Diagonalization of three-dimensional pseudo-Riemannian metrics

We give a short proof of the fact that any Riemannian or Lorentzian real analytic metric in dimension 3 can be locally adapted to the diagonal form. We use the classical Cauchy–Kowalevski Theorem to this purpose.     

Decomposability for division algebras of exponent two and associated forms

This article investigates the structure of quadratic forms and of division algebras of exponent two over fields of characteristic different from two with the property that the third power of the fundamental ideal in the associated Witt ring is torsion free.      

Periodic solutions for some nonautonomous second order Hamiltonian systems

The existence and multiplicity of periodic solutions are obtained for nonautonomous second order Hamiltonian systems by the minimax methods in critical point theory.     

关于Hutton定理的一个注

It is proved in this paper that there is a bijectionψ from J ∪ J' to δ∪δ' which satisfies:(1)ч|J:(J,C)→4(δ,≤)is a frame isomorphism;(2)ч|J':(J',C)→(δ',≤)is a coframe isomorphism,where J is the ordinary topology on[0,1],δ is the ordinary L-topology on L-unit interval I(L),and L is a frame with an order-reversing involution.This result improves Theorem 3 in Hutton's paper.     

Integrals, partitions and MacMahon's Theorem

In two previous papers, the study of partitions with short sequences has been developed both for its intrinsic interest and for a variety of applications. The object of this paper is to extend that study in various ways. First, the relationship of partitions with no consecutive integers to a theorem of MacMahon and mock theta functions is explored independently. Secondly, we derive in a succinct manner a relevant definite integral related to the asymptotic enumeration of partitions with short sequences. Finally, we provide the generating function for partitions with no sequences of length K and part exceeding N.     

On a period map for SU(2) conformal vacua

We study some properties of a natural period map associated to SU(2) theta functions or, in other words, to SU(2) conformal vacua. In particular we will consider for such a map an analogue of the classical Torelli’s problem. The main result of the paper is a sufficient conditions for our period map to have the infinitesimal Torelli’s property.      

On a question of Sós about 3‐uniform friendship hypergraphs

The well‐known Friendship Theorem states that if G is a graph in which every pair of vertices has exactly one common neighbor, then G has a single vertex joined to all others (a “universal friend”). V. Sós defined an analogous friendship property for 3‐uniform hypergraphs, and gave a construction satisfying the friendship property that has a universal friend. We present new 3‐uniform hypergraphs on 8, 16, and 32 vertices that satisfy the friendship property without containing a universal friend. We also prove that if n ≤ 10 and n ≠ 8, then there are no friendship hypergraphs on n vertices without a universal friend. These results were obtained by computer search using integer programming. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 253–261, 2008     

Relatively spectral morphisms and applications to K-theory

Spectral morphisms between Banach algebras are useful for comparing their K-theory and their “noncommutative dimensions” as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral information is only known over a dense subalgebra. We investigate such relatively spectral morphisms. We prove a relative version of the Density Theorem regarding isomorphism in K-theory. We also solve Swan's problem for the connected stable rank, in fact for an entire hierarchy of higher connected stable ranks that we introduce.     

A generalized Fourier inversion Theorem

In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier inversion Theorem for strictly-unconditionally integrable Fourier transforms. Our results generalize and improve those previously obtained by Ruy Exel in the case of Abelian groups. Supported by CAPES, Brazil.     

On Gleason’s Theorem without Gleason

The original proof of Gleason’s Theorem is very complicated and therefore, any result that can be derived also without the use of Gleason’s Theorem is welcome both in mathematics and mathematical physics. In this paper we reprove some known results that had originally been proved by the use of Gleason’s Theorem, e.g. that on the quantum logic ℒ(H) of all closed subspaces of a Hilbert space H, dim H≥3, there is no finitely additive state whose range is countably infinite. In particular, if dim H=n, then on ℒ(H) there is a unique discrete state, namely m(A)=dim A/dim H, A∈ℒ(H). Dedicated to Pekka J. Lahti on the occasion of his 60th birthday. The paper has been supported by the Center of Excellence SAS–Physics of Information–I/2/2005, the grant VEGA No. 2/6088/26 SAV, by Science and Technology Assistance Agency under the contract APVV-0071-06, Bratislava, Slovakia.