factorial designs whose run size is always a power of 2 (4, ...

A new class of symmetric functions called factorial Schur symmetric functions has recently been discovered in connection with a branch of mathematical physics. We align this theory more closely with the s tandard symmetric function theory, giving the factorial Schur function a tableau definition, introducing a shift operator and a new generat ing function with which we extend to factorial symme...

Recent work on multistratum fractional factorial designs is set in a general and unified framework, and a criterion for selecting multistratum fractional factorial designs that takes stratum variances into account is proposed. Application of the general theory is illustrated on designs of experiments with multiple processing stages, including split-lot designs, blocked strip-plot designs, and p...

We explore an operation on graphs that is analogous to the factorial of a positive integer. We develop formulas for the factorials of complete graphs, odd cycles and complete bipartite graphs, and we prove some properties of the factorial operation. We conclude with a list of open questions. This paper explores some properties of a factorial operation that associates to each graph G a graph G! ...

We prove that a nodal quartic threefold X containing no planes is Q-factorial provided that it has not more than 12 singular points, with the exception of a quartic with exactly 12 sin-gularities containing a quadric surface. We give some geometrical constructions related to the latter quartic.

In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....