Estimates for the Derivatives of the Poisson Kernel on Nilpotent Meta-Abelian Groups

Let S be a semi direct product \(S=N\rtimes A\) where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic with ? ^k , k?>?1. We consider a class of second order left-invariant differential operators on S of the form \(\mathcal{L}_\alpha=L^a+\Delta_\alpha,\) where α?∈?? ^k , and for each a?∈?? ^k , L ^a is left-invariant second order differential operator on N and \(\Delta_\alpha=\Delta-\langle\alpha,\nabla\rangle,\) where Δ is the usual Laplacian on ? ^k . Using some probabilistic techniques (skew-product formulas for diffusions on S and N respectively, the concept of the derivative of a measure, etc.) we obtain an upper bound for the derivatives of the Poisson kernel for \(\mathcal{L}_\alpha.\) During the course of the proof we also get an upper estimate for the derivatives of the transition probabilities of the evolution on N generated by L ^σ(t), where σ is a continuous function from [0,?∞?) to ? ^k .     

Support vector machine regression (SVR/LS-SVM)--an alternative to neural networks (ANN) for analytical chemistry? Comparison of nonlinear methods on near infrared (NIR) spectroscopy data

In this study, we make a general comparison of the accuracy and robustness of five multivariate calibration models: partial least squares (PLS) regression or projection to latent structures, polynomial partial least squares (Poly-PLS) regression, artificial neural networks (ANNs), and two novel techniques based on support vector machines (SVMs) for multivariate data analysis: support vector regression (SVR) and least-squares support vector machines (LS-SVMs). The comparison is based on fourteen (14) different datasets: seven sets of gasoline data (density, benzene content, and fractional composition/boiling points), two sets of ethanol gasoline fuel data (density and ethanol content), one set of diesel fuel data (total sulfur content), three sets of petroleum (crude oil) macromolecules data (weight percentages of asphaltenes, resins, and paraffins), and one set of petroleum resins data (resins content). Vibrational (near-infrared, NIR) spectroscopic data are used to predict the properties and quality coefficients of gasoline, biofuel/biodiesel, diesel fuel, and other samples of interest. The four systems presented here range greatly in composition, properties, strength of intermolecular interactions (e.g., van der Waals forces, H-bonds), colloid structure, and phase behavior. Due to the high diversity of chemical systems studied, general conclusions about SVM regression methods can be made. We try to answer the following question: to what extent can SVM-based techniques replace ANN-based approaches in real-world (industrial/scientific) applications? The results show that both SVR and LS-SVM methods are comparable to ANNs in accuracy. Due to the much higher robustness of the former, the SVM-based approaches are recommended for practical (industrial) application. This has been shown to be especially true for complicated, highly nonlinear objects.     

Optimization of immunoaffinity enrichment and detection: toward a comprehensive characterization of the phosphotyrosine proteome of K562 cells by liquid chromatography-mass spectrometry

Phosphorylation of protein tyrosine residues regulates many cell functions and has also been proved to be involved in oncogenesis. Thus, the identification of the phosphotyrosine (pTyr) proteome of cells is a very important task. Since tyrosine phosphorylation represents only around 1% of the total human phosphoproteome, the study of pTyr proteins is rather challenging. Here we report the optimization study of the phosphotyrosine proteome using K562 cells as a model system. A substantial segment of the phosphotyrosine proteome of K562 cells was characterized by immunoaffinity enrichment with 4G10 and PYKD1 antibodies followed by LC-MS/MS analysis. 480 non-redundant pTyr peptides corresponding to 342 pTyr proteins were found. 141 pTyr peptides were not described elsewhere. The mass spectrometry approach involving high-resolving FTMS analysis of precursor ions and subsequent detection of CID fragments in a linear ion trap was considered as optimal. For detection of low abundant pTyr peptides pooling of individual immunoaffinity enrichments for one LC-MS/MS analysis was crucial. The enrichment properties of the monoclonal PYKD1 antibody were presented for the first time, also in comparison to the 4G10 antibody. PYKD1 was found to be more effective for protein enrichment (1.2 and 5% efficiency at peptide and protein level correspondingly), while 4G10 showed better results when peptide enrichment was performed (15% efficiency versus 3.6% at protein level). Substantially different subsets of the phosphoproteome were enriched by these antibodies. This finding together with previous studies demonstrates that comprehensive pTyr proteome characterization by immunoprecipitation requires multiple antibodies to be used for the affinity enrichment.     

