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.     

On fuzzy multi-valued functions part 2: Some topological properties

In this paper new topological concepts connected with fuzzy multi-valued functions theory-as presented in the first part of this work-are introduced and their properties are investigated. As will be shown in future papers these concepts and properties are indispensable in connection with the analysis of fuzzy economic systems.     

Pointwise consistency of the hermite series density estimate

The Hermite series estimate of a density f?L_p, p > 1, convergessin the mean square to f (x) for almost all x? |R, ifN (n) → ∞ and N (n) / n² → ) as n → ∞, where N is the number of the Hermite functions in the estimate while n is the number of observations. Moreover, the mean square and weak consistency are equivalent. For m times differentiable densities, the mean squares convergence rate is O(n^?(2m?1)/2m). Results for complete convergence are also given.     

Control problems in fuzzy systems

This paper deals with some problems of the control of fuzzy systems described by means of a relational equation of the type: X_{κ + 1} = U_κ ° X_κ ° R. The basic aspects such as mutual identification and control, stabilization control, control with constraints, generation of control rules of a fuzzy logic controller, important from the theoretical and applicational point of view are discussed and illustrated by means of numerical examples.