On Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs

A defining set of a t-(v, k, λ) design is a partial design which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given t-design. The complete list of minimal defining sets of 2-(6, 3, 6) designs, 2-(7, 3, 4) designs, the full 2-(7, 3, 5) design, a 2-(10, 4, 4) design, 2-(10, 5, 4) designs, 2-(13, 3, 1) designs, 2-(15, 3, 1) designs, the 2-(25, 5, 1) design, 3-(8, 4, 2) designs, the 3-(12, 6, 2) design, and 3-(16, 8, 3) designs are given to illustrate the efficiency of the algorithm. Also, corrections to the literature are made for the minimal defining sets of four 2-(7, 3, 3) designs, two 2-(6, 3, 4) designs and the 2-(21, 5, 1) design. Moreover, an infinite class of minimal defining sets for 2-((v) || 3){v\choose3} designs, where v ≥ 5, has been constructed which helped to show that the difference between the sizes of the largest and the smallest minimal defining sets of 2-((v) || 3){v\choose3} designs gets arbitrarily large as v → ∞. Some results in the literature for the smallest defining sets of t-designs have been generalized to all minimal defining sets of these designs. We have also shown that all minimal defining sets of t-(2n, n, λ) designs can be constructed from the minimal defining sets of their restrictions when t is odd and all t-(2n, n, λ) designs are self-complementary. This theorem can be applied to 3-(8, 4, 3) designs, 3-(8, 4, 4) designs and the full 3-(8 || 4)3-{8 \choose 4} design using the previous results on minimal defining sets of their restrictions. Furthermore we proved that when n is even all (n − 1)-(2n, n, λ) designs are self-complementary.     

Endogenous reference points in bargaining

We allow the reference point in (cooperative) bargaining problems with a reference point to be endogenously determined. Two loss averse agents simultaneously and strategically choose their reference points, taking into consideration that with a certain probability they will not be able to reach an agreement and will receive their disagreement point outcomes, whereas with the remaining probability an arbitrator will distribute the resource by using (an extended) Gupta–Livne bargaining solution (Gupta and Livne in Manag Sci 34:1303–1314, 1988). The model delivers intuitive equilibrium comparative statics on the breakdown probability, the loss aversion coefficients, and the disagreement point outcomes.     

No fluctuation approximation in any desired precision for univariate function matrix representations

The operator involving problems are mostly handled by using the matrix representations of the operators over a finite set of appropriately chosen basis functions in a Hilbert space as long as the related problem permits. The algebraic operator which multiplies its operand by a function is the focus of this work. We deal with the univariate case for simplicity. We show that a rapidly converging scheme can be constructed by defining an appropriate fluctuation operator which projects, in fact, to the complement of the space spanned by appropriately chosen finite number of basis functions. What we obtain here can be used in efficient numerical integration also.     

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.     

Bacterial cellulose films with controlled microstructure–mechanical property relationships

Bacterial cellulose (BC) films with different porosities have been developed in order to obtain improved mechanical properties. After 13 days of incubation of Gluconobacter xylinum bacteria in static culture, BC pellicles have been set. BC films have been compression molded after water dispersion of BC pellicles and filtration by applying different pressures (10, 50, and 100 MPa) to obtain films with different porosities. Tensile behavior has been analyzed in order to discuss the microstructure–property relationships. Compression pressure has been found as an important parameter to control the final mechanical properties of BC films where slightly enhanced tensile strength and deformation at break are obtained increasing mold compression pressure, while modulus also increases following a nearly linear dependence upon film porosity. This behavior is related to the higher densification by increasing mold compression pressure that reduces the interfibrillar space, thus increasing the possibility of interfibrillar bonding zones. Network theories have been applied to relate film elastic properties with individual nanofiber properties.     

The static bike relocation problem with multiple vehicles and visits

This paper introduces the static bike relocation problem with multiple vehicles and visits, the objective of which is to rebalance at minimum cost the stations of a bike sharing system using a fleet of vehicles. The vehicles have identical capacities and service time limits, and are allowed to visit the stations multiple times. We present an integer programming formulation, implemented under a branch-and-cut scheme, in addition to an iterated local search metaheuristic that employs efficient move evaluation procedures. Results of computational experiments on instances ranging from 10 to 200 vertices are provided and analyzed. We also examine the impact of the vehicle capacity and of the number of visits and vehicles on the performance of the proposed algorithms.     

Chemometrical Interpretation of Lake Waters after their Chemical Analysis by Using Aas,Flame Photometry and Titrimetric Techniques

This article reports the distribution of trace metals and major ions in lake waters of Sultansazl L < L , a reedfield near Kayseri, Turkey. The determination of elements such as Cr, Ni, Cu, Cd and Pb in lake water samples was performed by AAS after a preconcentration step using a column packed with Amberlite XAD-16 resin. Both flame- and graphite furnace-atomic absorption spectrometry was used to determine these metals in lake water samples. The concentrations of the metals bound to humic substances, and free metal ions were determined after their sorption-elution on the resin, separately. The column method optimized with sodium tetraborate reagent was used in determining the free metal ions. In the determinations of Ca²⁺ and Mg²⁺, K⁺ , and SO2-4 , Cl ^m and total hardness, flame atomic absorption spectrometry, flame photometry, and titrimetry were used, respectively. In order to evaluate the analytical data by multivariate statistical techniques which enable feature reduction and grouping of the pollutant sources in lake waters from their chemical composition, principal component analysis (PCA), cluster analysis (CA) and correlation analysis were used. As a consequence of multivariate statistical evaluation, main anthropogenic sources like traffic, industry and agricultural processes were drawn to be responsible from the pollution in the environment investigated.