An algorithm is described to convert Lorentz and gauge invariant expressions in non– Abelian gauge theories with matter into a standard form, consisting of a linear combination of basis invariants. This algorithm is needed for computer calculations of effective actions. The defining properties of the basis invariants are reported. The number of basis invariants up to mass dimension 16 are prese...

We report on two recent results based on the evaluation of five-loop massless propagators in QCD and QED: (i) corrections of order α 4 s to the absorptive part of the polarization function in QCD with n f = 3; (ii) the five-loop contribution to the β function of quenched QED.

We critically evaluate the use of cluster and periodic slab models in describing the NH3/Si(001) molecule–surface reaction system. We show that considerable discrepancies in the relative adsorbate energetics originate in the limitations of the small cluster and slab models commonly used. These limitations in turn are the consequence of the balance that must be struck between the competing deman...

Let X be a Banach space and E be a closed bounded subset of X. For x ∈ X we set D(x,E) = sup{‖x− e‖ : e ∈ E}. The set E is called remotal in X if for any x ∈ X, there exists e ∈ E such that D(x,E) = ‖x− e‖ . It is the object of this paper to give new results on remotal sets in L(I,X), and to simplify the proofs of some results in [5].

In the causal set program, the development of a dynamics is one of the most crucial issues. In this report, a candidate for a dynamics, sequential growth models, is studied with focus on the author’s personal work. Causal set formalism is introduced using the more general mathematics of partial orders. Sequential growth models are investigated as a possible dynamics for causal sets. Among them,...

The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.

Let A ⊂ R be a set-germ at 0 ∈ R such that 0 ∈ A. We say that r ∈ S is a direction of A at 0 ∈ R if there is a sequence of points {xi} ⊂ A\{0} tending to 0 ∈ R such that xi ‖xi‖ → r as i → ∞. Let D(A) denote the set of all directions of A at 0 ∈ R. Let A, B ⊂ R be subanalytic set-germs at 0 ∈ R such that 0 ∈ A ∩ B. We study the problem of whether the dimension of the common direction set, dim(D...

The Central Sets Theorem is a powerful theorem, one of whose consequences is that any central set in N contains solutions to any partition regular system of homogeneous linear equations. Since at least one set in any finite partition of N must be central, any of the consequences of the Central Sets Theorem must be valid for any partition of N. It is a result of Beiglböck, Bergelson, Downarowicz...