X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

Further study of Saint-Venant's principle in linear viscoelasticity

Summary For a viscoelastic beam loaded at one end and otherwise traction-free, it is shown that a certain integral measure of the strain in that portion of the beam at a distance greater than or equal tos decays exponentially with increasings. This is a different integral decay estimate from that obtained previously by Edelstein [2] and leads immediately to a pointwise decay estimate for strains.

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Zusammenfassung Für einen viskoelastischen Balken, der am einen Ende belastet ist, wird gezeigt, dass ein gewisses Integralmass der Verzerrung in Entfernungen, die grösser oder gleichs sind, mit zunehmendems exponentiell abnimmt. Es handelt sich dabei um eine andere Integral-Abschätzung, als sie früher von Edelstein [2] aufgestellt wurde. Sie führt direkt zu einer punktweisen Abschätzung für die Verzerrungen.

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Submitted by R.E.N. as a partial fulfillment of the requirements for the Ph.D. degree at Illinois Institute of Technology, Chicago, Illinois 60616.     

Strings with dimension-dependent intercept

By changing the boundary conditions of the relativistics string in extra dimensions, the intercept α(0) is lowered to $\text{1 ?}\text{1}\text{16}\text{(26 ?D}{}_0\text{)}$ in the modified orbital model, where D₀ is the dimensionality of the Poincaré-invariant subspace of space-time. In the modified model of the spinning string, the boson intercept becomes $\text{1}\text{2}\text{?}\text{1}\text{8}\text{(10 ? D}{}_{\mathrm{o}}\text{)}$, while the fermion intercept stays at zero. The projective invariance of the ground state is broken, giving the “photon” mass by a Higgs-like mechanism. Unfortunately, the strings have a negative “G parity”, so the usual, unshifted strings appear as intermediate states in the scattering amplitudes. Also, some of the amplitudes are not dual.     

Compactness in fuzzy topological spaces

Since earlier approaches to compactness in fuzzy spaces have serious limitations, we propose a new definition of fuzzy space compactness. In doing so, we observe that it is possible to have degrees of compactness, which we call α-compactness (α a member of a designated lattice). We obtain a Tychonoff Theorem for an arbitrary product of α-compact fuzzy spaces and a 1-point compactification. We prove that the fuzzy unit interval is α-compact.     

Characterization of pure high-grade DCIS on magnetic resonance imaging using the evolving breast MR lexicon terminology: can it be differentiated from pure invasive disease?

Magnetic resonance imaging (MRI) is now a recognized method of imaging the breast. Unfortunately, there is lack of standardization in the MRI terminology used to characterize the appearance of breast lesions. Moreover, cases of mixed histologies are often imaged. We retrospectively identified cases of pure high-grade ductal carcinoma in situ (DCIS) using the recently introduced breast MRI lexicon and characterized the lesions in order to try and identify features that might distinguish high-grade DCIS from invasive disease. Five-year review of our institution's database revealed 637 patients underwent gadolinium-enhanced breast MRI examination. Twenty patients had histologically proven pure high-grade DCIS. After excluding patients with previous chemotherapy or inadequate MRI examination, 13 patients were analyzed and compared to the 13 most recent cases of pure invasive breast carcinoma. The morphological and dynamic features were then compared. High-grade DCIS cases were significantly more likely to show focal branching pattern (P=.03) and to have an irregular contour (P=.03), compared with invasive disease. Although of marginal statistical significance, DCIS lesions are more likely to have a lower morphological score than invasive carcinoma (P=.06), whilst the latter is more likely to show ring enhancement (P=.07). Use of breast MRI for staging at our institution shows that pure DCIS and pure invasive cancers are both rare entities. Despite the relatively limited numbers, we identified features that would help to differentiate high-grade DCIS from invasive carcinoma on MRI.     

Structural anisotropy and internal magnetic fields in trabecular bone: coupling solution and solid dipolar interactions

We investigate the use of intermolecular multiple-quantum coherence to probe structural anisotropy in trabecular bone. Despite the low volume fraction of bone, the bone-water interface produces internal magnetic field gradients which modulate the dipolar field, depending on sample orientation, choice of dipolar correlation length, correlation gradient direction, and evolution time. For this system, the probing of internal magnetic field gradients in the liquid phase permits indirect measurements of the solid phase dipolar field. Our results suggest that measurements of volume-averaged signal intensity as a function of gradient strength and three orthogonal directions could be used to non-invasively measure the orientation of structures inside a sample or their degree of anisotropy. The system is modeled as having two phases, solid and liquid (bone and water), which differ in their magnetization density and magnetic susceptibility. A simple calculation using a priori knowledge of the material geometry and distribution of internal magnetic fields verifies the experimental measurements as a function of gradient strength, direction, and sample orientation.