Remote sensing of pollutants using femtosecond laser pulse fluorescence spectroscopy

The fluorescence spectrum of ethanol molecules induced by femtosecond laser pulses has been recorded as the fingerprint of the molecules. It was demonstrated that, if this is combined with a LIDAR technique, the fluorescence from pollutants in the atmosphere could be detected over a long distance. PACS 42.68.Wt; 42.62.Fi; 42.65.Re     

Synthesis of methacrylate derivatives oligomers by dithiobenzoate‐RAFT‐mediated polymerization

Reversible addition fragmentation chain transfer (RAFT) was used to synthesize methacrylic acid oligomers and oligo(methacrylic acid)‐b‐poly(methyl methacrylate) (PMAA‐b‐PMMA) with targeted degree of polymerization ≈ 10. Characterization is by size‐exclusion chromatography (SEC) and electrospray mass‐spectrometry. SEC data are presented as hydrodynamic volume distributions (HVDs), the only proper means to present comparative and meaningful SEC data when there is no unique relationship between size and molecular weight. The RAFT agent, (4‐cyanopentanoic acid)‐4‐dithiobenzoate (CPADB), produced dithiobenzoic acid as a side product during the polymerization of methacrylate derivatives. Precipitation in diethyl ether proved to be an easy way to remove this impurity from the PMAA‐RAFT oligomers. Both unpurified and purified macro‐RAFT agent were used to prepare amphiphilic PMAA‐b‐PMMA copolymers. Diblock copolymer prepared from the purified PMAA homopolymer had a narrower HVD in comparison to those obtained from the equivalent unpurified macro‐RAFT agent. This work shows that while cyanoisopropyl‐dithiobenzoate or CPADB are good RAFT agents for methacrylate derivatives, they exhibit some instability under typical polymerization conditions, and thus when oligomers are targeted, optimal control requires checking for the degradation product and appropriate purification steps when necessary (the same effect is present for larger polymers but is unimportant). © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2277–2289, 2008     

A perturbed hard-sphere equation of state extended to imidazolium-based ionic liquids

A perturbed hard-sphere equation of state (EOS) has been previously employed to predict pressure–volume–temperature properties of some ionic liquids (ILs) with phosphonium-, pyridinium-, and pyrrolidinium cations. In this work, we have extended the considered EOS to another class of ILs in compressed states. This class consists of 14 imidazolium-based ILs. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 0.1 to 200 MPa. From 1,122 data points examined for the aforementioned ILs, the total average absolute deviation was found to be 1.05%.     

Fourth power diophantine equations in Gaussian integers

In this paper, we examine a class of fourth power diophantine equations of the form \(x^4+kx^2y^2+y^4=z^2\) and \(ax^4+by^4=cz^2\), in the Gaussian integers, where a and b are prime integers.     

Characterization of solution sets of convex optimization problems in Riemannian manifolds

Archiv der Mathematik - In this paper, a characterization of the solution sets of convex smooth optimization programmings on Riemannian manifolds, in terms of the Riemannian gradients of the cost...     

Multiplicatively and non-symmetric multiplicatively norm-preserving maps

Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖ _X and ‖.‖ _Y denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖ _Y = ‖fg‖ _X , for certain elements f and g in the domain. Then we show that if α ∈ ℂ {0} and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖ _X = ‖Tf Tg + α‖ _Y , f,g ∈ A, then T is injective and there exist a homeomorphism φ: c(B) → c(A) between the Choquet boundaries of B and A, an invertible element η ∈ B with η(Y) ⊆ {1, −1} and a clopen subset K of c(B) such that for each f ∈ A,

Maximum flow problem on dynamic generative network flows with time-varying bounds

This paper considers a new class of network flows, called dynamic generative network flows in which, the flow commodity is dynamically generated at a source node and dynamically consumed at a sink node and the arc-flow bounds are time dependent. Then the maximum dynamic flow problem in such networks for a pre-specified time horizon T is defined and mathematically formulated in both arc flow and path flow presentations. By exploiting the special structure of the problem, an efficient algorithm is developed to solve the general form of the dynamic problem as a minimum cost static flow problem.     

Nonsmooth Optimization Techniques on Riemannian Manifolds

We present the notion of weakly metrically regular functions on manifolds. Then, a sufficient condition for a real valued function defined on a complete Riemannian manifold to be weakly metrically regular is obtained, and two optimization problems on Riemannian manifolds are considered. Moreover, we present a generalization of the Palais–Smale condition for lower semicontinuous functions defined on manifolds. Then, we use this notion to obtain necessary conditions of optimality for a general minimization problem on complete Riemannian manifolds.     

Klein Gordon Oscillators in Commutative and Noncommutative Phase Space with Psudoharmonic Potential in the Presence and Absence Magnetic Field

We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in the absence of magnetic field. In this work, we obtain energy spectrum and wave function in different situations by NU method so we show our results in tables.