Vacuum stability in Nambu-Jona-Lasinio models

In Nambu-Jona-Lasinio models for a dynamical breakdown of chiral symmetry, unrenormalized divergences hinder a direct comparison of vacuum energies of different solutions. The choice of a stable vacuum in the presence of several solutions to the equations for fermion masses can nevertheless be performed since, for unstable states, tachyons appear in the spectrum of composite scalar bosons.     

Theory of Valuations on Manifolds: A Survey

This is a non-technical survey of a recent theory of valuations on manifolds constructed in [A10], [A11], [AF] and [A12], and actually a guide to this series of articles. We also review some recent related results obtained by a number of people. Received: February 2006, Revision: June 2006, Accepted: June 2006     

Towards a new edition of the “Guide to the expression of uncertainty in measurement”

The “Guide to the expression of uncertainty in measurement” (GUM) is an extremely important document. It unifies methods for calculating measurement uncertainty and enables the consistent interpretation and comparison of measurement results, regardless of who obtained these measurements and where they were obtained. Since the document was published in 1995, it has been realised that its recommendations do not properly address an important class of measurements, namely, non-linear indirect measurements. This drawback prompted the initiation of the revision of the GUM in the Working Group 1 of the Joint Committee for Guides in Metrology, which commenced in October 2006. The upcoming revision of the GUM provides the metrological community with an opportunity to improve this important document, in particular, to reflect developments in metrology that have occurred since the first GUM publication in 1995. Thus, a discussion of the directions for this revision is important and timely. By identifying several shortcomings of the GUM and proposing directions for its improvement, we hope this article will contribute to this discussion. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

Features of the foaming of acrylamide-acrylic acid copolymers

The processes that occur during the processing and foaming of thermosetting composites based on a random copolymer of acrylamide and acrylic acid—softening, foaming, and curing of the copolymer—are studied with the use of methods of chemical kinetics, Fourier transform infrared spectroscopy, and thermomechanical analysis. The above processes are coordinated with respect to time and temperature; prognostic methods for calculating the dynamics of these processes and the properties of foam materials as functions of the composition of the original foam-forming composite and the foaming conditions are proposed.     

Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole

We provide a rigorous definition of quasi-normal modes for a rotating black hole. They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature. If the black hole rotates slowly enough, we show that these poles form a discrete subset of \mathbb C{\mathbb C} . As an application we prove that the local energy of linear waves in that background decays exponentially once orthogonality to the zero resonance is imposed.     

Nonnegative Fourier–Jacobi Coefficients and Some Classes of Functions

Fourier–Jacobi series with nonnegative Fourier–Jacobi coefficients are considered. Under special restrictions on the Jacobi weight function, we establish in terms of Fourier–Jacobi coefficients a necessary and sufficient condition in order that the sum of the Fourier–Jacobi series should possess certain structural properties.     

Confinement and properties of vacuum states in two-dimensional electrodynamics of massless quarks

Connections between the properties of vacuum states and the confinement phenomenon are investigated for QED₂.     

On the least values of -norms for the Kontorovich–Lebedev transform and its convolution

We establish analogs of the Hausdorff–Young and Riesz–Kolmogorov inequalities and the norm estimates for the Kontorovich–Lebedev transformation and the corresponding convolution. These classical inequalities are related to the norms of the Fourier convolution and the Hilbert transform in L_p spaces, 1p∞. Boundedness properties of the Kontorovich–Lebedev transform and its convolution operator are investigated. In certain cases the least values of the norm constants are evaluated. Finally, it is conjectured that the norm of the Kontorovich–Lebedev operator is equal to . It confirms, for instance, by the known Plancherel-type theorem for this transform when p=2.     

On constants in some inequalities for intermediate derivatives on a finite interval

Let L_q (1q<∞) be the space of functions f measurable on I=[−1,1] and integrable to the power q, with normL_∞ is the space of functions measurable on I with normWe denote by AC the set of all functions absolutely continuous on I. For nN, q[1,∞] we setW_n,q={f:f⁽ⁿ⁻¹⁾AC, f⁽ⁿ⁾L_q}.In this paper, we consider the problem of accuracy of constants A, B in the inequalities (1)|| f^(m)||_qA|| f||_p+B|| f^(m+k+1)||_r, mN, kW; p,q,r[1,∞], fW_m+k+1,r.