We study a dynamic coordination process in which agents are uncertain about the actions of their fellow agents, and anticipate strategically relevant information. Because of the uncertainty and learning, (ir)reversibility of actions has important strategic consequences. We find that the reversibility option can either enhance or hamper efficient coordination, and we characterize the direction o...

We extend Post’s programme to finite levels of the Ershov hierarchy of ∆2 sets, and characterise, in the spirit of Post [9], the degrees of the immune and hyperimmune d.c.e. sets. We also show that no properly d.c.e. set can be hh-immune, and indicate how to generalise these results to n-c.e. sets, n > 2.

For optical studies of boiling heat transfer process, it is essential that the refractive index and its dependence on temperature for the test liquid be known. In this work a simple set-up was built to measure the refractive index of Fluorinert Liquid PF-5060 with temperature compensation and temperature control. The pinhole laser light beam was used for determining the refraction angle. The re...

Let ∆ be a rank 2 hyperbolic root system. Then ∆ has generalized Cartan matrix H(a, b) = ( 2 −b −a 2 ) indexed by a, b ∈ Z with ab ≥ 5. If a 6= b, then ∆ is non-symmetric and is generated by one long simple root and one short simple root, whereas if a = b, ∆ is symmetric and is generated by two long simple roots. We prove that if a 6= b, then ∆ contains an infinite family of symmetric rank 2 hy...

Weprovide a simple set of sufficient conditions for theweak convergence of discrete-time, discrete-state Galton–Watson branching processes with immigration to continuous-time, continuous-state branching processes with immigration.

We show that in the c.e. weak truth table degrees if b < c then there is an a which contains no hypersimple set and b < a < c. We also show that for every w < c in the c.e. wtt degrees such that w is hypersimple, there is a hypersimple a such that w < a < c. On the other hand we know that there are intervals which contain no hypersimple set.

A practical and green method for the synthesis of 5H-dibenzo[b,i]xanthene-tetraones and spiro[dibenzo[b,i]xanthene-13,3'-indoline]-pentaones by the condensation of 2-hydroxynaphthalene-1,4-dione with aldehydes or isatins, respectively, in the presence of a catalytic amount of cellulose sulfuric acid (CSA) under solvent-free conditions at 100 °C is described. The significant features of this pro...

Cellulose sulfuric acid was used as an efficient biopolymer-based catalyst for the synthesis of tetrahydropyrimido[4,5-b]quinoline-2,4,6-triones and hexahydro-2H-pyrazolo[5,4-b]quinoline-6-ones via three component reaction of aldehyde, 5,5-dimethyl-1,3-cyclohexadione and 6-amino-1,3-dimethyluracil or 5-amino-3-methyl-1-phenypyrazole under solvent-free conditions at 90 oC. The major advantages o...

Cellulose sulfuric acid was used as an efficient biopolymer-based catalyst for the synthesis of tetrahydropyrimido[4,5-b]quinoline-2,4,6-triones and hexahydro-2H-pyrazolo[5,4-b]quinoline-6-ones via three component reaction of aldehyde, 5,5-dimethyl-1,3-cyclohexadione and 6-amino-1,3-dimethyluracil or 5-amino-3-methyl-1-phenypyrazole under solvent-free conditions at 90 oC. The major advantages o...

An incomplete degree is cuppable if it can be joined by an incomplete degree to a complete degree. For sets fulfilling some type of simplicity property one can now ask whether these sets are cuppable with respect to a certain type of reducibilities. Several such results are known. In this paper we settle all the remaining cases for the standard notions of simplicity and all the main strong redu...