The structure of Valdivia compact lines

We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed ℵ₁, every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author.     

Minimal infeasible constraint sets in convex integer programs

In this paper we investigate certain aspects of infeasibility in convex integer programs, where the constraint functions are defined either as a composition of a convex increasing function with a convex integer valued function of n variables or the sum of similar functions. In particular we are concerned with the problem of an upper bound for the minimal cardinality of the irreducible infeasible subset of constraints defining the model. We prove that for the considered class of functions, every infeasible system of inequality constraints in the convex integer program contains an inconsistent subsystem of cardinality not greater than 2 ⁿ , this way generalizing the well known theorem of Scarf and Bell for linear systems. The latter result allows us to demonstrate that if the considered convex integer problem is bounded below, then there exists a subset of at most 2 ⁿ −1 constraints in the system, such that the minimum of the objective function subject to the inequalities in the reduced subsystem, equals to the minimum of the objective function over the entire system of constraints.     

Nonlinear dynamics and complexity in the generalized Lorenz system

Nonlinear Dynamics - Dynamics of magnetized fluids is much more complex than expected from the standard magnetohydrodynamics. Besides chaotic behavior that often appears in nonlinear dynamical...     

Remarks on the Analytic Centers of Convex Sets

In this paper we analyze properties of the analytic centers for perturbed convex problems. In particular we study the continuity of convex regions with respect to such characteristics as boundedness, full dimensionality and the existence of an analytic centre. Furthermore, we state the necessary and sufficient conditions for the existence of the analytic centre for possibly unbounded regions and we show that the analytic centre is identical for any minimal representation of the convex set. We are also concerned with the limiting behaviour of the central path as it approaches the set of optimal solutions of the problem.     

Noncommutative Dynamics of Random Operators

We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra А on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ . We show that every a ∊ А defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita–Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra А which can be used to define a state dependent dynamics; i.e., the pair (А, ϕ), where ϕ is a state on А, is a “dynamic object.” Only if certain additional conditions are satisfied, the Connes–Nikodym–Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (А, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics.     

On ideals and congruences in bcc-algebras

We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences.     

A proof of uniqueness of the Gurariĭ space

We present a short and elementary proof of isometric uniqueness of the Gurari? space.     

Silicate Xerogels with Dopant-Induced Chirality

A series of silicate xerogels with entrapped chiral amino acids have been obtained via sol-gel technology. The transparent, glassy samples obtained exhibit chirality in the bulk due to the presence of the entrapped asymmetric molecules. Measurements of the optical activity of the doped xerogel samples revealed that the entrapment did not significantly influence the optical activity observed for liquid solutions of the amino acids. Thus, the sol-gel method enables the preparation of amorphous optical materials exhibiting properties of strictly spatially defined molecular systems. Apart from the obvious optical applications, such porous materials with asymmetric centers might find interesting applications in chiral chemical syntheses and separations.     

Preparation, Structure, and Thermal Decomposition of Co(II) Complexeswith 2,3- and 2,5-Dichlorobenzoic Acid and Imidazole

Summary.  The reaction products of Co(II)-2,3- and -2,5-dichlorobenzoate with imidazole (1, 2; CoL ₂⋯2imdċ2H₂O, L=C₇H₃Cl₂O, imd=imidazole) were characterized by their spectroscopic and thermochemical properties. The compounds crystallize in the monoclonic system with space group = P2₁/c, a=13.848(3), b=12.841(3) ?, c= 7.064(2) ?, β=98.12 °, V=1243.5(4) ?³, Z=2 for 1 and space group =P2₁/n, a=13.293(3), b= 6.964(2), c=13.800(3) ?, β=108.92(3) °, V=1208.6(4) ?³, Z=2 for 2. The complexes lose their crystal water in one step at 333 K and subsequently decompose to CoO with intermediate formation of Co₃O₄. Received August 9, 1999. Accepted (revised) February 11, 2000     

Cis-coordination of the chromate anions in helical Co/Ni block-type polymeric systems. Structural and spectroscopic characteristics of catena(μ-CrO4-O,O′)[Co(HIm)3H2O] and catena(μ-CrO4-O,O′)[Co0.43Ni0.57(HIm)3H2O]

Two polymeric complexes: catena(μ-CrO₄-O,O′)[Co(HIm)₃H₂O] (1) and catena(μ-CrO₄-O,O′)[Co_0.43Ni_0.57(HIm)₃H₂O] (2) (where HIm=imidazole) with a cis-bridging coordination mode of the CrO₄ ²⁻ anion have been synthesized and characterized by X-ray and spectroscopic methods. These crystals were isolated from nine systems of varying reagent molar ratios and three excluding anions: Cl⁻, NO₃ ⁻ and SO₄ ²⁻ exclusively as mer [M(HIm)₃O₃]-type isomers. The unit cell of these isostructural complexes (monoclinic crystal system P2₁ /n) contains two independent helixes, left- and right handed, stabilized by intrahelical and interhelical hydrogen bonding and π–π interaction between pairs of the imidazole rings from neighbouring helixes. The Raman spectra at 77 K of 1 and 2 deconvoluted into lorentzian components revealed the block-type polymeric structure of the complexes. Moreover, the solution studies at millimolar concentrations of 1 and 2 indicated their complete decomposition in water. Four K electronic spectral analysis of the crystals (band deconvolution into gaussian components) enhanced with the data obtained in the polarized light allowed for assignment of the bands to the respective d–d transition (D_4h symmetry). It was found that the metallic centres are independently absorbing species, which supports the suggestion of a block-type structure of the polymers. The respective crystal field parameters for Co and Ni were calculated.