A New Fluorescent Sensor Based on 1H-pyrazolo[3,4-b]quinoline Skeleton. Part 2

A novel fluorescent dye bis-(pyridin-2-yl-methyl)-(1,3,4-triphenyl-1H-pyrazolo[3,4-b]quinolin-6-ylmethyl)-amine (P1) has been synthesized and investigated by means of steady state and time-resolved fluorescence techniques. This compound acts as sensor for fluorescence detection of small inorganic cations (lithium, sodium, barium, magnesium, calcium, and zinc) in highly polar solvents such as acetonitrile. The mechanism which allows application of this compound as sensor is an electron transfer from the electron-donative part of molecule (amine) to the acceptor part (pyrazoloquinoline derivative), which is retarded upon complexation of the electro-donative part by inorganic cations. The binding constants are strongly dependent on the charge density of the analyzed cations. The 2/1 complexes of P1 with Zn(++) and Mg(++) cations posses large binding constants. Moreover, in the presence of these cations a significant bathochromic shift of fluorescence is observed. The most probable explanation of such behaviour is the formation of intramolecular excimer. This is partially supported by the quantum chemical calculations.     

On-Line Dimension for Posets Excluding Two Long Incomparable Chains

For a positive integer k, let k?+?k denote the poset consisting of two disjoint k-element chains, with all points of one chain incomparable with all points of the other. Bosek, Krawczyk and Szczypka showed that for each k?≥?1, there exists a constant c _k so that First Fit will use at most $c_kw^2$ chains in partitioning a poset P of width at most w, provided the poset excludes k?+?k as a subposet. This result played a key role in the recent proof by Bosek and Krawczyk that O(w ^16logw ) chains are sufficient to partition on-line a poset of width w into chains. This result was the first improvement in Kierstead’s exponential bound: (5 ^w ???1)/4 in nearly 30 years. Subsequently, Joret and Milans improved the Bosek–Krawczyk–Szczypka bound for the performance of First Fit to 8(k???1)² w, which in turn yields the modest improvement to O(w ^14logw ) for the general on-line chain partitioning result. In this paper, we show that this class of posets admits a notion of on-line dimension. Specifically, we show that when k and w are positive integers, there exists an integer t?=?t(k,w) and an on-line algorithm that will construct an on-line realizer of size t for any poset P having width at most w, provided that the poset excludes k?+?k as a subposet.     

Computing the Longest Previous Factor

The Longest Previous Factor   array gives, for each position i$i$ in a string y$y$, the length of the longest factor (substring) of y$y$ that occurs both at i$i$ and to the left of i$i$ in y$y$. The Longest Previous Factor array is central in many text compression techniques as well as in the most efficient algorithms for detecting motifs and repetitions occurring in a text. Computing the Longest Previous Factor array requires usually the Suffix Array and the Longest Common Prefix array. We give the first time–space optimal algorithm that computes the Longest Previous Factor array, given the Suffix Array and the Longest Common Prefix array. We also give the first linear-time algorithm that computes the permutation that applied to the Longest Common Prefix array produces the Longest Previous Factor array.     

Perfect matchings in random intersection graphs

Let W ₁,??,W _n be independent random subsets of [m]={1,??,m}. Assuming that each W _i is uniformly distributed in the class of d-subsets of?[m] we study the uniform random intersection graph G _s (n,m,d) on the vertex set {W ₁,??W _n }, defined by the adjacency relation: W _i ??W _j whenever |W _i ??W _j |?Rs. For even?n we show that as n,m???? the edge density threshold for the property that G _s (n,m,d) contains a perfect matching is asymptotically the same as that for G _s (n,m,d) being connected.     

Experimental and modeling study on the pyrolysis and oxidation of n-decane and n-dodecane

High pressure n-decane and n-dodecane shock tube experiments were conducted to assist in the development of a Jet A surrogate kinetic model. Jet A is a kerosene based jet fuel composed of hundreds of hydrocarbons consisting of paraffins, olefins, aromatics and naphthenes. In the formulation of the surrogate mixture, n-decane or n-dodecane represent the normal paraffin class of hydrocarbons present in aviation fuels like Jet A. The experimental work on both n-alkanes was performed in a heated high pressure single pulse shock tube. The mole fractions of the stable species were determined using gas chromatography and mass spectroscopy. Experimental data on both n-decane and n-dodecane oxidation and pyrolysis were obtained for temperatures from 867 to 1739 K, pressures from 19 to 74 atm, reaction times from 1.15 to 3.47 ms, and equivalence ratios from 0.46 to 2.05, and ∞. Both n-decane and n-dodecane oxidation showed that the fuel decays through thermally driven oxygen free decomposition at the conditions studied. This observation prompted an experimental and modeling study of n-decane and n-dodecane pyrolysis using a recently submitted revised n-decane/iso-octane/toluene surrogate model. The surrogate model was extended to n-dodecane in order to facilitate the study of the species and the 1-olefin species quantified during the pyrolysis of n-dodecane and n-decane were revised with additional reactions and reaction rate constants modified with rate constants taken from literature. When compared against a recently published generalized n-alkane model and the original and revised surrogate models, the revised (based on our experimental work) and extended surrogate model showed improvements in predicting 1-olefin species profiles from pyrolytic and oxidative n-decane and n-dodecane experiments. The revised and extended model when compared to the published generalized n-alkane and surrogate models also showed improvements in predicting species profiles from flow reactor n-decane oxidation experiments, but similarly predicted n-decane and n-dodecane ignition delay times.     

Theoretical determination of the 1H NMR spectrum of ethanol

GIAO calculations of the ¹H NMR chemical shifts for ethanol at the SCF and DFT levels of theory are presented. The importance of molecular geometry and basis set is discussed. Vibrational correction to the hydroxyl proton chemical shift is also considered in calculations for the monomer of ethanol. The final theoretical results for the monomer obtained at the optimized DFT/B3LYP/6-311G(d,p) geometry with the 6-311G++ (d,p) basis set for NMR are in very good agreement with gas phase experimental data. For the liquid phase ethanol the hydrogen bonding effects are taken into account by performing calculations on various clusters of ethanol. It is shown that inaccuracy due to molecular geometry and basis set in the monomer of ethanol is magnified significantly in calculations for its clusters. In this context the structure of liquid ethanol as predicted recently by quantum cluster equilibrium (QCE) theory is discussed.     

On integrable rational potentials of the Dirac equation

The one-dimensional Dirac equation with a rational potential is reducible to an ordinary differential equation with a Riccati-like coefficient. Its integrability can be studied with the help of differential Galois theory, although the results have to be stated with recursive relations, because in general the equation is of Heun type. The inverse problem of finding integrable rational potentials based on the properties of the singular points is also presented; in particular, a general class of integrable potentials leading to the Whittaker equation is found.     

Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane

We study α-harmonic functions on the complement of the sphere and on the complement of the hyperplane in Euclidean spaces of dimension bigger than one, for α?∈?(1,2). We describe the corresponding Hardy spaces and prove the Fatou theorem for α-harmonic functions. We also give explicit formulas for the Martin kernel of the complement of the sphere and for the harmonic measure, Green function and Martin kernel of the complement of the hyperplane for the symmetric α-stable Lévy processes. Some extensions for the relativistic α-stable processes are discussed.