Modular properties of the hard hexagon model

The physical quantities (or powers thereof) in the hard-hexagon model that were computed exactly by Baxter are shown to be modular functions with respect to the number-theoretic group ₁[N]. This allows us to determine the analytic structure of, the partition function per site in the thermodynamic limit, and, the density, as functions of the activityz.     

Taylor Series Expansion in Discrete Clifford Analysis

Discrete Clifford analysis is a discrete higher-dimensional function theory which corresponds simultaneously to a refinement of discrete harmonic analysis and to a discrete counterpart of Euclidean Clifford analysis. The discrete framework is based on a discrete Dirac operator that combines both forward and backward difference operators and on the splitting of the basis elements $\mathbf{e}_j = \mathbf{e}_j^+ + \mathbf{e}_j^-$ into forward and backward basis elements $\mathbf{e}_j^\pm $ . For a systematic development of this function theory, an indispensable tool is the Taylor series expansion, which decomposes a discrete (monogenic) function in terms of discrete homogeneous (monogenic) building blocks. The latter are the so-called discrete Fueter polynomials. For a discrete function, the authors assumed a series expansion which is formally equivalent to the Taylor series expansion in Euclidean Clifford analysis; however, attention needed to be paid to the geometrical conditions on the domain of the function, the convergence and the equivalence to the given discrete function. We furthermore applied the theory to discrete delta functions and investigated the connection with Shannon sampling theorem (Bell Sys Tech J 27:379–423, 1948). We found that any discrete function admits a series expansion into discrete homogeneous polynomials and any discrete monogenic function admits a Taylor series expansion in terms of the discrete Fueter polynomials, i.e. discrete homogeneous monogenic polynomials. Although formally the discrete Taylor series expansion of a function resembles the continuous Taylor series expansion, the main difference is that there is no restriction on discrete functions to be represented as infinite series of discrete homogeneous polynomials. Finally, since the continuous expansion of the Taylor series expansion of discrete delta functions is a sinc function, the discrete Taylor series expansion lays a link with Shannon sampling.     

On the additive splitting procedures and their computer realization

Two additive splitting procedures are defined and studied in this paper. It is shown that these splitting procedures have good stability properties. Some other splitting procedures, which are traditionally used in mathematical models used in many scientific and engineering fields, are sketched. All splitting procedures are tested by using six different numerical methods for solving differential equations. Many conclusions, which are related both to the comparison of the additive splitting procedures with the other splitting procedures and to the influence of the numerical methods for solving differential equations on the accuracy of the splitting procedures, are drawn.     

Quantitative multiplex CARS spectroscopy in congested spectral regions

A novel procedure is developed to describe and reproduce experimental coherent anti-Stokes Raman scattering (CARS) data, with particular emphasis on highly congested spectral regions. The approach, exemplified here with high-quality multiplex CARS data, makes use of spontaneous Raman scattering results. It is shown that the underlying vibrational Raman response can be retrieved from the multiplex CARS spectra, so that the Raman spectrum can be reconstituted, provided an adequate signal-to-noise ratio (SNR) is present in the experimental data and sufficient a priori knowledge of the vibrational resonances involved exists. The conversion of CARS to Raman data permits a quantitative interpretation of CARS spectra. This novel approach is demonstrated for highly congested multiplex CARS spectra of adenosine mono-, di-, and triphosphate (AMP, ADP, and ATP), nicotinamide adenine dinucleotide (NAD+), and small unilamellar vesicles (SUVs) of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). Quantitative determination of nucleotide concentrations and composition analysis in mixtures is demonstrated.     

Matrix pre-coated MALDI MS targets for small molecule imaging in tissues

A new sample preparation method for MALDI tissue imaging has been developed for the analysis of low molecular weight compounds that employs matrix pre-coated MALDI targets. Tissue sections need only to be transferred onto the pre-coated target before analysis for fast and easy sample preparation. Pre-coated targets have a homogenous matrix coating with uniform crystals of approximately 1–2 μm and do not require solvents that may lead to analyte delocalization within a tissue section. We report here the use of matrix pre-coated targets for imaging of lipids, peptides, and pharmaceuticals in tissues.     

