ESR identification of a new N2− defect in X-ray irradiated NaN3

A relatively weak ESR spectrum is observed in single crystals of NaN₃ after X-ray irradiation at 77 K. This spectrum, which has an anisotropic g value and exhibits a resolved 5-line hyperfine structure with components in the ratio 1:2:3:2:1, corresponds to a single unpaired electron interacting symmetrically with two spin-one nuclei, in three inequivalent sites. The spin-Hamiltonian parameters are: g_x = 2.0054 ± 0.0005, g_y = 2.0045 ± 0.0005, g_z = 1.9688 ± 0.0005, |A_x| = 4.0 ± 0.2 G, |A_y| = 20.0 ± 0.2 G, and |A_z| = 4.9 ± 0.2 G, c-axis, and y is perpendicular to the c-axis. This spectrum, which is clearly different from that of substitutional N₂^?reported by Gelerinter and Silsbee, is attributed to interstitial N₂^?.     

Chemical reactivity and surface-enhanced raman scattering

A mechanism is proposed for surface-enhanced Raman scattering for pyridine which explains the enhancement, the anodizalion “activation”, the significance of silver, the photographitization of coordinated pyridine and formate, the participation of surface roughness, and the irreversibly held yet liquid-like nature of surface pyridine.     

AB initio calculations of the electronic properties of N4− in KN3

The energies of the ground state and low-lying excited states of the N₄^? defect in KN₃ have been calculated using ab initio techniques. A rectangular equilibrium geometry with dimensions X = 2.76 and Z = 2.47 a.u. and ground state symmetry of Γ₄⁺ was determined by calculating N₄^? as a free radical. For this ground state the unpaired electron is in a π orbital which is consistent with the experimental hyperfine tensor only if one edge of the N₄^? radical is parallel to the c axis in KN₃. These results were used to calculate the X²Γ₄⁺ state of N₄^? in the crystal field of KN₃, yielding an energy of ?217.899 Hartrees. The isotropic hyperfine constant was calculated to be a = 2.1 G and the components of the anisotropic hyperfine tensor as B_xx = ?3.4 G, B_yy = 7.0 G and B_zz = ?3.6 G, in good agreement with experimental and INDO results. Several excited states were calculated for the N₄^? defect in KN₃. When an estimate was made of the correlation energy, the transition energy of the X²Γ₄⁺→A²Γ₃^? transition agreed well with the peak energy of the 780 nm absorption band which has been attributed to N₄^?.     

Uniqueness of the inversive plane of order 7

A search has shown that any inversive plane of order 7 must be isomorphic with the Miquelian plane. The method used was explicitly set out in a companion paper, which was concerned with a plane of order 5.     

Linear relativistic hamiltonians

A 2(2J + 1)-component relativistic Hamiltonian H that describes free particles of mass m and spin J is said to be linear if it has the form $\text{H = h}\text{x}\text{?}\text{·}\text{p}\text{+ gm}$, where $\text{x}\text{\_.}\text{= i[H,}\text{x}\text{]}{}_{\mathrm{?}}$, h is a numerical factor, and g commutes with x and p. All such Hamiltonians are found, provided that the metric is either the unit matrix or ?₃ and provided that the theory is invariant under the discrete symmetries. If the operator Γ in the generator $\text{K}\text{=}\text{1}\text{2}\text{[}\text{x}\text{, H]}{}_{\mathrm{+}}\text{+ Γ}$ of Lorentz boosts is required to be local, there are only two possibilities; either Γ = 0, which generalizes the Dirac spin-$\text{1}\text{2}$ theory, or $\text{Γ = ??}{}_3\text{(}\text{1}\text{2m}\text{)}\text{S × p}$, which generalizes the Sakata-Taketani spin-0 and spin-1 theories. The relationship to linear manifestly covariant equations and its significance is discussed.     

The paley-wiener theorem for the radon transform

We prove that the support of a complex-valued function f in ?^k is contained in a convex set K if and only if the support of its Radon transform k(s, ω) is, for each ω, contained in s ≦ S_K (ω); here S_K is the support function of the set K. This theorem is used to determine the propagation speeds of hyperbolic differential equations with constant coefficients, to prove the nonexistence of point spectrum for a certain class of partial differential operators, and to give a simple reduction of Lions' convolution theorem to the one-dimensional convolution theorem of Titchmarsh.     

Number fluctuation analysis of random locomotion. Statistics of a Smoluchowski process

We analyze a scheme, originally suggested by Smoluchowski, by which a diffusion coefficientD can be estimated by measuring the number of particles occupying a fixed region of a surface at various times. An expression is derived relating the variance of the estimated valueD to several experimental parameters. This expression is evaluated numerically to determine how statistical uncertainty depends on adjustable variables. Particular attention is given to experiments involving locomotion of migrating leukocytes.     

Viscoelastic shear properties of in vivo breast lesions measured by MR elastography

Elastography is a technique to assess the viscoelastic properties of tissue by measuring an acoustic wave propagating though the object. Here, the technique is applied in the course of standard MR mammography to 15 patients with different pathologies (six breast cancer cases, six fibroadenoma cases and three mastopathy cases). Low-frequency mechanical waves are coupled longitudinally into the tissue in order to obtain sufficient wave amplitude throughout the entire breast. This leads to the presence of a substantial fraction of compressional waves, which contribute to the total displacement field. It is shown theoretically that the correct evaluation of these contributions from the compressional wave is rather difficult due to the almost incompressible nature of tissue. To overcome this problem, it is proposed to apply the curl-operator to the measured displacement field in order to completely remove contributions from the compressional wave. Results from simulations and a breast phantom demonstrate the feasibility of the technique. The in vivo results show a good separation between breast cancer and benign fibroadenoma utilizing the shear modulus. Breast cancer appears on average 2.2 (P<.001) times stiffer. All breast cancer cases showed a good delineation to the surrounding breast tissue with an average elevation of a factor of 3.3 (P< 1.4 x 10(-6)). The results as obtained for the shear viscosity do not indicate to be useful for separating benign from malignant lesions.