Cycles throughk vertices in bipartite tournaments

We give a simple proof that everyk-connected bipartite tournament has a cycle through every set ofk vertices. This was conjectured in [4].This research was done while the first author was visiting Laboratoire de Recherche en Informatique, universite Paris-Sud whose hospitality and financial support is gratefully acknowledged     

Some remarks on spreading models and mixed Tsirelson spaces

We prove that if a Banach space with a bimonotone shrinking basis does not contain spreading models but every block sequence of the basis contains a further block sequence which is a spreading model for every , then every subspace has a further subspace which is arbitrarily distortable. We also prove that a mixed Tsirelson space , such that , does not contain spreading models.

     

Function spaces not containing ℓ<Subscript>1</Subscript>

For Ω bounded and open subset of andX a reflexive Banach space with 1-symmetric basis, the function spaceJF _X (Ω) is defined. This class of spaces includes the classical James function space. Every member of this class is separable and has non-separable dual. We provide a proof of topological nature thatJF _X (Ω) does not contain an isomorphic copy of ℓ₁. We also investigate the structure of these spaces and their duals.     

Cycles and paths in bipartite tournaments with spanning configurations

We give necessary and sufficient conditions in terms of connectivity and factors for the existence of hamiltonian cycles and hamiltonian paths and also give sufficient conditions in terms of connectivity for the existence of cycles through any two vertices in bipartite tournaments.     

Minimal colorings for properly colored subgraphs

We give conditions on the minimum numberk of colors, sufficient for the existence of given types of properly edge-colored subgraphs in ak-edge-colored complete graph. The types of subgraphs we study include families of internally pairwise vertex-disjoint paths with common endpoints, hamiltonian paths and hamiltonian cycles, cycles with a given lower bound of their length, spanning trees, stars, and cliques. Throughout the paper, related conjectures are proposed.Research supported by a European Union PECO grant under identification number CIPA3510PL929589, while on leave at University Paris-XI     

Thermal decomposition of halo-bis(piperidyldithio-carbamates) of As(III), Sb(III) and Bi(III)

Simultaneous TG/DTG/DTA studies under non-isothermal conditions have been carried out in air and nitrogen on some halo-dithiocarbamates of the general formula XM[S₂CN(CH₂)₅]₂ (X=Cl, Br and I; andM=As, Sb and Bi).E* values for the 1st stage of decomposition were determined by graphical methods and the TTN temperatures were calculated from the TG profiles. A possible mechanism of the decomposition reaction is suggested, based on the thermoanalytical and pyrolysis results and the mass spectral data. The kinetic analysis data on five of the above dithiocarbamates and nine complexes of the general formula M[S₂CN<]₃ (M=As, Sb and Bi; and N<=NEt₂, N(CH₂)₅ and N(CH₂)₄O) were studied by the QIA (quasi-isothermal analysis) technique in air atmosphere. An example of kinetic parameter (k andn) estimation for the first decomposition stage is given for Bi[S₂CN(CH₂)₅]₃, with the assumption of different kinetic equations.

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Zusammenfassung Einige helo-Dithiocarbamate der allgemeinen Formal XM[S₂CN(CH₂)₅]₂ (X=Cl, Br und I;M=As, Sb und Bi) wurden mittels simultaner TG/DTG/DTA unter nichtisothermen Bedingungen in Luft und Stickstoff untersucht. Für den ersten Zersetzungsschritt wurden E^*-Werte durch graphische Methoden bestimmt und die TIN-Temperaturen aus den TG-Profilen berechnet. Ein auf den Ergebnissen der Thermogravimetrie und Pyrolyse sowie auf massenspektroskopischen Daten beruhender möglicher Mechanismus wird vorgeschlagen. Fünf der angeführten Dithiocarbamate und 9 Komplexe der allgemeinen Formel M[S₂CN<]₃] (M=As, Sb und Bi;N=NEt₂, N(CH₂)₅ und N(CH₂)₄O) wurden mittels QIA (quasi-isotherme Analyse) in Luft untersucht. Als Beispiel ist die Bestimmung der kinetischen Parameter (k undn) für den ersten Schritt der Zersetzung von Bi[S₂CN(CH₂)₅]₃ unter Annahme verschiedener kinetischer Gleichungen angegeben.

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, - XM[S₂CN(CH₂)₅]₂, =Cl, r l, a M=As, Sb Bi. ^a , -. - . M[S₂CN<]₃, M=As, Sb Bi, a N<=NEt₂, N(CH₂)₅ N(CH₂)₄O. k ³[S₂N(₂)₅]₃.

     

A Parallel Reduction of Hamiltonian Cycle to Hamiltonian Path in Tournaments

We propose a parallel algorithm which reduces the problem of computing Hamiltonian cycles in tournaments to the problem of computing Hamiltonian paths. The running time of our algorithm is O(log n) using O(n²/log n) processors on a CRCW PRAM, and O(log n log log n) on an EREW PRAM using O(n²/log n log log n) processors. As a corollary, we obtain a new parallel algorithm for computing Hamiltonian cycles in tournaments. This algorithm can be implemented in time O(log n) using O(n²/log n) processors in the CRCW model and in time O(log²n) with O(n²/log n log log n) processors in the EREW model.     

On the Structure of a Certain Class of Mixed Tsirelson Spaces

We study Banach spaces of the form We call such a space a p-space, p[1,), if for every k the space is isomorphic to _pk and the sequence (p_k) strictly decreases to p. We examine the finite block representability of the spaces _r in a p-space proving that it depends not only on p but also on the sequences (p_k) and (n_k). Assuming that _i n_i ^1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c ₀ is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if n_km1/pkm-1/pk_m-1 increases to infinity for a subsequence (n_km) , then ₁ embeds into X. We also investigate complemented minimality for the class of spaces where is either a subsequence of the sequence of Schreier classes ( _n)_{n N} or a subsequence of ( _n)_{n N}.     

Quasi-minimality and tightness by range in spaces with unconditional basis

We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e., of type (4) in the Ferenczi-Rosendal list within the framework of Gowers’ classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with an asymptotically unconditional basis.