On the extent of star countable spaces

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ? X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω ₁-monolithic compact space X, if C _p (X)is star countable then it is Lindelöf.     

A Direct Splitting Method for Nonsmooth Variational Inequalities

We propose a direct splitting method for solving a nonsmooth variational inequality in Hilbert spaces. The weak convergence is established when the operator is the sum of two point-to-set and monotone operators. The proposed method is a natural extension of the incremental subgradient method for nondifferentiable optimization, which strongly explores the structure of the operator using projected subgradient-like techniques. The advantage of our method is that any nontrivial subproblem must be solved, like the evaluation of the resolvent operator. The necessity to compute proximal iterations is the main difficulty of other schemes for solving this kind of problem.     

Ultrasound‐assisted emulsification microextraction coupled with high‐performance liquid chromatography for the simultaneous determination of fragrance allergens in cosmetics and water

A simple, inexpensive, and environmentally friendly method based on ultrasound‐assisted emulsification microextraction followed by solidification of floating organic drop and high‐performance liquid chromatography coupled to diode array detection was developed for the simultaneous determination of 18 potentially allergenic fragrance substances. Several parameters affecting the microextraction process were investigated in detail by the “one‐variable‐at‐a‐time” approach. Optimal conditions were the following: 50 μL of 2‐dodecanol as extraction solvent, 10 mL of sample containing 150 g/L of salt, and 5 min of sonication at 35°C. Under the optimized conditions, method showed good linearity in the selected ranges, with squared correlation coefficients ranging from 0.948 to 0.999. Limits of detection ranged from 0.001 to 0.154 μg/mL and enrichment factors from 9 to 237. Precision of the method, expressed as relative standard deviation, was checked at two levels obtaining good results (3.3–14.4%). Recovery studies were made in baby bath water and in eau de cologne showing acceptable accuracy. Finally, the developed method was successfully applied to different commercial cosmetic and water samples. The most commonly found analyte was linalool followed by cinnamal and lilial. Most of the analyzed samples contained at least one of the target compounds.     

A compact HL-space need not have a monolithic hyperspace

We show that Kunen's example of a compact L-space, constructed under CH, can be modified so that it has a non-monolithic hyperspace. This answers a question of Bell's. This example is also relevant to a question of Arhangel'skii's.

     

Derivation of the amplitude equation for a hydromagnetic convective problem

The amplitude equation for a convective system under a vertical magnetic field is derived. The coefficients in these equations have been numerically calculated for infinite Prandtl number fluids and for boundary conditions both free and rigid top and bottom. The results confirm that, for realistic parameter values only stationary convection can be present and the pattern is made by convective rolls.     

On the product of homogeneous spaces

Within the class of Tychonoff spaces, and within the class of topological groups, most of the natural questions concerning ‘productive closure’ of the subclasses of countably compact and pseudocompact spaces are answered by the following three well-known results: (1) [ZFC] There is a countably compact Tychonoff space X such that X × X is not pseudocompact; (2) [ZFC] The product of any set of pseudocompact topological groups is pseudocompact; and (3) [ZFC+ MA] There are countably compact topological groups G₀, G₁ such that G₀ × G₁ is not countably compact.In this paper we consider the question of ‘productive closure” in the intermediate class of homogeneous spaces. Our principal result, whose proof leans heavily on a simple, elegant result of V.V. Uspenski?, is this: In ZFC there are pseudocompact, homogeneous spaces X₀, X₁ such that X₀ × X₁ is not pseudocompact; if in addition MA is assumed, the spaces X_i may be chosen countably compact.Our construction yields an unexpected corollary in a different direction: Every compact space embeds as a retract in a countably compact, homogeneous space. Thus for every cardinal number α there is a countably compact, homogeneous space whose Souslin number exceeds α.     

Über Antimon(V)-bromchloride und ihre Stabilisierung durch Elektronendonatoren

SbCl₃Br₂ may be stabilized by electron donors. Crystalline 1:1 adducts with diethyl ether, tetrahydrofurane, triphenylphosphine oxide and -sulphide were isolated. Their bonding properties, regarding the donor strengths, are discussed. The tetrahydrofurane adduct takes up three molecules of CCl₄ in the presences of CCl₄ · SbCl₃Br₂ · OP(C₆H₅)₃ is converted in introbenzene into SbCl₃Br₂ · O₂NC₆H₅ which, at room temperature, transforms in the course of 15 hours to heteropolar compounds of the general formula [SbCl_nBr_4?n · (O₂NC₆H₅)₂]+[SbCl_mBr_6?m]^?, with m + n = 6 and n = 1, 2, 3, 4.     

A compact F-space not co-absolute with βN−N

We show that if every Parovi?enko space of weight $\text{c}$ is co-absolute with $\text{β}\text{N}\text{?}\text{N}$, then .     

A counterexample concerning line-free groups and complete Erdos space

We present a weakly closed, one-dimensional, line-free subgroup of the separable Banach space that is not homeomorphic to complete Erdos space. The existence of this example disproves a conjecture of Dobrowolski, Grabowski, and Kawamura.

     

New Nematic Phase in Lyotropic Binary Liquid Crystals Detected by Positron Annihilation Techniquest

A new nematic phase in lyotropic binary liquid crystalline systems consisting of sodium dodecyl sulfate-water was detected, for the first time, in the absence of additives by utilizing positron annihilation techniques. Lyotropic and thermotropic phase transitions were also investigated by the same methods. The positron annihilation parameters have also indicated a better definition of the concentration ranges at which each phase exists in the system studied. Crossed polarized light microscopy was applied to substantiate these results.