On the directed Full Degree Spanning Tree problem

We study the parameterized complexity of a directed analog of the Full Degree Spanning Tree problem where, given a digraph $D$ and a nonnegative integer $k$, the goal is to construct a spanning out-tree $T$ of $D$ such that at least $k$ vertices in $T$ have the same out-degree as in $D$. We show that this problem is W[1]-hard even on the class of directed acyclic graphs. In the dual version, called Reduced Degree Spanning Tree, one is required to construct a spanning out-tree $T$ such that at most $k$ vertices in $T$ have out-degrees that are different from that in $D$. We show that this problem is fixed-parameter tractable and that it admits a problem kernel with at most $8k$ vertices on strongly connected digraphs and $O\left(k^2\right)$ vertices on general digraphs. We also give an algorithm for this problem on general digraphs with running time $O(5.942^k?n^{O\left(1\right)})$, where $n$ is the number of vertices in the input digraph.     

Rhodamine-Based Cu2+ -Selective Fluorosensor: Synthesis, Mechanism, and Application in Living Cells

A rhodamine B-based fluorescence probe (1) for the sensitive and selective detection of Cu²⁺ ion has been designed and synthesized using pyridine moiety. The optical properties of this compound have been investigated in acetonitrile-water binary solution (7:3 v/v). Compound 1 is found to be an excellent sensor for a biologically/physiologically very important transition metal ion (Cu²⁺) using only the two very different modes of measurements (absorption and emission); one case displayed intensity enhancement whereas in other case showed intensity depletion (quenching). A mechanistic investigation has been performed to explore the static nature of quenching process. The sensor has been found to be very effective in sensing Cu²⁺ ion inside living cells also.     

Self-assembling two-dimensional nanophotonic arrays for reflectivity-based sensing

We propose a nanoplasmonic platform that can be used for sensing trace levels of heavy metals in solutions via simple optical reflectivity measurements. The considered example is a lead sensor, which relies on the lead-mediated assembly of glutathione-functionalized gold nanoparticles (NPs) at a self-healing water/DCE liquid | liquid interface (LLI). Capillary forces tend to trap each NP at the LLI while the negatively charged ligands prevent the NPs settling too close to each other. In the presence of lead, due to chelation between the lead ion and glutathione ligand, the NPs assemble into a dense quasi-2D interfacial array. Such a dense assembly of plasmonic NPs can generate a remarkable broad-band reflectance signal, which is absent when NPs are adsorbed at the interface far apart from each other. The condensing effect of the LLI and the plasmonic coupling effect among the NP array gives rise to a dramatic enhancement of the reflectivity signals. Importantly, we show that our theory of the optical reflectivity from such an array of NPs works in perfect harmony with the physics and chemistry of the system with the key parameter being the interparticle distance at the interface. As a lead sensor, the system is fast, stable, and can achieve detection limits down to 14 ppb. Future alternative recognizing ligands can be used to build sister platforms for detecting other heavy metals.

We propose a nanoplasmonic platform that can be used for sensing trace levels of heavy metals in solutions via simple optical reflectivity measurements at the liquid–liquid interface.     

The queue length distributions in the finite buffer bulk-service MAP/G/1 queue with multiple vacations

We consider a finite buffer batch service queueing system with multiple vacations wherein the input process is Markovian arrival process (MAP). The server leaves for a vacation as soon as the system empties and is allowed to take repeated (multiple) vacations. The service- and vacation- times are arbitrarily distributed. We obtain the queue length distributions at service completion, vacation termination, departure, arbitrary and pre-arrival epochs. Finally, some performance measures such as loss probability, average queue lengths are discussed. Computational procedure has been given when the service- and vacation- time distributions are of phase type (PH-distribution).     

On quasi-transitive semigroup actions

A semigroup S acts quasi-transitively on a space X if the orbits form a partition of X. Some results are proved giving characterisations of normal quasi-transitive acts and quasi-transitive acts for which the action maps satisfy various other conditions. Finally a result concerning the effect of quasi-transitive action by a continuum semigroup on a subspace of the plane is proved.     

Altered phase model for polymer clay nanocomposites

This paper describes a multiscale approach used to model polymer clay nanocomposites (PCNs) based on a new altered phase concept. Constant-force steered molecular dynamics (SMD) is used to evaluate nanomechanical properties of the constituents of intercalated clay units in PCNs, which were used in the finite element model. Atomic force microscopy and nanoindentation techniques provided additional input to the finite element method (FEM) model. FEM is used to construct a representative PCN model that simulates the composite response of intercalated clay units and the surrounding polymer matrix. From our simulations we conclude that, in order to accurately predict mechanical response of PCNs, it is necessary to take into account the molecular-level interactions between constituents of PCN, which are responsible for the enhanced nanomechanical properties of PCNs. This conclusion is supported by our previous finding that there is a change in crystallinity of polymeric phase due to the influence of intercalated clay units. The extent of altered polymeric phase is obtained from observations of a zone of the altered polymeric phase surrounding intercalated clay units in the "phase image" of PCN surface, obtained using an atomic force microscope (AFM). An accurate FEM model of PCN is constructed that incorporates the zone of the altered polymer. This model is used to estimate elastic modulus of the altered polymer. The estimated elastic modulus for the altered polymer is 4 to 5 times greater than that of pure polymer. This study indicates that it is necessary to take into account molecular interactions between constituents in nanocomposites due to the presence of altered phases, and furthermore provides us with a new direction for the modeling and design of nanocomposites.     

