The Cauchy problem for the 2D magnetohydrodynamic-α equations

In this paper, we consider the Cauchy problem for the 2D incompressible magnetohydrodynamics-$\alpha$ (MHD-$\alpha$) equations. We obtain the global solution for the 2D incompressible MHD-$\alpha$ simulation model in the fractional index Sobolev space, and prove that the incompressible MHD-$\alpha$ equations reduce to the incompressible homogeneous MHD equations as $\alpha \to 0$, and the solution of MHD-$\alpha$ equations will converge to the weak solution of the corresponding MHD equations. Moreover, it is convenient to construct a numerical algorithm based on an iteration scheme in our proof.     

A glimpse of deductive systems in algebra

The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.     

Existence results for variational-hemivariational problems with lack of convexity

We establish existence results of Hartmann-Stampacchia type for a class of variational-hemivariational inequalities on closed and convex sets (either bounded or unbounded) in a Hilbert space.     

On the existence of three solutions for the Dirichlet problem on the Sierpinski gasket

We apply a recently obtained three-critical-point theorem of B. Ricceri to prove the existence of at least three solutions of certain two-parameter Dirichlet problems defined on the Sierpinski gasket. We also show the existence of at least three nonzero solutions of certain perturbed two-parameter Dirichlet problems on the Sierpinski gasket, using both the mountain pass theorem of Ambrosetti and Rabinowitz and that of Pucci and Serrin.     

Weak solutions for nonlinear antiplane problems leading to hemivariational inequalities

We analyze the antiplane shear deformation of an elastic cylinder in frictional contact with a rigid foundation, for static processes, under the small deformation hypothesis. Based on the Knaster–Kuratowski–Mazurkiewicz technique in the theory of the hemivariational inequalities, we prove that the model has at least one weak solution. Moreover, we present several examples of constitutive laws and friction laws for which our theoretical results are valid. Finally, we comment on the conditions which guarantee the uniqueness of the solution.     

The Attractive Traveling Salesman Problem

In the Attractive Traveling Salesman Problem the vertex set is partitioned into facility vertices and customer vertices. A maximum profit tour must be constructed on a subset of the facility vertices. Profit is computed through an attraction function: every visited facility vertex attracts a portion of the profit from the customer vertices based on the distance between the facility and customer vertices, and the attractiveness of the facility vertex. A gravity model is used for computing the profit attraction. The problem is formulated as an integer non-linear program. A linearization is proposed and strengthened through the introduction of valid inequalities, and a branch-and-cut algorithm is developed. A tabu search algorithm is also implemented. Computational results are reported.     

Microdistillation and analysis of volatiles from eight ornamental Salvia taxa

Volatile compounds from seven Salvia species and one interspecific hybrid growing at the Dallas Arboretum and Botanical Garden, Texas, US. Salvia coccinea, S. farinacea, S. greggii, S. leucantha, S. longispicata x farinacea, S. madrensis, S. roemeriana and S. splendens were investigated for their chemical compositions using a microdistillation technique. Volatiles were analyzed by gas chromatography (GC) and gas chromatography-mass spectrometry (GC/MS). One hundred and twenty seven compounds were identified representing 94.3-99.7% of the oils. The major components in each of the seven species were as follows: S. coccinea (Z)-3-hexenal (31%), viridiflorol (19%); S. farinacea 1-octen-3-ol (30%) and (Z)-3-hexenal (23%); S. greggii 1,8-cineole (22%), borneol (17%), camphene (11%) and alpha-pinene (10%); S. leucantha limonene (35%) and alpha-pinene (17%); S. longispicata x farinacea 1-octen-3-ol (50%) and (Z)-3-hexenal (24%); S. madrensis (Z)-3-hexenal (53%); S. roemeriana limonene (49%) and alpha-pinene (20%); and S. splendens (Z)-3-hexenal (36%), 2,5-dimethoxy-p-cymene (19%) and linalool (11%). The microdistillation method was fast, practical and a useful technique that enabled the isolation of the volatiles in samples when only limited quantities were available.     

Essential oil composition, antimicrobial and cytotoxic activities of two endemic Stachys cretica subspecies (Lamiaceae) from Turkey

The chemical compositions of the water-distilled essential oil of Stachys cretica ssp. lesbiaca Rech. fil. and S. cretica ssp. trapezuntica Rech. fil. were determined by GC and GC-MS. Altogether 63 compounds were identified. The sesquiterpene hydrocarbon, germacrene D (20.3% and 12.9% respectively) was the main component identified in both oils. Furthermore, ethanol, light petroleum, dichloromethane, ethyl acetate and n-butanol extracts prepared from the aerial parts of the plants were tested for their antimicrobial activities against six bacterial strains and the yeast Candida albicans. The extracts exhibited no antibacterial activity, but the light petroleum and n-butanolic fractions showed low antifungal activities. Crude ethanolic extracts of the two subspecies were tested for their ability to inhibit the growth of HL-60 and Ishikawa human tumor cell lines. The IC50 values were 100 microg/mL for the HL-60 cell line and 200 microg/mL for the Ishikawa cell line.     

Determination of brominated phenols in water samples by on-line coupled isotachophoresis with capillary zone electrophoresis

A method for determination of nine brominated phenols as environmental risk compounds was developed by on-line coupled capillary isotachophoresis and capillary zone electrophoresis (ITP–CZE). For ITP step, 1 × 10⁻² mol L⁻¹ hydrochloric acid with 3 × 10⁻² mol L⁻¹ ammediol pH 9.1 was used as the leading electrolyte, and 3 × 10⁻² mol L⁻¹ β-alanine with 2 × 10⁻² mol L⁻¹ sodium hydroxide pH 10.05 was used as the terminating electrolyte. As the background electrolyte for CZE separation, 2.5 × 10⁻² mol L⁻¹ β-alanine with 2.5 × 10⁻² mol L⁻¹ lysine pH 9.6 was used. All electrolytes contained 0.05% or 0.1% (m/v) hydroxyethylcellulose to suppress the electroosmotic flow. UV detection at wavelength 220 nm was used. Detection limits in order of tens of nmol L⁻¹ were achieved. Good repeatability of migration times (less than 0.33% RSD) and good repeatability of peak areas (less than 7.19% RSD) at concentration level 5 × 10⁻⁸ mol L⁻¹ were observed. Developed ITP–CZE method was applied to determination of brominated phenols in spiked tap and river water samples.