Information sources with different cost scales and the principle of conservation of entropy

Summary The aim of this paper is to provide a mathematically rigorous and sufficiently general treatment of the basic information-theoretic problems concerning sources with symbols of different costs and noiseless coding in a general sense. The main new concepts defined in this paper are the entropy rate (entropy per unit cost) of a source with respect to a stochastic cost scale and the encoding (in particular decodable encoding) of a source in a general sense. On the basis of these concepts, we prove some general theorems on the relation of entropy rates with respect to different cost scales and on the effect of encoding to the entropy rate. In particular, the principle of conservation of entropy and the noiseless coding theorem are proved under very general conditions.The main results of this research have been reported at the Second Congress of Bulgarian Mathematicians, Varna, August 1967, at the International Symposium on Information Theory, San Remo, September 1967 and at the Colloquium on Information Theory, Debrecen, September 1967.     

Hamiltonian chains in hypergraphs

A cyclic ordering of the vertices of a k‐uniform hypergraph is called a hamiltonian chain if any k consecutive vertices in the ordering form an edge. For k = 2 this is the same as a hamiltonian cycle. We consider several natural questions about the new notion. The main result is a Dirac‐type theorem that provides a sufficient condition for finding hamiltonian chains in k‐uniform hypergraphs with large (k − 1)‐minimal degree. If it is more than than the hypergraph contains a hamiltonian chain. © 1999 Wiley & Sons, Inc. J Graph Theory 30: 205–212, 1999     

GC-MS of amino acids as their trimethylsilyl/t-butyldimethylsilyl Derivatives: In model solutions III

Summary Fragmentation patterns of the essential amino acids (AAs) as their silyl derivatives have been obtained with the aid of ion trap detection (ITD). Three derivatizing reagents, hexamethyldisilazane+trifluoroacetic acid (HMDS+TFAA),bis-(trimethylsilyl)trifluoroacetamide (BSTFA) andN-methyl-N-(t-butyldimethylsilyl)trifluoroacetamide (MTBSTFA) were used. Simple and multiple derivatives obtained with each reagent have been investigated, with regard to their sensitivity and selectivity. Our study performed in the concentration range of 5-2000 ng amino acids has shown that, contrary to literature data, thirteen of the twenty-two AAs investigated including the TBDMS derivatives give rise to more than one peak when eluted. As a result of ion/molecule interaction the very informative ions of high masses, ([M]⁺, [M+TMS/(TBDMS)]⁺, [M+1]⁺) are formed with considerable intensities. The fragments [M-CH₃]⁺, [M-C₄H₉]⁺, [M-(CH₃)₂Si]⁺, [M-TMS/(TBDMS)COO]⁺, [M-TBDMSOH]⁺, [M-TBDMSO]⁺, [M-TBDMSNH]⁺ and numerous others could be utilized for identification purposes. Presented at Balaton Symposium on High Performance Separation Methods, Siófok, Hungary, September 1–3, 1999     

The technical applicability of Stirling engines in a Hungarian village

This study presents the utilization of forestry by-products in case of a small village using Stirling engines. At first, the yearly heat and power demands of a selected small, Hungarian village were specified, and then, the annual fuel potential of the surrounding woods was calculated. The main aim of the work was to compare these amounts of energy and find out whether the village could suffice its own energy demands only with forestry by-products. It was calculated that the different kinds of forestry by-products would be abundant enough for this purpose. Therefore, a concept of a sustainable system was developed, which contains a small-scale district heating system in the village. The system is based on chopped wood-fueled Stirling engines, which can realize combined heat and power production. Besides the heat, the village may also use the power production of the Stirling engines. The technology reduced the pollutant emission of the village as well, CO emission practically disappeared. As the results show, the three goals of the work have been achieved: to take advantage of the locally available energy sources, to use cheap and easily storable sources and to decrease the air pollution in the village.     

Development of the suzuki-miyaura cross-coupling reaction: use of air-stable potassium alkynyltrifluoroborates in aryl alkynylations

The palladium-catalyzed cross-coupling reaction of potassium alkynyltrifluoroborates with aryl halides or triflates proceeds readily with moderate to excellent yields. The potassium alkynyltrifluoroborates are air- and moisture-stable crystalline solids that can be stored indefinitely, which will provide an advantage in applications to combinatorial chemistry. The alkynyl cross-coupling reaction can be effected using 9 mol % of PdCl2(dppf).CH2Cl2 as catalyst in THF or THF-H2O in the presence of Cs2CO3 as the inorganic base. A variety of functional groups are tolerated in both partners.     

Triplet state spectroscopic studies on some 5,10,15,20-tetrakis(methoxyphenyl)porphyrins

Extensive triplet state spectroscopic investigations were carried out with a series of 5,10,15,20-tetrakis(methoxyphenyl)porphyrins. Triplet absorption spectra, triplet lifetime, triplet quantum yield and quantum yield for singlet oxygen production were determined with different absorption and emission techniques, using the frequency-doubled beam of a Nd:YAG laser. It has been found that these synthetic porphyrins are effective photosensitizers which can be used as model compounds to investigate the theoretical and instrumental aspects of PDT.     

Bounds on Maximal Families of Sets Not Containing Three Sets with A ∩ B ⊂ C, A ⊄ B

Lower and upper estimates are given on the size of a family of subsets of an n-element set containing no three distinct sets satisfying A ∩ B ⊂ C, A ⊄ B. This is a sharpening of an earlier result where the same question was solved under the condition that there are no three distinct sets such that A ∩ B ⊂ C. The second author was supported by the Hungarian National Foundation for Scientific Research grant numbers NK062321, AT048826, the Bulgarian National Science Fund under Grant IO-03/2005 and the projects of the European Community: INTAS 04-77-7171, FIST–MTKD-CT-2004-003006.