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.     

Nonoscillation,oscillation and growth of solutions of nonlinear difference equations of second order

Sufficient conditions are obtained which guarantee that all solutions (or all bounded solutions) of a class of second order nonlinear difference equations are nonoscillatory. Oscillation criteria and theorems concerning the growth of solutions 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.     

Magnetic-field-induced radiationless transitions

A quantum-mechanical theory of the magnetic field effect on radiationless transitions in an isolated molecule is presented. The mechanism of this phenomenon is a second-order process relying on the simultaneous radiationless relaxation of an excited electronic state and the interaction of the molecule with a constant uniform magnetic field.     

Crystal and molecular structure of glycinium diphenylphosphate

The crystal and molecular structure of glycinium diphenylphosphate, C₁₄H₁₆NO₆P, has been determined by X-ray methods. The crystals are orthorhombic:Pbca (No. 61),a=11.412(3),b=24.624(7),c=10.775(3) Å,Z=8. The structure was solved by direct methods and refined to anR value of 0.043 for 1289 nonzero independent amplitudes. The molecule exists in the structure as⁺NH₃CH₂CO₂H,(C₆H₅O)₂PO ₂ ^– and is planar except for the N atom, which deviates by 0.49 Å from the plane defined by C(1), C(2), O(5), and O(6) atoms, respectively. The conformation of the diphenylphosphate anion isgauche with respect to both P-O ester bonds. There are four crystallographically independent hydrogen bonds, three of the N-HO type and one of the O-HO type.