MR microscopy of water diffusion tensor in biological systems

Diffusion tensor imaging (DTI) of the control and mechanically injured spinal cord of a ratin vitro andin vivo are reported.In vitro experiments were done on a home-built 6.4 T magnetic resonance microscope. Results for formaline-fixed samples show significant differences in diffusion tensor components between gray matter and white matter of the control spinal cord. Moreover, it is shown that already 6–10 min after the injury DTI can detect changes in water diffusion in areas extending far beyond the region of primary tissue damage.In vivo experiments were performed using a 9.4 T Magnex magnet and Bruker Medspec imaging system. Good-quality DTI images, free from motion artifacts were obtained. Results from control samples confirm differences in water diffusion between white matter and gray matter, observedin vitro. In vivo experiments show that characteristic changes in water diffusion observedin vitro 6–10 min after injury are preserved 60–360 min after injury, without significant alteration during this time.     

Letter: Rotation of the Universe and the Angular Momenta of Celestial Bodies

We discuss the equation of motion of the rotating homogenous and isotropic model of the Universe. We show that the model predicts the presence of a minimum in the relation between the mass of an astronomical object and its angular momentum. We show that this relation appears to be universal, and we predict the masses of structures with minimal angular momenta in agreement with observations. In such a manner we suggest the possibility at acquirement of angular momenta of celestial bodies during their formation from the global rotation of the Universe.     

Non-Hamiltonian systems separable by Hamilton–Jacobi method

We show that with every separable classical Stäckel system of Benenti type on a Riemannian space one can associate, by a proper deformation of the metric tensor, a multi-parameter family of non-Hamiltonian systems on the same space, sharing the same trajectories and related to the seed system by appropriate reciprocal transformations. These systems are known as bi-cofactor systems and are integrable in quadratures as the seed Hamiltonian system is. We show that with each class of bi-cofactor systems a pair of separation curves can be related. We also investigate the conditions under which a given flat bi-cofactor system can be deformed to a family of geodesically equivalent flat bi-cofactor systems.     

Handling effects of reinforced preference and counter-veto in credibility of outranking

The aim of this paper is to generalize the way of computing the credibility of outranking in a multiple criteria aggregation procedure, in view of taking into account two new effects called reinforced preference and counter-veto. These effects concern only those criteria for which, as soon as action a is “judged very strongly preferred” to action b, one wishes that the credibility of outranking of a over b is greater than that for the case where (all things equal elsewhere) the preference is not “judged very strong”. To achieve this goal, we propose two complementary ways. The first one involves a reinforced preference threshold which affects the concordance degree, and the second one involves a counter-veto threshold which affects the insertion of discordance degree in the calculation of the credibility of outranking. The introduction of these two new effects remains compatible with the handling of ordinal preference scales. The resulting new index of the credibility of outranking can be used, in particular, in ELECTRE methods.     

Note on Symmetric Words in Metabelian Groups

We completely describe n-symmetric words in a free metabelian group.     

Separable Banach spaces which admitl n ∞ approximations

In this paper we study a class of separable Banach spaces which can be approximated by certain special finite-dimensional subspaces. This class is characterized in Theorem 1.1, from which it follows that the space of continuous scalar-valued functions on a compact metric space always belongs to this class, and that every member of this class has a monotone basis. Supported in part by N.S.F. Grant 11-5020. Supported in part by N.S.F. Grant GP-3579.     

Crystal and molecular structure of glycinehydroxamic acid

Glycinehydroxamic acid, C₂H₆N₂O₂ (NH₂CH₂C(O)NHOH), was synthesized and its crystal and molecular structure determined by single-crystal X-ray diffraction methods. The crystals are monoclinic:P2 ₁/c C _2h ⁵ , No. 14),a=5.682(2),b=7.133(2),c=9.540(3) Å,=104.38(4)°,Z=4. The structure has been solved by direct phase determination methods, and refined to anR value of 0.042 for 633 nonzero independent amplitudes. The molecule of the title compound exists in the structure as a zwitterion, NH ₃ ⁺ -CH₂-C(O)-N-OH. The hydroxamate group is planar and the N (amino) atom, from the glycine part of the molecule, deviates by 1.43 Å from the best molecular plane defined by O(1), N(1), C(1), and O(2) atoms, respectively.The molecules are held together by a network of N⁺-HO, N⁺-H¯N, and O-HO hydrogen bonds.     

NMR studies of mixed-ligand iron(III) dithiocarbamates

¹H NMR studies of mixed-ligand iron (III) dithiocarbamates have been carried out using the following ligands: N,N-diethyldithiocarbamate, morpholinyl-N-, and piperidyl-N-carbodithioate. The ligand exchange equilibria gave all species of the general formula Fe(dtc)_n(dtc′)_3?n, where n = 0-3 with nearly random statistical distribution of Fe(Et₂dtc)_n(morphdtc)_3?n complexes. Magnetic moments of the mixed-ligand complexes have been determined. Both the magnetic moment and isotropic shift temperature dependences confirmed the cross-over properties of these mixed-ligand complexes.     

On fuzzy multi-valued functions part 3: Fixed-point theorem

In this paper a Fixed-Point Theorem and an application is presented.