Abstract. The framework of dimensional analysis is used for case-based reasoning. For all case descriptions in engineering and physics consisting of real-valued quantities with physical units, the Pi-Theorem of Buckingham can be shown to derive appropriate similarity conditions and provide an appropriate case adaptation. The advantages of the Pi-Theorem are mainly based on the properties of the...

The framework of dimensional analysis is used for case-based reasoning. For all case descriptions in engineering and physics consisting of real-valued quantities with physical units, the Pi-Theorem of Buckingham can be shown to derive appropriate similarity conditions and provide an appropriate case adaptation. The advantages of the Pi-Theorem are mainly based on the properties of the so-called...

We give a spectral theorem for unital representions of Hermitian commutative unital ∗-algebras by possibly unbounded operators in a pre-Hilbert space. A more general result is known for the case in which the ∗-algebra is countably generated. 1. Statement of the Main Result Our main result is the following: Theorem 1. Let π be a unital representation of a Hermitian commutative unital ∗-algebra A...

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GLn(AK). Let S be a set of finite places of K, such that the sum ∑ v∈S Nv −2/(n+1) is convergent. Then π is uniquely determined by the collection of the local components {πv | v 6∈ S, v finite} of π. Combining this theorem with base change, it is p...

The Equivalence Theorem is commonly used to calculate perturbatively amplitudes involving gauge bosons at energy scales higher than gauge boson masses. However, when the scalar sector is strongly interacting the theory is non-perturbative. We show that the Equivalence Theorem holds in the large N limit at next-to-leading order by calculating the decay widths h → W+W− and h → π+π−. We also show,...

We prove a freeness theorem for low-rank subgroups of one-relator groups. Let F be free group, and let w∈F nonprimitive element. The primitivity rank w, π(w), is the smallest subgroup containing w as an imprimitive Then any group G=F∕⟨⟨w⟩⟩ generated by fewer than π(w) elements free. In particular, if π(w)>2, then G does not contain Baumslag–Solitar hypothesis that π(w)>2 implies presentation co...

We use the recent proof of Jacquet’s conjecture due to Harris and Kudla, and the Burger-Sarnak principle to give a proof about the relationship between the existence of trilinear forms on representations of GL2(ku) for a non-Archimedean local field ku and local epsilon factors which was earlier proved only in the odd residue characteristic by this author in [P1]. The same method gives a global ...

In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let π be a group and let M → N be a homomorphism between projective Z[π]-modules such that Zp⊗Z[π]M → Zp⊗Z[π]N is injective; for which other right Z[π]-modules V is the induced map V ⊗Z[π] M → V ⊗Z[π] N also injective? Our main theorem gives a new criterion which combin...