Variable selection in near-infrared spectroscopy: benchmarking of feature selection methods on biodiesel data

In the present work, microwave heating initiated precipitation polymerization was developed to prepare podophyllotoxin (PPT) molecularly imprinted polymers (MIPs), resulting in much shorter polymerization time and better particle morphology. Prior to the polymerization, ultraviolet and FTIR spectroscopy were used to study the interactions between PPT and the functional monomers. The synthesized parameters were respectively optimized and the optimal conditions for the efficient adsorption property were template: PPT, 1 mmol; functional monomer: acrylamide, 6 mmol; bi-crosslinker: ethylene glycol dimethacrylate, 20 mmol and divinylbenzene, 20 mmol; porogen: acetonitrile, 40 mL; initiator: azobisisobutyronitrile, 0.01mol L?1; polymerization temperature: 60°C. FTIR spectroscopy, SEM and thermal analysis were used to characterize the MIPs. The results of the equilibrium rebinding experiments and the competitive adsorption experiments showed that these imprinted polymers exhibited good adsorption ability for the PPT. Scatchard analysis illustrated that two and one types of binding sites were generated in the MIPs and non-imprinted polymers (NIPs), respectively. Using the prepared MIPs as the solid phase extraction (SPE) sorbent, PPT was extracted selectively and efficiently from Dysosma versipellis, Sinopodophyllum hexandrum and Diphylleia sinensis. The regression equation was y=5.873×10?x+17075.659 with the correlation coefficient of 0.9994 in the concentration range of 0.005-0.4 mg mL?1. After washing and eluting the SPE column with methanol and MeOH/acetic acid solution (v/v, 9:1), the limits of detection were 0.12-0.18 μg mL?1 and their recoveries were in the range of 89.5-91.1% with all RSDs lower than 3.7.     

The S1/S2 exciton interaction in 2-pyridone·6-methyl-2-pyridone: Davydov splitting, vibronic coupling, and vibronic quenching

The excitonic splitting between the S(1) and S(2) electronic states of the doubly hydrogen-bonded dimer 2-pyridone[middle dot]6-methyl-2-pyridone (2PY·6M2PY) is studied in a supersonic jet, applying two-color resonant two-photon ionization (2C-R2PI), UV-UV depletion, and dispersed fluorescence spectroscopies. In contrast to the C(2h) symmetric (2-pyridone)(2) homodimer, in which the S(1) ← S(0) transition is symmetry-forbidden but the S(2) ← S(0) transition is allowed, the symmetry-breaking by the additional methyl group in 2PY·6M2PY leads to the appearance of both the S(1) and S(2) origins, which are separated by Δ(exp) = 154 cm(-1). When combined with the separation of the S(1) ← S(0) excitations of 6M2PY and 2PY, which is δ = 102 cm(-1), one obtains an S(1)/S(2) exciton coupling matrix element of V(AB, el) = 57 cm(-1) in a Frenkel-Davydov exciton model. The vibronic couplings in the S(1)/S(2) ← S(0) spectrum of 2PY·6M2PY are treated by the Fulton-Gouterman single-mode model. We consider independent couplings to the intramolecular 6a(') vibration and to the intermolecular σ(') stretch, and obtain a semi-quantitative fit to the observed spectrum. The dimensionless excitonic couplings are C(6a(')) = 0.15 and C(σ(')) = 0.05, which places this dimer in the weak-coupling limit. However, the S(1)/S(2) state exciton splittings Δ(calc) calculated by the configuration interaction singles method (CIS), time-dependent Hartree-Fock (TD-HF), and approximate second-order coupled-cluster method (CC2) are between 1100 and 1450 cm(-1), or seven to nine times larger than observed. These huge errors result from the neglect of the coupling to the optically active intra- and intermolecular vibrations of the dimer, which lead to vibronic quenching of the purely electronic excitonic splitting. For 2PY·6M2PY the electronic splitting is quenched by a factor of ~30 (i.e., the vibronic quenching factor is Γ(exp) = 0.035), which brings the calculated splittings into close agreement with the experimentally observed value. The 2C-R2PI and fluorescence spectra of the tautomeric species 2-hydroxypyridine·6-methyl-2-pyridone (2HP·6M2PY) are also observed and assigned.     

