p-Laplacian problems with nonlinearities interacting with the spectrum

The aim of this paper is investigating the existence and the multiplicity of weak solutions of the quasilinear elliptic problem $$\left\{\begin{array}{ll}-\Delta_p u\ =\ g(x, u) \quad {\rm in} \quad \Omega,\\ u=0 \qquad \qquad \qquad {\rm on}\quad \partial\Omega,\end{array}\right.$$ where ${1 < p < + \infty, \Delta_p u = {\rm div}(|\nabla {u}|^{p-2}\nabla {u})}$ , Ω is an open bounded domain of ${\mathbb{R}^N (N \geq 3)}$ with smooth boundary ?Ω and the nonlinearity g behaves as u ^p?1 at infinity. The main tools of the proof are some abstract critical point theorems in Bartolo et al. (Nonlinear Anal. 7: 981–1012, 1983), but extended to Banach spaces, and two sequences of quasi–eigenvalues for the p–Laplacian operator as in Candela and Palmieri (Calc. Var. 34: 495–530, 2009), Li and Zhou (J. Lond. Math. Soc. 65: 123–138, 2002).     

Probing transient Hoogsteen hydrogen bonds in canonical duplex DNA using NMR relaxation dispersion and single-atom substitution

Nucleic acids transiently morph into alternative conformations that can be difficult to characterize at the atomic level by conventional methods because they exist for too little time and in too little abundance. We recently reported evidence for transient Hoogsteen (HG) base pairs in canonical B-DNA based on NMR carbon relaxation dispersion. While the carbon chemical shifts measured for the transient state were consistent with a syn orientation for the purine base, as expected for A(syn)?T(anti) and G(syn)?C(+)(anti) HG base pairing, HG type hydrogen bonding could only be inferred indirectly. Here, we develop two independent approaches for directly probing transient changes in N-H···N hydrogen bonds and apply them to the characterization of transient Hoogsteen type hydrogen bonds in canonical duplex DNA. The first approach takes advantage of the strong dependence of the imino nitrogen chemical shift on hydrogen bonding and involves measurement of R(1ρ) relaxation dispersion for the hydrogen-bond donor imino nitrogens in G and T residues. In the second approach, we assess the consequence of substituting the hydrogen-bond acceptor nitrogen (N7) with a carbon (C7H7) on both carbon and nitrogen relaxation dispersion data. Together, these data allow us to obtain direct evidence for transient Hoogsteen base pairs that are stabilized by N-H···N type hydrogen bonds in canonical duplex DNA. The methods introduced here greatly expand the utility of NMR in the structural characterization of transient states in nucleic acids.     

A comprehensive mathematical approach to exotic option pricing

This work illustrates how several new pricing expressions for exotic options can be derived within a Lévy framework by employing a unique pricing expression. To the purpose, a unifying formula is obtained by solving some nested Cauchy problem for pseudodifferential equations generalizing Black–Scholes PDE. The main result extends (Agliardi R. The quintessential option pricing formula under Lévy processes. Applied Mathematics Letters 2009; 22:1626‐1631) and is a powerful tool for generating new valuation expressions. Several examples of pricing formulas under the Lévy processes are provided to illustrate the flexibility of the method. Some of them are new in the financial literature. Finally, many existing pricing formulas of the traditional Gaussian model are easily obtained as a by‐product. Copyright © 2012 John Wiley & Sons, Ltd.     

On the inter-instrument and the inter-laboratory transferability of a tandem mass spectral reference library. 3. Focus on ion trap and upfront CID

Mass spectral libraries represent versatile tools for the identification of small bioorganic molecules. Libraries based on electron impact spectra are rated robust and transferable. Tandem mass spectral libraries are often considered to work properly only on the instrument that has been used to build the library. An exception from that rule is the 'Wiley Registry of Tandem Mass Spectral Data, MSforID'. In various studies with data sets from different kinds of tandem mass spectrometric instruments, the outstanding sensitivity and robustness of this tandem mass spectral library search approach was demonstrated. The instrumental platforms tested, however, mainly included various tandem-in-space instruments. Herein, the results of a multicenter study with a focus on upfront and tandem-in-time fragmentation are presented. Five laboratories participated and provided fragment ion mass spectra from the following types of mass spectrometers: time-of-flight (TOF), quadrupole-hexapole-TOF, linear ion trap (LIT), 3-D ion trap and LIT-Orbitrap. A total number of 1231 fragment ion mass spectra were collected from 20 test compounds (amiloride, buphenin, cinchocaine, cyclizine, desipramine, dihydroergotamine, dyxirazine, dosulepin, ergotamine, ethambutol, etofylline, mefruside, metoclopramide, phenazone, phentermine, phenytoin, sulfamethoxazole, sulfamoxole, sulthiame and tetracycline) on seven electrospray ionization instruments using 18 different instrumental configurations for fragmentation. For 1222 spectra (99.3%), the correct compound was retrieved as the best matching compound. Classified matches (matches with 'relative average match probability' >40.0) were obtained for 1207 spectra (98.1%). This high percentage of correct identifications clearly supports the hypothesis that the tandem mass spectral library approach tested is a robust and universal identification tool.     