Total Synthesis of Δ12‐Prostaglandin J3: Evolution of Synthetic Strategies to a Streamlined Process

The total synthesis of Δ¹²‐prostaglandin J₃ (Δ¹²‐PGJ₃, 1 ), a reported leukemia stem cell ablator, through a number of strategies and tactics is described. The signature cross‐conjugated dienone structural motif of 1 was forged by an aldol reaction/dehydration sequence from key building blocks enone 13 and aldehyde 14 , whose lone stereocenters were generated by an asymmetric Tsuji–Trost reaction and an asymmetric Mukaiyama aldol reaction, respectively. During this program, a substituent‐governed regioselectivity pattern for the Rh‐catalyzed C?H functionalization of cyclopentenes and related olefins was discovered. The evolution of the synthesis of 1 from the original strategy to the final streamlined process proceeded through improvements in the construction of both fragments 13 and 14 , exploration of the chemistry of the hitherto underutilized chiral lactone synthon 57 , and a diastereoselective alkylation of a cyclopentenone intermediate. The described chemistry sets the stage for large‐scale production of Δ¹²‐PGJ₃ and designed analogues for further biological and pharmacological studies.     

A simple and sensitive assay for the quantitative analysis of paclitaxel and metabolites in human plasma using liquid chromatography/tandem mass spectrometry

A sensitive and specific LC-MS/MS assay for the determination of paclitaxel and its 3'p- and 6-alpha-hydroxy metabolites is presented. A 200 microL plasma aliquot was spiked with a 13C6-labeled paclitaxel internal standard and extracted with 1.0 mL tert-butylmethylether. Dried extracts were reconstituted in 0.1 M ammonium acetate-acetonitrile (1:1, v/v) and 25 microL volumes were injected onto the HPLC system. Separation was performed on a 150 x 2.1 mm C18 column using an alkaline eluent (10 mm ammonium hydroxide-methanol, 30:70, v/v). Detection was performed by positive ion electrospray followed by tandem mass spectrometry. The assay quantifies a range for paclitaxel from 0.25 to 1000 ng/mL and metabolites from 0.25 to 100 ng/mL using 200 microL human plasma samples. Validation results demonstrate that paclitaxel and metabolite concentrations can be accurately and precisely quantified in human plasma. This assay is now used to support clinical pharmacologic studies with paclitaxel.     

A simple and sensitive assay for the quantitative analysis of rivastigmine and its metabolite NAP 226-90 in human EDTA plasma using coupled liquid chromatography and tandem mass spectrometry

A sensitive and specific high-performance liquid chromatography/tandem mass spectrometry (HPLC/MS/MS) assay for the determination of rivastigmine and its major metabolite NAP 226-90 is presented. A 100 microL plasma aliquot was spiked with a structural analogue of rivastigmine as internal standard (PKF214-976-AE-1) and proteins were precipitated by adding 200 microL of methanol. After centrifugation a volume of 100 microL of the clear supernatant was mixed with 100 microL of methanol/water (30:70, v/v) and volumes of 25 microL were injected onto the HPLC system. Separation was acquired on a 150 x 2.0 mm i.d. Gemini C18 column using a gradient system with 10 mM ammonium hydroxide and methanol. Detection was performed by using a turboionspray interface and positive ion multiple reaction monitoring by tandem mass spectrometry. The assay quantifies rivastigmine from 0.25 to 50 ng/mL and its metabolite NAP 226-90 from 0.50 to 25 ng/mL, using human plasma samples of 100 microL. Validation results demonstrate that rivastigmine and metabolite concentrations can be accurately and precisely quantified in human EDTA plasma. This assay is now used to support clinical pharmacologic studies with rivastigmine.     

Bioanalytical LC–MS/MS validation of therapeutic drug monitoring assays in oncology

Therapeutic drug monitoring (TDM) has shown to benefit patients treated with drugs of many drug classes, among which is oncology. With an increasing demand for drug monitoring, new assays have to be developed and validated. Guidelines for bioanalytical validation issued by the European Medicines Agency and US Food and Drug Administration are applicable for clinical trials and toxicokinetic studies and demand fully validated bioanalytical methods to yield reliable results. However, for TDM assays a limited validation approach is suggested based on the intended use of these methods. This review presents an overview of publications that describe method validation of assays specifically designed for TDM. In addition to evaluating current practice, we provide recommendations that could serve as a guide for future validations of TDM assays.