Secants of Lagrangian Grassmannians

We study the dimensions of secant varieties of Grassmannian of Lagrangian subspaces in a symplectic vector space. We calculate these dimensions for third and fourth secant varieties. Our result is obtained by providing a normal form for four general points on such a Grassmannian and by explicitly calculating the tangent spaces at these four points.     

Cartesian product stabilization of 3-manifolds

The Cartesian product of a closed, orientable prime geometric 3-manifold and a closed orientable surface is unique except for the case of the Cartesian product of a special class of Seifert manifolds and a torus. The same type of uniqueness holds for stabilization of 3-manifolds by an n-dimensional torus. Cartesian squares of Seifert fibered 3-manifolds are completely classified.     

A Few Remarks on the Operator Norm of Random Toeplitz Matrices

We present some results concerning the almost sure behavior of the operator norm of random Toeplitz matrices, including the law of large numbers for the norm, normalized by its expectation (in the i.i.d. case). As tools we present some concentration inequalities for suprema of empirical processes, which are refinements of recent results by Einmahl and Li.     

The complexity of some acyclic improper colourings

In this paper we will consider acyclic bipartition of the vertices of graphs, where acyclic means that the edges whose endpoints are in different parts of the partition induce a forest. We will require that the vertices belonging to the same partition induce graphs from particular class. We will search for acyclic bipartitions of cubic and subcubic graphs.     

A characterization of quadratic-multiplicative mappings

In the spirit of some earlier studies of Jean Dhombres, Roman Ger and Ludwig Reich we discuss the alienation problem for quadratic and multiplicative mappings.     

Corrosion inhibition of magnesium alloy AZ31 in chloride-containing solutions by aqueous permanganate

In this work, corrosion of the AZ31 magnesium alloy was examined in 0.05 M NaCl solutions containing 0.01–0.150 mol/dm³ of potassium permanganate as a corrosion inhibitor. A set of electrochemical impedance spectroscopy, linear sweep voltammetry, and hydrogen evolution measurements revealed high inhibitor effectiveness at relatively high (0.150 mol/dm³) KMnO₄ concentrations. Based on data of energy-dispersive X-ray analysis, scanning electron microscopy, and Raman spectroscopy, a mechanism of the corrosion inhibition of AZ31 alloy by potassium permanganate in chloride-containing media was proposed.

     

Fractionation of bacteria by electrophoresis as pre-separation method before MALDI-MS detection

The present study attempted to apply the capillary electrophoresis technique for the fractionation and separation of S. Staphylococcus hominis and Escherichia coli bacteria isolated from urine samples and the detection of migrated fraction with spectrometric method. This involved the selection of suitable conditions for separation as well as the identification of pathogens. The result of the research was the separation of Gram-negative and Gram-positive bacteria, as well as their subsequent identification by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry using two different approaches (culture of fractions on an agar plate and direct analysis of the collected fractions). The preliminary results provide a solid basis for further research on the use of electromigration techniques with LDI detection to identify pathogens such as bacteria and viruses in biological samples.     

Subsolidus phase diagram of Cu2OCuOMoO3 system

Five chemical compounds, CuMoO₄, Cu₃Mo₂O₉, Cu₂Mo₃O₁₀, Cu₆Mo₄O₁₅, and Cu_4?x Mo₃O₁₂ (0.10 ? x ? 0.40), were identified in the system Cu₂OCuOMoO₃ and characterized by DTA, X-ray powder patterns, ir spectra, and magnetic properties. Cupric molybdates CuMoO₄ and Cu₃Mo₂O₉ are stable in air up to 820 and 855°C, respectively, melting at these temperatures with simultaneous decomposition (oxygen loss). Congruent mp of cuprous molybdates Cu₂Mo₃O₁₀ and Cu₆Mo₄O₁₅, in argon, are 532 and 466°C, respectively. Nonstoichiometric phase Cu_4?x Mo₃O₁₂ = Cu²⁺₃Cu⁰_1?xMo⁶⁺₃O₁₂, melts in argon between 630 and 650°C depending on the value of x and at 525–530°C undergoes polymorphic transformation. Areas of coexistence of the above-mentioned phases are determined. The μ_eff of Cu²⁺ ions and θ values are: 1.80 B.M. and 28°K for CuMoO₄, 1.71 B.M. and ? 12°K for Cu₃Mo₂O₉, and 1.74 B.M. and ? 93°K for Cu_4?xMo₃O₁₂. Below 200°K CuMoO₄ becomes antiferromagnetic. Cu₂Mo₃O₁₀ and Cu₆Mo₄O₁₅ show weak temperature-independent paramagnetism.     

Absolutely summing multipliers on abstract Hardy spaces

We study summing multipliers from Banach spaces of analytic functions on the unit disc of the complex plane to the complex Banach sequence lattices. The domain spaces are abstract variants of the classical Hardy spaces generated by the complex symmetric spaces. Applying interpolation methods, we prove the Hausdorff Young and Hardy-Littlewood type theorems. We show applications of these results to study summing multipliers from the Hardy-Orlicz spaces to the Orlicz sequence lattices. The obtained results extend the well-known results for the Hp spaces.