The quintessential option pricing formula under Lévy processes

The basic digital method for option pricing developed in Ingersoll [J. Ingersoll, Digital contracts: Simple tools for pricing complex derivatives, Journal of Business 73 (1) (2000) 67–88] and Buchen and Skipper [P. Buchen, M. Skipper, The quintessential option pricing formula, School of Mathematics and Statistics, University of Sydney, 2003, pp. 1–31] is generalized to a Lévy environment. The approach is combined with the mathematical methodology of Boyarchenko and Levendorski [S.I. Boyarchenko, S.Z. Levendorski, Non-Gaussian Merton–Black–Scholes theory, World Scientific, 2002] that employs pseudo-differential operators whose symbol is expressed in terms of the characteristic exponent of the underlying Lévy process. Some new valuation formulas are obtained.     

Unusually high enantioselectivity in high-performance liquid chromatography using cellulose tris(4-methylbenzoate) as a chiral stationary phase

The cellulose tris(4-methylbenzoate) chiral stationary phase (CSP) (commercially known as Chiralcel OJ-H) exhibited an extremely high enantioselectivity when used in the HPLC resolution of N-thiocarbamoyl-3-(4′-prenyloxy)-phenyl-5-phenyl-4,5-dihydro-(1H) pyrazole (Compound 1), in both normal-phase and polar organic conditions. Using n-hexane–ethanol (80:20, v/v) as a mobile phase, an enantioseparation factor value of 138.5 was found. In order to modulate the elution time of the longer retained enantiomer, a simple HPLC procedure was developed. The optimized analytical protocol was based on the stopped flow technique and did not involve any change in mobile phase composition. The stronger interaction energy of the (S) enantiomer compared to that of the (R) enantiomer was mainly attributed to the formation of a hydrogen bonding between the amino group of the thiocarbamoyl moiety and the carbonyl oxygen of the CSP.     

Selection of Anti‐gluten DNA Aptamers in a Deep Eutectic Solvent

Herein, we show the feasibility of using deep eutectic solvents as a faster way of selecting aptamers targeting poorly water‐soluble species. This unexplored concept is illustrated for gluten proteins. In this way, aptamer‐based gluten detection can be performed directly in the extraction media with improved detectability. We envision deep implications for applications not only in food safety control but also in biomedicine.     

Cauchy problem for p-evolution equations

We consider p-evolution equations with real characteristics. We give a condition, on the lower order terms, that is sufficient for well-posedness of the Cauchy problem in Sobolev spaces.     

Trajectories Joining Two Submanifolds under the Action of Gravitational and Electromagnetic Fields on Static Spacetimes

In this paper we present existence and multiplicity results for orthogonal trajectories joining two submanifolds under the action of gravitational and electromagnetic fields on static spacetimes. These trajectories are critical points of unbounded functionals and they can be found by using a variant of the saddle point theorem and the relative category theory.     

Rapid and direct analysis of gamma-hydroxybutyric acid in urine by capillary electrophoresis-electrospray ionization ion-trap mass spectrometry

The present work was aimed at the development of a capillary electrophoretic analysis of gamma-hydroxybutyric acid (GHB) using electrospray ion trap mass spectrometry to achieve the direct and unequivocal detection of this analyte in human urine. Optimized capillary electrophoretic conditions were: injection, 20 s at 0.5 psi (1 psi = 6894.76 Pa); buffer electrolyte, 12.5 mM ammonium formate adjusted to pH 8.35 with diethylamine; fused silicacapillary: 100 cm x 50 microm i.d.; separation voltage, 25 kV (forward polarity) + 0.5 psi; room temperature. Electrospray and mass spectrometric conditions were: drying gas and nebulizing gas (nitrogen) at flow rate 3 l/min, temperature 250 degrees C, nebulizer pressure: 10 psi; sheath liquid solution: methanol-water (90:10) containing 0.1% ammonia delivered at 3 microl/min; spray voltage 3.5 kV. Mass spetrometric detection was carried out in the selected ion monitoring mode of negative molecular ions at 103 m/z for GHB and 115 m/z for maleic acid (I.S.). Under these conditions the baseline separation of GHB and the I.S. was obtained. The selectivity of the analysis allowed for direct injection of unextracted urine, previously diluted 1:4 with water. Linearity was assessed in the GHB concentration range from 80 to 1280 microg/ml in urine. Analytical sensitivity (as limit of detection) resulted about 5 microg/ml in water and 20 microg/ml in original urine. Analytical precision was fairly acceptable with R.S.D. values lower than 5% for migration times and 18% for quantitation in real samples, in both intra day and day-to-day experiments. On these grounds, the developed method can be adopted for rapid identification of acute intoxications from GHB in humans.