Bromination of regioisomeric fluorine-containing β-aminovinyl ketones

Bromination of -aminovinyl ketones (AVK) with geminal arrangement of the fluoroalkyl and amino groups gives N-bromo derivatives. Regioisomeric AVK with the amino groups in the -position relative to the fluoroalkyl group undergo bromination under analogous conditions to give a mixture of the -bromo and ,N-dibromo derivatives. -Bromo derivatives of AVK disproportionate upon storage.Division of Fine Chemical Synthesis, Institute of Organic Chemistry, Urals Branch, Russian Academy of Sciences, 620219 Ekaterinburg. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 746–749, March, 1992.     

On an inhomogeneous deformation of a generalized Neo-Hookean material

We study the inhomogeneous deformation of a wedge of an incompressible generalized power-law Neo-Hookean material. We find solutions which have a boundary layer structure, in the sense that adjacent to the boundary the solution is inhomogeneous, while in the core region the solution is homogeneous. It is found that such solutions have an associated pressure field that is bounded. Inhomogeneous solutions are also possible when the pressure varies logarithmically with the radial coordinate. We also establish explicit exact solutions for specific values of the parameter. The results reduce to the Neo-Hookean solution when the power law exponent is set to unity.     

Equilibrium triangulations of the complex projective plane

Starting with the well-known 7-vertex triangulation of the ordinary torus, we construct a 10-vertex triangulation of P² which fits the equilibrium decomposition of P² in the simplest possible way. By suitable positioning of the vertices, the full automorphism group of order 42 is realized by a discrete group of isometries in the Fubini-Study metric. A slight subdivision leads to an elementary proof of the theorem of Kuiper-Massey which says that P² modulo conjugation is PL homeomorphic to the standard 4-sphere. The branch locus of this identification is a 7-vertex triangulation P ₂ ⁷ of the real projective plane. We also determine all tight simplicial embeddings of P ₂ ¹⁰ and P ₂ ⁷ .     

Die Strommer-Zykliden des Flaggenraumes

According to H. BRAUNER a flag space is a three-dimensional affine space with an absolute {,f,F}, wheref is a line in the plane of infinity andF a point onf. A cyclide is a surface of order 4 that intersects only atf. A STROMMER-cyclide is a cyclide generated by translation of a circle in an isotropic plane. In this paper we proof that all STROMMER-cyclides can be generated by translation of an isotropic circle along a divergent Newton-parabola or a conic in a full isotropic plane. We give normal-forms and CAD-pictures of these surfaces. Finaly some geometrical results about STROMMER-cyclides are developed.

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Herrn o.Prof. Dr. Gy. Strommer zum 70. Geburtstag gewidmet.     

Inverse problems of the theory of separately continuous mappings

The present paper investigates the problem of constructing a separately continuous function defined on the product of two topological spaces that possesses a specified set of points of discontinuity and the related special problem of constructing a pointwise convergent sequence of continuous functions that possesses a specified set of points of nonuniform convergence and set of points of discontinuity of a limit function. In the metrizable case the former problem is solved for separable F-sets whose projections onto every cofactor is of the first category. The second problem is solved for a pair of embedded F.Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1209–1220, September, 1992.     

On locally optimal nonparametric tests

Summary There is an abundancy of problems in which no parametric model realistically describes the situation and in which, accordingly, we have to resort to nonparametric methods. As the numerical problems connected with nonparametric tests are becoming less and less important, rank tests, permutation tests and the like are becoming more and more part of the standard armatory of applied statisticians. The lack of tabulated critical values, for instance, should no longer be a serious objection against the use of permutation tests in practice; cf. Edgington (1987).The rationale underlying permutation and rank tests has been outlined in quite a number of text books and papers; cf. Fraser (1957), Lehmann (1959), Hájek-Sidák (1967) or Witting (1970). Roughly speaking, permutation tests are constructibel if the data can be condensed by means of a sufficient and complete statistic allowing for the proper kind of conditioning. Rank tests arise if the underlying problem is invariant with respect to (w.r.t.) a large group of transformations which leads to a maximal invariant statistic consisting of (signed) ranks.Most practical nonparametric problems, however, are too complex to be tractable by just one of those approaches. Many of them, however, can be handled by a combination of both techniques. In this paper we outline the logic underlying that combined reduction method and apply it to construct locally most powerful tests. Moreover, we discuss what we label Hoeffding's transfer problem, i.e. the uniformity aspect of locally most powerful tests with respect to the starting point at the boundary. We are concentrating on the discussion of the nonparametric two-sample location and scale problem. Further important problems are mentioned in Section III.This is a written account of an invited lecture delivered by the third author on occasion of the 14th Symposium über Operations Research, Ulm, September 6–8, 1989.     

Point interactions with inner structure as a limit of separable potentials

Interactions of zero radius with an additional inner channel are considered. The corresponding generalized Krein resolvents in a functional sector are approximated in the weak sense with the aid of interactions of rank 1. The cut-off procedure of the interaction is explicitly described in prepresentation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 182, pp. 113–122, 1990.     

A criterion for flatness in minimal area metrics that define string diagrams

It has been proposed that the string diagrams of closed string field theory be defined by a minimal area problem that requires that all nontrivial homotopy curves have length greater than or equal to 2. Consistency requires that the minimal area metric be flat in a neighbourhood of the punctures. The theorem proven in this paper, yieds a criterion which if satisfied, will ensure this requirement. The theorem states roughly that the metric is flat in an open set,U if there is a unique closed curve of length 2 through every point inU and all of these closed curves are in the same free homotopy class.Supported in part by funds provided by the US Department of Energy (DOE) under contract # DE-AC02-76ER03069     

Iodine photodissociation laser system Perun II

A construction and exploitation of a medium size iodine photodissociation laser system Perun II is reported. This laser produced pulses of infrared light (=1.315m) up to 50 J in energy and 300 ps in duration. The diameter of the beam is 82 mm. The beam divergence is about 4×10^–4 rad. The laser beam can be focused in a focal spot of a power density exceeding 10¹⁴ W/cm². The resuls of measurements of basic plasma parameters on an Al foil target are also presented. A recent improvement of the system includes a conversion to the second harmonic by a DKDP crystal.Presented at bilateral international seminar of High Temperature Laser Plasma and High Gain Iodine Lasers held on 4 July 1991 in the Inst. of Physics, Czechosl. Acad. Sci., in Prague (organized by Division of Optics of the Inst. of Physics, Czechosl. Acad. Sci., and Physical Section (Plasma Division) of the Union of Czech Mathematicians and Physicists.