Gravitons in Minkowski space-time interactions and results of astrophysical interest

A review is presented of the quantization procedures applicable to linear gravitational fields in Minkowski space-time and of various interactions processes involving gravitons. The discussion is mainly concerned with those processes that in the Feynman diagrammatic approach involve gravitons on external lines and are of particular astrophysical interest because of their contribution to background gravitational radiation in the universe. More specifically they are graviton production from particle-antiparticle annihilation, gravitational bremsstrahlung, scattering of gravitons and photoproduction. Among the topics discussed are also, the graviton-particle vertex and some of its applications, and the problem of coherent emission of gravitational radiation in the laboratory.     

Location Problems with Different Norms for Different Points

Given a finite set in a linear space X, we consider two problems. The first problem consists of finding the points minimizing the maximum distance to the points in A; the second problem looks for the points that minimize the average distance to the points in A. In both cases, we assume that the distances at different points are defined as

A combined measurement of thermal and mechanical relaxation

In order to describe relaxation the thermodynamic coefficient can be generalized into a complex frequency-dependent cross response function. We explore theoretically the possibility of measuring for a supercooled liquid near the glass transition. This is done by placing a thermistor in the middle of the liquid which itself is contained in a spherical piezoelectric shell. The piezoelectric voltage response to a thermal power generated in the thermistor is found to be proportional to but factors pertaining to heat diffusion and adiabatic compressibility κ_S(ω) do also intervene. We estimate a measurable piezoelectric voltage of 1 mV to be generated at 1 Hz for a heating power of 0.3 mW. Together with κ_S(ω) and the longitudinal specific heat c_l(ω) which may also be found in the same setup a complete triple of thermoviscoelastic response functions may be determined when supplemented with shear modulus data.     

On Some Types of Rigid Sets in Banach Spaces

One of the properties characterizing Euclidean spaces says - roughly speaking- that their unit sphere has nice invariant properties. More precisely, a finite dimensional normed space has an Euclidean norm if and only if the group of isometries acts transitively on its unit sphere (the norm is “transitive”); such property of the sphere is also called “rigidity”. More recently, another notion of “rigidity” for compact sets, connected with “isometric sequences”, received some attention. Infinite rigid sets are diametral; moreover, under suitable assumptions on the space, they are also contained in the boundary of a sphere. These notions are connected with many problems, in different areas. Here we discuss and compare these two notions of rigid set, trying to indicate new relations among them and with some other properties of sets. Several examples complete the paper.     

GSI anomaly and spin–rotation coupling

We propose a model in which a recently reported modulation in the decay of the hydrogenlike ions ¹⁴⁰Pr⁵⁸⁺, ¹⁴²Pm⁶⁰⁺ and ¹²²I⁵²⁺ arises from the coupling of rotation to the spin of electron and nucleus. The model shows that the spin–spin coupling of electron and nucleus does not contribute to the modulation and predicts that the anomaly cannot be observed if the motion of the ions is rectilinear, or if the ions are stopped in a target. It also supports the notion that the modulation frequency is proportional to the inverse of the atomic mass and that no modulation is expected for the β⁺${\beta }^{+}$-decay. The model predicts that for He-like ions the modulation is still present.     

Spin currents in non-inertial frames

The covariant Dirac equation and its solutions show that rotation and acceleration can be used to generate and control spin currents.     

Eigenvalue Asymptotics of the Stokes Operator for Fractal Domains

The leading asymptotic term for the function that counts theeigenvalues of the Stokes operator is determined for fairlygeneral underlying bounded domains. Moreover, the remainderis estimated in terms of the fractality of the boundary of thedomain. The results obtained resemble corresponding ones forthe Dirichlet Laplacian. 1991 Mathematics Subject Classification:35P20.     

Study of the spectral properties of inhomogeneous granular materials

The variation of the spectral properties of semi-transparent (polystyrene: PS), transparent (potassium bromide: KBr) and opacified particles (silver coated silica spheres: Ag-SiO₂) is presented from 0.25 to 20 μm. The spectral properties of binary mixtures PS/KBr and PS/Ag-SiO₂ are also studied. The sensitivity of the spectral properties to the particle diameters causes the near-normal hemispherical spectral reflectance R to decrease when the particle size increases from 10 to 1800 μm. The addition of KBr transparent particles to PS powders results in an increase in the reflectance values of the mixtures in the near and mid-infrared wavelength range. Furthermore, the effect of the addition of opacified reflecting particles depends on the wavelength region and on the PS content ([PS]). For < < 1.64 μm, R decreases when [PS] decreases from 1 to 0.56 and then R increases for [PS] values decreasing from 0.56 to 0. For < > 1.64 μm, R decreases when PS content increases from 0 to 1.     

On weak*-extensible Banach spaces

We study the stability properties of the class of weak*-extensible spaces introduced by Wang, Zhao, and Qiang showing, among other things, that weak*-extensibility is equivalent to having a weak*-sequentially continuous dual ball (in short, w*SC) for duals of separable spaces or twisted sums of w*SC spaces. This shows that weak*-extensibility is not a 3$3$-space property, solving a question posed by Wang, Zhao, and Qiang. We also introduce a restricted form of weak*-extensibility, called separable weak*-extensibility, and show that separably weak*-extensible Banach spaces have the Gelfand–Phillips property, although they are not necessarily w*SC spaces.