Hill-Type Formula and Krein-Type Trace Formula for Hamiltonian Systems

In this paper, we give a survey on the Hill-type formula and its applications.Moreover, we generalize the Hill-type formula for linear Hamiltonian systems and Sturm-Liouville systems with any self-adjoint boundary conditions, which include the standard Neumann, Dirichlet and periodic boundary conditions. The Hill-type formula connects the infinite determinant of the Hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions. Further, based on the Hill-type formula, we derive the Krein-type trace formula. As applications, we give nontrivial estimations for the eigenvalue problem and the relative Morse index.     

Regularization of Quantum Relative Entropy in Finite Dimensions and Application to Entropy Production

The fundamental concept of relative entropy is extended to a functional that is regular-valued also on arbitrary pairs of nonfaithful states of open quantum systems. This regularized version preserves almost all important properties of ordinary relative entropy such as joint convexity and contractivity under completely positive quantum dynamical semigroup time evolution. On this basis a generalized formula for entropy production is proposed, the applicability of which is tested in models of irreversible processes. The dynamics of the latter is determined by either Markovian or non-Markovian master equations and involves all types of states.     

Enantioseparation of dansyl amino acids and dipeptides by chiral ligand exchange capillary electrophoresis based on Zn(II)-l-hydroxyproline complexes coordinating with γ-cyclodextrins

A chiral ligand exchange capillary electrophoresis (CLE-CE) method using Zn(II) as the central ion and l-4-hydroxyproline as the chiral ligand coordinating with γ-cyclodextrin (γ-CD) was developed for the enantioseparation of amino acids (AAs) and dipeptides. The effects of various separation parameters, including the pH of the running buffer, the ratio of Zn(II) to l-4-hydroxyproline, the concentration of complexes and cyclodextrins (CDs) were systematically investigated. After optimization, it has been found that eight pairs of labeled AAs and six pairs of labeled dipeptides could be baseline-separated with a running electrolyte of 100.0 mM boric acid, 5.0 mM ammonium acetate, 3.0 mM Zn(II), 6.0 mM l-hydroxyproline and 4.0 mM γ-CD at pH 8.2. The quantitation of AAs and dipeptides was conducted and good linearity (r² ≥ 0.997) and favorable repeatability (RSD ≤ 3.6%) were obtained. Furthermore, the proposed method was applied in determining the enantiomeric purity of AAs and dipeptides. Meanwhile, the possible enantiorecognition mechanism based on the synergistic effect of chiral metal complexes and γ-CD was explored and discussed briefly.     

Intramolecular Alkylation of Aromatic Compounds XXXVI [1]. Stereoselective Synthesis of C/D-cis-Configured Ergolines

Summary.  The stereoselective synthesis of cis-ergoline is presented. Starting from rac-N-benzoyl tryptophan methyl ester, the key compound indolinylmethylpyridin-3-one was prepared via a seven-step reaction in good yield. Since its cyclization to the desired ergolinone failed, the key compound was reduced to yield the two diastereomeric pyridin-3-ols; only one of them cyclized in trifluoromethanesulfonic acid, affording cis-ergoline. Catalytic hydrogenation of the latter gave N,N′-dimethyldihydroergoline, the X-ray crystallography of which revealed both the correct structure and identical relative configurations at C-5a and C-6a (SS or RR). Hydroboration and subsequent perruthenate oxidation of the Δ⁹-ergoline provided access to the regioisomeric ergolinols and ergolinones. Received December 27, 2001. Accepted January 15, 2002     

pePC-SAFT: Modeling of polyelectrolyte systems: 1. Vapor–liquid equilibria

A molecular thermodynamic model for polyelectrolyte systems—called pePC-SAFT—is proposed. The effect of charged monomers within the polyelectrolyte chain is explicitly taken into account in the reference term by replacing the hard-chain contribution of the PC-SAFT model by a charged-hard-chain contribution. Moreover, counterion condensation is accounted for to determine the effective number of charges along the polyion as well as of free counterions. The electrostatic contribution of the free counterions is described by a Debye–Hückel term.     

Halogenated arenes in the Duff reaction at high pressures

The reaction of fluorobenzene with urotropine in trifluoroacetic acid (TFAA) at high pressures and temperatures affords predominantly fluorobenzaldehydes andN-(fluorophenylmethyl)trifluoroacetamides. The yields of these products depend considerably on the reaction conditions. The rates of their formation have the maximum values at the momemt of the phase transition (PT) of TFAA. A new efficient cyclic (dynamic) regime is proposed for the synthesis at high pressures. The regime involves periodically occurring PT of the solvent. The change in the relative rate of product formation with the degree of fluorobenzene conversion is wave-like.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 319–323, February, 1995.     

Advantages of using a modified orthogonal sampling configuration originally designed for LC-ESI-MS to couple CE and MS for the determination of antioxidant phenolic compounds found in virgin olive oil

A ThermoFinnigan sheath liquid flow capillary electrophoresis-mass spectrometry system designed for coupling via a co-axial interface was coupled through an adapted via an alternative, commercially available interface for orthogonal sampling. The affordable, reversible structural alterations made in the commercial LC-MS interface resulted in improved analytical performance.The results of a conventional capillary electrophoresis (CE) method using a commercial co-axial source to determine antioxidant phenolic acids present in virgin olive oil, were compared with those obtained by using a modified orthogonal sampling position. In both cases, separations were done using a 10 mM ammonium acetate/ammonium hydroxide buffer solution at pH 10.0 and a constant applied voltage of 25 kV. The operating variables for the mass spectrometry interface were re-optimized for the modified orthogonal orientation. This allowed the sheath liquid, sheath gas flow rates and capillary voltage to be lowered with respect to the co-axial coupling configuration. In addition, the orthogonal sampling position provided a higher selectivity by effect of ion sampling excluding larger droplets—with an increased momentum along the axis—which were drained through the sink at the bottom of the ion source. Also, the new configuration facilitated sample ionization, improved electrospray stability and led to stronger signals as a result.The new system was validated in terms of precision (repeatability), linearity, and limits of detection and quantification. A comparison of the validation data with the results previously obtained by using a commercial co-axial configuration revealed the adapted orthogonal sampling position to provide better repeatability in both migration times and relative peak areas (<1% and 7% respectively with n = 15 replicates), a good linear range (with levels in the microgram-per-litre region) and lower limits of detection—especially for the compounds detected with the lowest sensitivity when co-axial ESI was used, as HFA, GEN, FER and VAN finding LOD among 24-3.0 μg L⁻¹ respectively.     

Evaluation of isotope-coded protein labeling (ICPL) in the quantitative analysis of complex proteomes

An evaluation of the ICPL (isotope-coded protein labeling) non-isobaric labeling technique was performed using two different biological models. Two samples containing phage T4 capsids were mixed in a 1:1 ratio after being labeled with the light or heavy versions of the ICPL reagent. The analysis of this proteome demonstrated the feasibility of this approach for differential quantitative proteomics and was employed to optimize the experimental parameters of the ICPL workflow. ICPL-mediated analysis of two more complex proteomes, those of a Salmonella enterica serovar Typhimurium virulent strain and an isogenic attenuated mutant, and its comparison with the results obtained in a 2D-PAGE “classical” approach confirmed that ICPL is a valuable alternative to other labeling techniques currently in use. In addition, our results suggest that labeling at the peptide level instead of following the standard ICPL workflow should increase both the number of proteins quantified and the reliability of the quantification.