On the flow numbers of signed complete and complete bipartite graphs

We determine the flow numbers of signed complete and signed complete bipartite graphs.     

A robust linearization scheme for nonlinear diffusion in type-II superconductors

We study a nonlinear partial differential equation strongly motivated by the modelling of processes in type-II superconductors in a bounded domain along with appropriate boundary condition. We design a robust and efficient linear approximation scheme based on fix-point principle. The convergence of approximations to a weak solution of the original problem is proved. We also present some numerical examples to show the efficiency of the proposed method.     

Simultaneous Derivatization and Dispersive Liquid–Liquid Microextraction for Fatty Acid GC Determination in Water

Simultaneous derivatization and dispersive liquid–liquid microextraction technique for gas chromatographic determination of fatty acids in water samples is presented. One hundred microlitre of ethanol:pyridine (4:1) were added to 4 mL aqueous sample. Then a solution containing 0.960 mL of acetone (disperser solvent), 10 μL of carbon tetrachloride (extraction solvent) and 30 μL of ethyl chloroformate (derivatization reagent) were rapidly injected into the aqueous sample. After centrifugation, 1 μL sedimented phase with the analytes was analyzed by gas chromatography. The effects of extraction solvent type, derivatization, extraction, and disperser solvents volume, extraction time were investigated. The calibration graphs were linear up to 10 mg L^?1 for azelaic acid (R ² = 0.998) and up to 1 mg L^?1 for palmitic and stearic acids (R ² = 0.997). The detection limits were 14.5, 0.67 and 1.06 μg L^?1 for azelaic, palmitic, and stearic acids, respectively. Repeatabilities of the results were acceptable with relative standard deviations (RSD) up to 13%. A possibility to apply the proposed method for fatty acids determination in tap, lake, sea, and river water was demonstrated.     

Infinitely Many Hypohamiltonian Cubic Graphs of Girth 7

The trivalent Coxeter graph of order 28 is the only known hypohamiltonian cubic graph of girth 7. In this paper we will construct an infinite family of hypohamiltonian cubic graphs of girth 7 and cyclic connectivity 6. The existence of cyclically 7-edge-connected hypohamiltonian cubic graphs other than the Coxeter graph, however, remains open.     

Exact solution of 3D Timoshenko beam problem: problem-dependent formulation

Problem-dependent interpolation functions for displacements and rotations are obtained from the exact analytical solution of the 3D Timoshenko beam problem by introducing a full set of boundary conditions. The developed methodology allows us to derive a new solution that coincides with the classical result of the engineering beam theory. In addition, the proposed interpolation enables exact strain recovery at any point within the problem domain.     

Shorter signed circuit covers of graphs

A signed circuit is a minimal signed graph (with respect to inclusion) that admits a nowhere-zero flow. We show that each flow-admissible signed graph on edges can be covered by signed circuits of total length at most , improving a recent result of Cheng et al. To obtain this improvement, we prove several results on signed circuit covers of trees of Eulerian graphs, which are connected signed graphs such that removing all bridges results in a collection of Eulerian graphs.     

Anion-free bambus[6]uril and its supramolecular properties

Methods for the preparation of anion-free bambus[6]uril (BU6) are presented. They are based on the oxidation of iodide anion, which is bound inside the macrocycle, utilizing dark oxidation by hydrogen peroxide or photooxidation in the presence of titanium dioxide. Anion-free BU6 was found to be insoluble in any of the investigated solvents; however, it dissolves in methanol/chloroform (1:1) or acetonitrile/water (1:1) mixtures in the presence of the tetrabutylammonium salt of a suitable anion. The association constants with halide ions, BF(4)(-), NO(3)(-), and CN(-), were measured by (1)H NMR spectroscopy. The highest association constant (8.9×10(5) M(-1)) was found for the 1:1 complex of BU6 with I(-) in acetonitrile/water mixture. A number of crystal structures of BU6 complexes with various anions were obtained. The influence of the anion size on the macrocycle diameter is discussed together with an unusual arrangement of the macrocycles into separate layers.     

Nowhere‐Zero Flows on Signed Complete and Complete Bipartite Graphs

Bouchet's conjecture asserts that each signed graph which admits a nowhere‐zero flow has a nowhere‐zero 6‐flow. We verify this conjecture for two basic classes of signed graphs—signed complete and signed complete bipartite graphs by proving that each such flow‐admissible graph admits a nowhere‐zero 4‐flow and we characterise those which have a nowhere‐zero 2‐flow and a nowhere‐zero 3‐flow.     

On the strong circular 5‐flow conjecture

The Strong Circular 5‐flow Conjecture of Mohar claims that each snark—with the sole exception of the Petersen graph—has circular flow number smaller than 5. We disprove this conjecture by constructing an infinite family of cyclically 4‐edge connected snarks whose circular flow number equals 5. © 2006 Wiley Periodicals, Inc. J Graph Theory