Joins of n-degenerate graphs and uniquely (m,n)-partitionable graphs

The Lick-White point-partition numbers generalize the chromatic number and the point-arboricity. Similarly, uniquely (m, n)-partitionable graphs generalize uniquely m-colorable graphs.Theorem 1 gives a method for constructing uniquely (m, n)-partitionable graphs as well as a sufficient condition for a join of mn-degenerate graphs to be uniquely (m, n)-partitionable. For the case n = 1, we obtain a necessary and sufficient condition (Lemma 1). As a consequence, an embedding result for uniquely (m, 1)-partitionable graphs is obtained (Theorem 2). Finally, uniquely (m, n)-partitionable graphs with minimal connectivity are constructed (Theorem 3).     

The characteristic exponents of the falling ball model

We study the characteristic exponents of the Hamiltonian system ofn (>=2) point massesm ₁,...,m _n freely falling in the vertical half line {q|q>=0} under constant gravitation and colliding with each other and the solid floorq=0 elastically. This model was introduced and first studied by M. Wojtkowski. Hereby we prove his conjecture: All relevant characteristic (Lyapunov) exponents of the above dynamical system are nonzero, provided thatm ₁>= ...>=m _n (i.e. the masses do not increase as we go up) andm ₁≠m ₂. Research partially supported by the Hungarian National Foundation for Scientific Research, No. 16425.     

Evolution of ochratoxin A content from must to wine in Port Wine microvinification

To study the evolution of ochratoxin A (OTA) content from must to wine during the making of Port Wine, grapes from the five most common varieties of Port Wine were harvested and combined in equal percentages in order to perform microvinifications. Three sets of assays were studied: a blank (A), where the most common Port Wine-making process was used; in the second (B), a solution of OTA was added to the initial must; in the third (C), the grapes were aspersed with an inoculating solution of OTA-producing fungi. Samples were collected, in duplicate, on four different occasions throughout the process. The influence of the addition of SO₂ to the must was also assessed in each set. The quantification of OTA was based on the standard reference method for wines (European Standard prEN 14133), which includes clean-up via immunoaffinity columns and HPLC with fluorescence detection. The limits of detection were 0.076 g/l for wine and 0.114 g/l for must. The method was validated by assessing the precision, accuracy and by obtaining an estimate of the global uncertainty. Overall, the levels of OTA observed during the vinifications dropped by up to 92%, and no grapes used in this work were contaminated naturally.     

Aminopyridine-benzoxanthene enantioselective receptor for sulfonylamino acids

Combination of a cis-tetrahydrobenzoxanthene skeleton with a benzoxazole and an amidopyridine provides an enantioselective receptor for sulfonylamino acids with chiral recognitions of up to 18. The structure of the complex between receptor 1 and the leucine triflate is known by X-ray analysis. The receptor racemic mixture can be suitably resolved through crystalization in the presence of leucine triflate as guest. Receptor 1 can be used for the enantioselective extraction of sulfonylamino acids from aqueous solutions of their salts.     

Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

We consider the system of hard balls with masses and radius r in the flat torus of size . We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost every selection of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the case . The method of that proof was primarily dynamical-geometric, whereas the present approach is inherently algebraic. Communicated by Eduard ZehnderSubmitted 17/10/02, accepted 01/12/03     

A trans-tetrahydrobenzoxanthene receptor for the resolution of racemic mixtures of sulfonylamino acids

An enantioselective cleft-type receptor for sulfonylamino acids has been prepared and its use for the resolution of the amino acid racemic mixture is shown.     

Nonclassical bonding in the novel structure of Ba2Bi3 and unexpected site preference in the coloring variant Ba2BiSb2

The new phase Ba(2)Bi(3) crystallizes in the W(2)CoB(2) structure type. Its structure contains rigorously planar anionic layers of (4.6.4.6)(4.6(2))(2) nets with three- and four-bonded Bi, that are separated by Ba atoms. An unexpected site preference is observed in the coloring variant Ba(2)BiSb(2) with Sb occupying only the three-bonded sites. The nonclassical bonding in the anionic network can be rationalized from a reformulation of the Zintl concept as (Ba(2+))(2)[Bi(3)](3)(-)(e(-)). Bonding distances suggest that the extra electron fills Bi-Bi antibonding states. The densities of states obtained from TB-LMTO-ASA calculations show metallic character for both compounds.