On almost self-complementary graphs

A graph is called almost self-complementary if it is isomorphic to one of its almost complements X^c-I, where X^c denotes the complement of X and I a perfect matching (1-factor) in X^c. Almost self-complementary circulant graphs were first studied by Dobson and Šajna [Almost self-complementary circulant graphs, Discrete Math. 278 (2004) 23-44]. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In particular, we give necessary and sufficient conditions on the order of an almost self-complementary regular graph, and construct infinite families of almost self-complementary regular graphs, almost self-complementary vertex-transitive graphs, and non-cyclically almost self-complementary circulant graphs.     

On non‐Newtonian incompressible fluids with phase transitions

A modified model for a binary fluid is analysed mathematically. The governing equations of the motion consists of a Cahn–Hilliard equation coupled with a system describing a class of non‐Newtonian incompressible fluid with p‐structure. The existence of weak solutions for the evolution problems is shown for the space dimension d=2 with p? 2 and for d=3 with p? 11/5. The existence of measure‐valued solutions is obtained for d=3 in the case 2? p< 11/5. Similar existence results are obtained for the case of nondifferentiable free energy, corresponding to the density constraint |ψ| ? 1. We also give regularity and uniqueness results for the solutions and characterize stable stationary solutions. Copyright © 2006 John Wiley & Sons, Ltd.     

Excess thermodynamics properties of propyl propanoate+hexane+cyclohexane at 298.15 K

Summary In this paper we present excess molar volumes and excess molar enthalpies of binary and ternary mixtures containing propyl propanoate, hexane and cyclohexane as components at 298.15 K. Excess molar volumes were calculated from the density of the pure liquids and mixtures. The density was measured using an Anton Paar DMA 60/602 vibrating-tube densimeter. Excess molar enthalpies were obtained using a Calvet microcalorimeter     

Operators which have a closed quasi-nilpotent part

We find several conditions for the quasi-nilpotent part of a bounded operator acting on a Banach space to be closed. Most of these conditions are established for semi-Fredholm operators or, more generally, for operators which admit a generalized Kato decomposition. For these operators the property of having a closed quasi-nilpotent part is related to the so-called single valued extension property.

     

Nonuniqueness of equilibrium states for axisymmetric elastic shells in tension

The problem of nonuniqueness of static axisymmetric solutions for a non-linearly elastic cylindrical shell in which the ends are pulled apart with a constant traction while retaining the radii of its ends fixed is studied. In the elastic case, we prove the existence of buckled states and the possibility of necking. In the hyperelastic case a global existence and nonuniqueness theorem is proved, via the energy criterion.     

Printable Bioelectronics To Investigate Functional Biological Interfaces

Thin‐film transistors can be used as high‐performance bioelectronic devices to accomplish tasks such as sensing or controlling the release of biological species as well as transducing the electrical activity of cells or even organs, such as the brain. Organic, graphene, or zinc oxide are used as convenient printable semiconducting layers and can lead to high‐performance low‐cost bioelectronic sensing devices that are potentially very useful for point‐of‐care applications. Among others, electrolyte‐gated transistors are of interest as they can be operated as capacitance‐modulated devices, because of the high capacitance of their charge double layers. Specifically, it is the capacitance of the biolayer, being lowest in a series of capacitors, which controls the output current of the device. Such an occurrence allows for extremely high sensitivity towards very weak interactions. All the aspects governing these processes are reviewed here.     

Direct On‐Surface Patterning of a Crystalline Laminar Covalent Organic Framework Synthesized at Room Temperature

We report herein an efficient, fast, and simple synthesis of an imine‐based covalent organic framework (COF) at room temperature (hereafter, RT‐COF‐1 ). RT‐COF‐1 shows a layered hexagonal structure exhibiting channels, is robust, and is porous to N₂ and CO₂. The room‐temperature synthesis has enabled us to fabricate and position low‐cost micro‐ and submicropatterns of RT‐COF‐1 on several surfaces, including solid SiO₂ substrates and flexible acetate paper, by using lithographically controlled wetting and conventional ink‐jet printing.