Revised PROMETHEE algorithm with reference values

Central European Journal of Operations Research - PROMETHEE method is a very popular quantitative method of decision-making with many benefits. However, the evaluation of alternatives in the...     

Tight upper bounds for the discrepancy of half-spaces

We show that the discrepancy of anyn-point setP in the Euclideand-space with respect to half-spaces is bounded byC _d n ^1/2−1/2d , that is, a mapping χ:P→{−1,1} exists such that, for any half-space γ, γ, |Σ _p∈P⋂γ χ(p)|≤C _d n ^1/2-1/2d . In fact, the result holds for arbitrary set systems as long as theprimal shatter function isO(m ^d ). This matches known lower bounds, improving previous upper bounds by a factor. Part of this research was done at the Third Israeli Computational Geometry Workshop in Ramot and during a visit at Tel Aviv University in December 1993. Also supported in part by Charles University Grant No. 351 and Czech Republic Grant GAČR 201/93/2167.     

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

q-Sigma-algebra generated by balls

The q--algebra, i.e., the system of sets closed under complementation, countable disjoint unions, and containing the empty set, generated by the system of open balls coincides with the -field of Borel sets inR sun forn=1,2, and 3. A first step to extend the proof forn=4, 5, 6, and 7 is indicated.     

Encapsulation of magnetite in vesicles

The encapsulation of fine magnetite particles of 10 nm size and marker ANS within asolectin vesicles has been made by sonication of the mixture in water. For the proof of encapsulation of magnetite in vesicles the electron microscope and spectrofluoriphotometer technique were used. The theory for the calculation of the magnetic force acting on the system consisted of non-capsulated magnetic particles dispersed in water and magnetic vesicles was developed.This work was supported by the Slovak Academy of Sciences within the framework of Project GAV No. 1361.     

Effect of nuclear structure on the single particle β− transitions in deformed nuclei

In the framework of the Nilsson model the calculations of the so called shape factor for the first forbidden ^– transitions 5/2^{+ 241}Pu 5/2^{– 241}Am and 7/2^{+ 177}Lu 7/2^{– 177}Hf are carried out. The dependence on the Nilsson potential parameters is studied. It turns out that for the transitions considered the calculated shape factor depends linearly on the electron energy and its slope is 10^–3 per 20 keV. This can affect the analysis of electron spectra if the endpoint energy is sufficiently large.     

The SO(3,3) group as a common basis for Dirac's and Proca's equations

Dirac's and Proca's equations are unified in the sense that the algebras of Dirac -matrices and Duffin-Kemmer-matrices are shown to furnish two distinct matrix representations of the Lie algebra of the SO(3,3)-group. This fact is then interpreted as evidence for the classical picture of particles described by the above-mentioned equations to be a relativistic top. It is also argued that the shape of the top is rod-like.     

Individual extraction constants of some dicarbollylcobaltate anions in the water-nitrobenzene system

Individual extraction constants of nine dicarbollylcobaltate anions in the two-phase water-nitrobenzene system were determined radiometrically assuming that the changes of Gibbs energy of the transfer of the tetraphenylarsonium cation, Ph₄As⁺, and of the tetraphenylborate anion, BPh ₄ ^– , from the aqueous into the nitrobenzene phase are equal. The constants obtained by this method were correlated with Hansch's constants of hydrophobity.     

The Inverse Scattering Method and Systems of Equations qxy = F(q,qy)

Consider equations of the form where q is in general a complex vector and the function F depends nontrivially both on q and on q_y. We show that a family S of such equations can be investigated by the inverse scattering method. If an equation (*) belongs to S, the function F depends linearly on q and algebraically on q_y. We show that the family S contains a subfamily in which each equation can be obtained from the two dimensional Toda lattice equations by a Bäcklund transformation.     

Structural phase transitions in ‘hcp’ C70 single-crystals

The thermal expansion of vapor-grownC ₇₀ single crystals ahs been investigated using high-resolution capacitance dilatometry from 5–380 K. Measurements were made both parallel and perpendicular to the hexagonalc-axis. Three first-order phase transitions which we associate with the consecutive disordering of theC ₇₀ molecules are observed upon heating at 280 K (long-axis spinning), 300 K (long-axis precession) and 355 K (quasi-free rotation), respectively. The highest-temperature transition exhibits a very large (50 K) thermal hysteresis. Powder and single-crystal X-ray diffraction show that the crystals are predominantly hexagonal-close-packed (HCP) with an idealc/a1.63 above 360 K andc/a1.84 at 295 K.