Luminescence-spectrum and strength properties of rhodamine 6G-doped silica gel films

Silica gel films dyed with rhodamine 6G in the sol stage are prepared and investigated. It is shown that the host matrix of the film loosens structurally as a result of intensification of the formation of dye molecular associates, lowering of the luminescence photon yield, and enhancement of the luminescence spectral sensitivity of such films to vapors of highly volatile organic solvents. Fiz. Tverd. Tela (St. Petersburg) 40, 466–471 (March 1998)     

Large sets in intuitionistic set theory

We consider properties of sets in an intuitionistic setting corresponding to large cardinals in classical set theory. Adding such ‘large set axioms’ to intuitionistic ZF set theory does not violate well-know metamathematical properties of intuitionistic systems. Moreover, we consider statements in constructive analysis equivalent to the consistency of such ‘large set axioms’.     

The synthesis of pyrazolo[1,2-a]pyrazoles. Regio- and stereo-selective 1,3-dipolar cycloadditions of (1Z)-rel-(4R,5R)-1-arylmethylene-4-benzoylamino-5-phenyl-3-pyrazolidinon-1 -azomethinimines

Reaction of rel-(4R,5R)-4-benzoylamino-5-phenyl-3-pyrazolidinone (4) with aromatic aldehydes 5a-f gave the corresponding (1Z)-rel-(4R,5R)-1-arylmethylene-4-benzoylamino-5-phenyl-3-pyrazolidinon-1-azomethinimines 6a-f . 1,3-Dipolar cycloadditions of azomethinimines 6a-f to various dipolarophiles, which were found to proceed regio- and stereo-selectively, afforded the corresponding pyrazolo[1,2-a]-pyrazoles 8a-f, 10 , and 13–16 . Reaction of azomethinimine 6a with hydrogen cyanide gave rel-(5R,6R)-6-benzoylamino-5,6-dihydro-3,5-diphenyl-1-oxo-1H,7H-pyrazolo[1,2-a][1,2,3]triazole (18) as a representative of a new ring system.     

Synthesis and NMR characterization of 4-[(2-tetrahydro-pyranyloxy)methyl]piperidine and intermediates

4-(Hydroxymethyl)piperidine was selectively protected with tetrahydropyranyl group in several steps to give the title compound. Use of ¹H and ¹⁹F nmr spectra in structure determination is discussed.     

Bias of LS estimators in nonlinear regression models with constraints. Part I: General Case

We derive expressions for the asymptotic approximation of the bias of the least squares estimators in nonlinear regression models with parameters which are subject to nonlinear equality constraints.The approach suggested modifies the normal equations of the estimator, and approximates them up to o _p(N ^–1), where N is the number of observations. The bias equations so obtained are solved under different assumptions on constraints and on the model. For functions of the parameters the invariance of the approximate bias with respect to reparametrisations is demonstrated. Singular models are considered as well, in which case the constraints may serve either to identify the parameters, or eventually to restrict the parameter space.