Tangent segments and orthogonality types in normed planes

The following characterizations of the Euclidean plane are obtained: the two tangent segments of the unit circle of a normed plane from each point of a disc centered at the origin with sufficiently large diameter have equal lengths; the lengths of the tangent segments from each point of a fixed circle centered at the origin are determined only by the radius of this circle. Three further characterizations of the Euclidean plane are obtained by considering properties of certain points related to an exterior point of the unit disc and the two tangent segments corresponding to it. To obtain one of these characterizations, the notion of arc-length orthogonality is introduced, and the Euclidean plane is also characterized via a relation between arc-length orthogonality and Birkhoff orthogonality.     

Active-feedback control of the magnetic boundary for magnetohydrodynamic stabilization of a fusion plasma

Stable operation with control on magnetohydrodynamic modes has been obtained in the modified reversed field experiment employing a set of 192 feedback controlled saddle coils. Improvements of plasma temperature, confinement (twofold), and pulse length (threefold) and, as a consequence of the magnetic fluctuation reduction, strong mitigation of plasma-wall interaction and mode locking are reported.     

Polynômes Harmoniques sur L'Espace du Bruit Blanc

Let denote the space of harmonic polynomial of . We study some properties of on the white noise space. We show that harmonic polynomials are characterized by an invariance property with respect to the S-transform, and that the closure (S)harm of harm in Hida's test-functionnals topology is exactly the kernel of the Gross Laplacian G. Lastly we show that Ker G is strictly contained in the space of functionnals of (S) which remain fixed under S-transform.     

Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bellman–Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (X,M models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called X,R models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example.     

Organophosphorus and carbamate pesticide analysis using an inhibition tyrosinase organic phase enzyme sensor; comparison by butyrylcholinesterase+choline oxidase opee and application to natural waters

Recent research performed in our laboratory (using a butyrylcholinesterase + choline oxidase enzyme electrode) suggested the validity of the biosensor approach using enzyme inhibition OPEEs (i.e. enzyme electrodes working in organic phase) in the case of organophosphorus and carbamate pesticides, which are poorly soluble in aqueous solutions. Since these pesticides are generally much more soluble in chloroform than in water, the present research aimed at analysing this class of pesticides using a tyrosinase inhibition OPEE operating in water-saturated chloroform medium. The tyrosinase biosensor was assembled using an oxygen amperometric transducer coupled to the tyrosinase enzyme, immobilized in kappa-carrageenan gel. Lastly a detailed comparison between the inhibition monoenzymatic tyrosinase and inhibition bienzymatic (butyrylcholinesterase + choline oxidase) OPEEs was performed and discussed in this work.     

An efficient route to all stereoisomeric enantiopure 6-amino-3-alkyl-3- azabicyclo[3.2.1]octane-6-carboxylic acids

A single-step synthesis on a gram scale of four pure stereoisomers of the 6-amino-3-azabicyclo[3.2.1]octane-6-carboxylic acid was carried out using (R)-1-phenylethylamine to confer chirality. The phenylethyl group, and the p-methoxy group linked to the N-atom, are easily removed by hydrogenolysis to afford the corresponding NH-3 derivatives. A series of N-3-alkyl compounds were prepared by way of a "one-pot" deprotection-alkylation procedure starting from the above key compounds. Their biological activity has been evaluated on the GABA receptor.     

On Grünbaum's Conjecture about Inner Illumination of Convex Bodies

In 1964 Grünbaum conjectured that any primitive set illuminating from within a convex body in E ^d , d ≥ 3 , has at most 2 ^d points. This was confirmed by V. Soltan in 1995 for the case d = 3 . Here we give a negative answer to Grünbaum's conjecture for all d ≥ 4 , by constructing a convex body K ⊂ E ^d with primitive illuminating sets of an arbitrarily large cardinality. Received December 1, 1997, and in revised form January 21, 1999.     

The Construction of Frobenius Manifolds¶from KP tau-Functions

Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux–Egoroff equations. This system of partial differential equations appears as a specific subset of the n-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions of this Darboux–Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy tau-function can be expressed in the KP tau-function. Received: 1 September 1998 / Accepted: 7 March 1999     

A Universal Cassette-Based System for the Dissolution of Solid Targets

Cyclotron-based radionuclides production by using solid targets has become important in the last years due to the growing demand of radiometals, e.g., ⁶⁸Ga, ⁸⁹Zr, ^43/47Sc, and ^52/54Mn. This shifted the focus on solid target management, where the first fundamental step of the radiochemical processing is the target dissolution. Currently, this step is generally performed with commercial or home-made modules separated from the following purification/radiolabelling modules. The aim of this work is the realization of a flexible solid target dissolution system to be easily installed on commercial cassette-based synthesis modules. This would offer a complete target processing and radiopharmaceutical synthesis performable in a single module continuously. The presented solid target dissolution system concept relies on an open-bottomed vial positioned upon a target coin. In particular, the idea is to use the movement mechanism of a syringe pump to position the vial up and down on the target, and to exploit the heater/cooler reactor of the module as a target holder. All the steps can be remotely controlled and are incorporated in the cassette manifold together with the purification and radiolabelling steps. The performance of the device was tested by processing three different irradiated targets under different dissolution conditions.