On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

Imidazolium Based Surface Active Ionic Liquids as Novel Micellar Media for Simultaneous and Sensitive Electrochemical Detection of Dopamine and Ascorbic Acid

Surface active ionic liquid (SAIL) micelle assisted, simultaneous and highly sensitive electrochemical sensing of dopamine (DA) and ascorbic acid (AA) is presented. Results presented herein establish that SAILs viz.1‐dodecyl‐3‐methyl imidazolium chloride ([DDMIM][Cl]), 1‐octyl‐3‐methyl imidazolium chloride ([OMIM][Cl]) and 1‐butyl‐3‐methyl imidazolium chloride ([BMIM][Cl]) exhibit a probe and SAIL nature/concentration specific impact on the redox behaviour of hydroquinone (H₂Q), dopamine (DA) and ascorbic acid (AA). To our observations, the electrochemical behaviour of DA and AA is affected oppositely by SAILs with the apparent effects being more appreciable in presence of [DDMIM][Cl]. In the presence of [DDMIM][Cl] micelles, the electro‐oxidation of AA was observed to occur at potentials about 350 mV less positive than required for electrooxidation of DA, an important advantage that minimises the interference of former in sensing of the later. The peak to peak potential separation of 350 mV observed in presence of [DDMIM][Cl] micelles is the largest to be reported so far. The DPV signal for DA and AA displayed a linear response in the concentration range of 6.6 to 99.9 μM and 6.6 to 131.5 μM respectively. Very low detection limits of 0.0161 μM for DA in presence of 39.8 μM AA and 0.0227 μM for AA in presence of 39.8 μM DA were estimated in micellar phase of [DDMIM][Cl].     

Opinion dynamics in networks with heterogeneous confidence and influence

We propose a discrete-time model of opinion dynamics. The neighborhood relationship is decided by confidence radius and influence radius of each agent. We investigate the influence of heterogeneity in confidence/influence distribution on the behavior of the network. The simulations suggest that the heterogeneity of single confidence or influence networks can promote the opinions to achieve consensus. It is shown that the heterogeneous influence radius systems converge in fewer time steps and more often in finite time than the heterogeneous confidence radius systems. We find that heterogeneity does not always promote consensus, and there is an optimal heterogeneity so that the relative size of the largest consensus cluster reaches maximum in heterogeneous confidence and influence networks.     

Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.      

The Formation of Luminescent Supramolecular Ternary Complexes in Water: Delayed Luminescence Sensing of Aromatic Carboxylates Using Coordinated Unsaturated Cationic Heptadentate Lanthanide Ion Complexes

The synthesis of four lanthanide ion complexes Eu?1, Eu?2, Tb?1 and Tb?2, from the heptadentate tri-arm cyclen (1,4,7,10-tetraazacyclododecane) ligands 1 and 2 that were made in one-pot syntheses is described. These coordinatively unsaturated complexes have two labile metal-bound water molecules, as demonstrated by X-ray crystallography. This was also confirmed by evaluating their hydration state (q～2) by measuring their lifetimes in D²O and H²O, respectively. The above complexes were all designed as being “photophysically silent” prior to the recognition of the anion, since they do not possess antenna that can participate in sensitisation of the Eu(III) or the Tb(III) excited state. However, the two water molecules can be displaced upon anion binding by the appropriate aromatic carboxylates to give ternary complexes in water, through either four- or six-member ring chelates (q～0), or possibly via a monodentate binding. In the case of Tb?1 and Tb?2, large luminescence enhancements were observed upon the formation of such ternary complexes with N,N-dimethylaminobenzoic acid at ambient pH. Such binding and luminescent enhancements were also observed for Tb?1 in the presence of salicylic acid. On all occasions, the anion recognition “switched” the emission “on” over two logarithmic units. At higher concentrations, the emission is reduced possibly due to quenching. In the case of aspirin, the binding was too weak to be measured, indicating that Tb?1 selectively detects salicylic acid, the active form of aspirin in water. In the case of Eu?1 and Eu?2, the affinity of these complexes towards such aromatic carboxylates was too weak for efficient ternary complex formation.     

Responsive polymers for analytical applications: A review

Stimuli-responsive polymers are capable of translating changes in their local environment to changes in their chemical and/or physical properties. This ability allows stimuli-responsive polymers to be used for a wide range of applications. In this review, we highlight the analytical applications of stimuli-responsive polymers that have been published over the past few years with a focus on their applications in sensing/biosensing and separations. From this review, we hope to make clear that while the history of using stimuli-responsive polymers for analytical applications is rich, there are still a number of directions to explore and exciting advancements to be made in this flourishing field of research.     

Scaling in Electrical Conductivity Measurements and Rheological Measurements of Monarch 700 Dispersions Stabilized by Polymers

For making stable dispersions of graphitic carbon black (Monarch 700), the effectiveness of three dispersants/polymers (hypermer LP1, hypermer B246, and OLOA 11000) in xylene is investigated. Hypermer LP1 (polyhydroxystearic acid) is a homopolymer and hypermer B246 (PEG 30-dipolyhydroxystearate) is a polyhydroxystearic acid/polyethylene oxide/polyhydroxystearic acid ABA block copolymer, while OLOA 11000 (polyisobutylene succinimide) has a polar head group (polyamine) attached to a hydrocarbon chain (polyisobutylene). Well-dispersed graphitic carbon black dispersions were prepared using dispersants at optimum concentrations. Percolation threshold and rheological threshold were determined by analyzing the variations in electrical conductivity and elastic modulus with concentration of carbon black. Above threshold concentration, scaling law was applied to experimental data of rheology (dynamic measurements) and electrical conductivity measurements to evaluate quality of the system. Effectiveness of polymers was investigated on the basis of value of critical exponent (t and t′, respectively) in scaling power law. Hypermer LP1 was proved to be a poor dispersant for Monarch 700 dispersions while other two polymers were found to be effective stabilizers.