We present the newest results for the determination of heavy-quark masses from low-energy moments of the vacuum polarization function. The results presented here update an earlier determination of the quark masses and incorporate new theoretical calculations of the low-energy moments of the vacuum polarization and new experimental data at the bottom threshold.

and Applied Analysis 3 where Hα is a Γ-open set, Gγ is a Σ-open set, and Mγ is a Γ-compact set. It is easy to see that {Gγ ×{0}}γ∈Ω is an open cover ofK×{0}, thus there is a finite subcoverGγ1 ×{0}, . . . , Gγn ×{0}. Then, Gγ1 × {0, 1} \Mγ1 × {1} ∪ · · · ∪Gγn × {0, 1} \Mγn × {1} 1.6 misses only finitely many Γ-compact sets Mγ1 × {1}, . . . ,Mγn × {1}. AsMγj j 1, 2, . . . , n is compact, we have...

We present a finite-size scaling approach for the calculations of the critical parameters of the few-body Schrödinger equation. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we added detailed calculations for the critical screening length and the critical exponents for the Yukawa potential...

Nadykto, Yu, Jakovleva, Herb and Xu have recently reported a DFT study on the structure and formation thermodynamics of sulfuric acid-base-water clusters, with ammonia and a handful of amines as bases [1]. This study partially overlaps with our previous work [2], and a significant part of the discussion in their manuscript concerns differences between their results and ours. This comment is int...

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.