Kinetics and mechanism of O-O bond cleavage in the reaction of [RuIII(edta)(H2O)]- with hydroperoxides in aqueous solution

The reactions of [Ru(III)(edta)(H(2)O)](-) (1) (edta = ethylenediaminetetraacetate) with tert-butylhydroperoxide ((t)BuOOH) and potassium hydrogenpersulfate (KHSO(5)) were studied kinetically as a function of oxidant concentration and temperature (10-30 degrees C) at a fixed pH of 6.1 using stopped-flow techniques. Kinetic results were analyzed by using global kinetic analysis techniques. The reaction was found to consist of two steps involving the rapid formation of a [Ru(III)(edta)(OOR)](2-) intermediate, which subsequently undergoes heterolytic cleavage to form [(edta)Ru(V)=O](-). Since [(edta)Ru(V)=O](-) was produced almost quantitatively in the reaction of 1 with the hydroperoxides (t)BuOOH and KHSO(5), the common mechanism is one of heterolytic scission of the O-O bond. The water soluble and easy to oxidize substrate 2,2'-azobis(3-ethylbenzithiazoline-6-sulfonate (ABTS), was employed to substantiate the mechanistic proposal. Reactions were carried out under pseudo-first order conditions for [ABTS] > [hydroperoxide] > [1], and were monitored as a function of time for the formation of the one-electron oxidation product ABTS (*+). The detailed suggested mechanism is consistent with the reported rate and activation parameters, and discussed in reference to the results reported for the reaction of [Ru(II)(edta)(H(2)O)](-) with H(2)O(2).     

SPM induced limitations for 40 Gbps chirped Gaussian pulses in optical channel

An analysis of self-phase modulation (SPM) induced nonlinearities in a 40 Gbps link with chirped Gaussian pulses of different duty cycles has been reported in this paper. In the present analysis only SPM effect has been considered to control the pulse propagation behavior through the fiber by appropriate selection of pulse width, peak power and channel length to suppress the other channel impairments caused by group velocity dispersion (GVD) and third order dispersion (TOD). The effect of SPM on the Q-factor for the transmission of 40 Gbps chirped pulses with different initial pulse widths and input peak powers has been investigated. It has been observed that a wider pulse having maximum negative chirp can withstand the nonlinear effect of SPM for relatively higher ranges of input peak power.     

Redox‐Active Metal–Organic Frameworks: Highly Stable Charge‐Separated States through Strut/Guest‐to‐Strut Electron Transfer

Molecular organization of donor and acceptor chromophores in self‐assembled materials is of paramount interest in the field of photovoltaics or mimicry of natural light‐harvesting systems. With this in mind, a redox‐active porous interpenetrated metal–organic framework (MOF), {[Cd(bpdc)(bpNDI)] ? 4.5 H₂O ? DMF}_n ( 1 ) has been constructed from a mixed chromophoric system. The μ‐oxo‐bridged secondary building unit, {Cd₂(μ‐OCO)₂}, guides the parallel alignment of bpNDI (N,N′‐di(4‐pyridyl)‐1,4,5,8‐naphthalenediimide) acceptor linkers, which are tethered with bpdc (bpdcH₂=4,4′‐biphenyldicarboxylic acid) linkers of another entangled net in the framework, resulting in photochromic behaviour through inter‐net electron transfer. Encapsulation of electron‐donating aromatic molecules in the electron‐deficient channels of 1 leads to a perfect donor–acceptor co‐facial organization, resulting in long‐lived charge‐separated states of bpNDI. Furthermore, 1 and guest encapsulated species are characterised through electrochemical studies for understanding of their redox properties.     

Dynamic Entangled Porous Framework for Hydrocarbon (C2–C3) Storage,CO2 Capture,and Separation

Storage and separation of small (C1–C3) hydrocarbons are of great significance as these are alternative energy resources and also can be used as raw materials for many industrially important materials. Selective capture of greenhouse gas, CO₂ from CH₄ is important to improve the quality of natural gas. Among the available porous materials, MOFs with permanent porosity are the most suitable to serve these purposes. Herein, a two‐fold entangled dynamic framework {[Zn₂(bdc)₂(bpNDI)]?4DMF}_n with pore surface carved with polar functional groups and aromatic π clouds is exploited for selective capture of CO₂, C2, and C3 hydrocarbons at ambient condition. The framework shows stepwise CO₂ and C₂H₂ uptake at 195 K but type I profiles are observed at 298 K. The IAST selectivity of CO₂ over CH₄ is the highest (598 at 298 K) among the MOFs without open metal sites reported till date. It also shows high selectivity for C₂H₂, C₂H₄, C₂H₆, and C₃H₈ over CH₄ at 298 K. DFT calculations reveal that aromatic π surface and the polar imide (RNC=O) functional groups are the primary adsorption sites for adsorption. Furthermore, breakthrough column experiments showed CO₂/CH₄ C₂H₆/CH₄ and CO₂/N₂ separation capability at ambient condition.