A Frobenius Theorem on Convenient Manifolds

 A Frobenius Theorem for finite dimensional, involutive subbundles of the tangent bundle of a convenient manifold is proved. As first key applications Lie’s second fundamental theorem and Nelson’s theorem are treated in the convenient case.     

Further remarks on simple flows of fluids with pressure-dependent viscosities

Recently Suslov and Tran (2008) [1] claimed to have found an error in one of the solutions given in the paper by Hron (2001) et al. [2] concerning the flows of fluids with pressure-dependent viscosities. We show that their arguments are related to the question of the continuity of the pressure, and we show that the original solution, although it is not a classical one, can be interpreted as a solution in a generalized sense. Mathematical and physical implications of such generalizations are briefly discussed. The discussion in the paper highlights the importance of recognizing what is meant by a “solution” to a partial differential equation, whether by a solution we mean a classical solution, a weak solution, or a solution in some other sense.     

The last dozen of years of OR research in Czechia and Slovakia

Central European Journal of Operations Research - The paper discusses operations research (OR) history and achievements in Czechia and Slovakia in 2010–2021 including the most significant OR...     

Mathematical modelling of rock bolt systems I

The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties.     

A conglomerate of exponential supercategories of the category of finitely generated topological spaces

Summary For every ordinaln > 1 we define a categoryT _n of topological spaces in ech's sense which is isomorphic to a category ofn-ary monorelational systems. We show that every categoryT _n is an exponential supercategory of the categoryB of finitely generated topological spaces, which means that well-behaved function spacesG ^H can be defined inT _n wheneverG B.     

Running time experiments on some algorithms for solving propositional satisfiability problems

Satisfiability problems are of importance for many practical problems. They are NP-complete problems. However, some instances of the SAT problem can be solved efficiently. This paper reports on a study concerning the behaviour of a variety of algorithmic approaches to this problem tested on a set of problems collected at FAW. The results obtained give a lot of insight into the algorithms and problems, yet also show some general technical and methodological problems associated with such comparisons.     

1,2endo-Trimethylenenorbornane. A novel isomer of adamantane

An easy approach to the novel adamantane isomer 1,2endo-trimethylenenorbornane (2) is described. Starting from a mixture of pent-4-ynylcyclopentadienes 3 the tricyclic monosaturated key intermediate 5 was prepared by intramolecular cycloaddition (→ 4 ) and subsequent regioselective reduction of the C(5), C(6) double bond. The title hydrocarbon 2 was obtained from 5 upon stereoselective hydrogenation by diimide. In addition specifically deuteriated analogues of 2 were prepared applying dideuteriodiimide. Compound 2 rearranged to 2endo, 6endo-trimethylenenorbornane (4-homobrendane, 10 ) in sulfuric acid as well as with aluminium bromide in carbon disulfide.     

The Adamantane Rearrangement of 1,2endo-Trimethylenenorbornane. Preliminary communication

1,2endo-Trimethylenenorbornane (1) in the presence of aluminium bromide in carbon disulfide at ?60° isomerizes at a much higher rate than its 2exo-isomer 2 to 2endo, 6endo-trimethylenenorbornane (3) as the sole product. By consequence, the hydrocarbon 2 being the next intermediate in the sequence of the adamantane rearrangement of 1 seems to be very unlikely.     

Alkyl and stannyl radical generation by CSn and SnSn bond dissociation in photolytically excited peralkylated tristannanes as studied by ESR and 119Sn-CIDNP

Tristannanes used as photochemical precursors for the synthesis of organic compounds react via triplet states followed by homolytic CSn and SnSn bond scission.     

A Uniqueness Result for a Model for Mixtures in the Absence of External Forces and Interaction Momentum

We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities ϱ _i of the fluids and their velocity fields u ⁽ⁱ⁾ are prescribed at infinity: ϱ _i |_∞ = ϱ _i∞ > 0, u ⁽ⁱ⁾|∞ = 0. Neglecting the convective terms, we have proved earlier that weak solutions to such a reduced system exist. Here we establish a uniqueness type result: in the absence of the external forces and interaction terms, there is only one such solution, namely ϱ _i ≡ ϱ _i∞, u ⁽ⁱ⁾ ≡ 0, i = 1, 2. This work was supported by the SFB 611 at the University of Bonn and the European HYKE network (contract no. HPRN-CT-2002-00282). The third author was also supported by the project CSF 201/03/0934, and by MSM 0021620839.