Thermal properties of ionic systems near the liquid-liquid critical point

Isobaric heat capacity per unit volume, C(p), and excess molar enthalpy, h(E), were determined in the vicinity of the critical point for a set of binary systems formed by an ionic liquid and a molecular solvent. Moreover, and, since critical composition had to be accurately determined, liquid-liquid equilibrium curves were also obtained using a calorimetric method. The systems were selected with a view on representing, near room temperature, examples from clearly solvophobic to clearly coulombic behavior, which traditionally was related with the electric permittivity of the solvent. The chosen molecular compounds are: ethanol, 1-butanol, 1-hexanol, 1,3-dichloropropane, and diethylcarbonate, whereas ionic liquids are formed by imidazolium-based cations and tetrafluoroborate or bis-(trifluromethylsulfonyl)amide anions. The results reveal that solvophobic critical behavior-systems with molecular solvents of high dielectric permittivity-is very similar to that found for molecular binary systems. However, coulombic systems-those with low permittivity molecular solvents-show strong deviations from the results usually found for these magnitudes near the liquid-liquid phase transition. They present an extremely small critical anomaly in C(p)-several orders of magnitude lower than those typically obtained for binary mixtures-and extremely low h(E)-for one system even negative, fact not observed, up to date, for any liquid-liquid transition in the nearness of an upper critical solution temperature.     

A Simple and Safe Synthesis of Cis-cyclopropanediamine Dihydrochloride

Cis-Cyclopropanediamine 4 is a very important component of compounds possesing anticancer activity (1). It was also used as a starting material for the synthesis of variety compounds on which the complexing abilities (2) and the Hetero-Cope-Rearrangement (3, 4) were studied.     

Novel high birefringent isothiocyanates based on quaterphenyl and phenylethynyltolane molecular cores

We report the synthesis of new laterally alkyl substituted high birefringent quaterphenyl and phenylethynyltolane liquid crystals with isothiocyanate terminal group. The thermal and optical properties such as birefringence are measured and discussed based on their molecular structures. The compounds exhibit birefringence (Δn) in the range of 0.44–0.63, and are expected to be appropriate components of high birefringent nematic mixtures for various applications.     

Dielectric and electro-optical response of a room temperature tri-component antiferroelectric mixture

Frequency- and temperature-dependent dielectric and switching parameters of a room temperature tri-component antiferroelectric liquid crystal mixture W-287 have been determined. Dielectric, optical texture and thermodynamic studies show wide room temperature range antiferroelectric SmC*_a (?91.1°C to <–25°C) phase in addition to high temperature paraelectric SmA* (?2.6°C) and ferroelectric SmC* (?4.4°C) phases. The dielectric studies carried out in the frequency range of 1–35 MHz under planar anchoring condition of the molecules show five different relaxation modes appearing in the SmA*, SmC* and SmC*_a phases. Using Curie–Weiss law fit, ferroelectric SmC* to paraelectric SmA* transition temperature has been found to be 91.8°C. The dielectric response of SmC*_a phase exhibits unusually three relaxation modes due to collective as well as individual molecular processes in addition to phason mode in the SmC* phase and amplitudon mode in the SmA* phase. Spontaneous polarisation, switching time and rotational viscosity have also been determined. The maximum value of P_S is ?300 nC/cm², whereas viscosity is moderate. Switching time is of the order of few milli seconds.     

Tunable two-component saccharide-based gels: The effect of the co-operation of two glucofuranose-based compounds having different gelating abilities

Addition of 1,2-O-(ethane-1,2-diyl)-α-d-glucofuranose, which is originally a poor organogelator, can support the gelating abilities of good glucofuranose-based organogelators. The properties of such two-component gels can be tuned by changing the proportion of the saccharides. The saccharide's ability to form two-component gels can be explained on the basis of its crystal structure, particularly, the way in which sugar molecules stack (or not) into hydrogen bond-based chains and the architecture of these chains. The thermal stability of the obtained two-component gels was characterised by measuring its T _gel temperature. SEM and XRD techniques were used to characterise the xerogels.

Addition of poor gelator increases the thermal stability of the gel formed by good gelator