Existence and uniqueness of optimal dynamic pricing and advertising controls without concavity

We consider a pricing and advertising dynamic-optimization problem where the goodwill dynamics evolve à la Nerlove–Arrow. The firm maximizes its profit over a finite-planning horizon corresponding to the product’s lifespan, and it turns out that the Hamiltonian is non-concave. We show the existence and uniqueness of an optimal solution under some mild conditions.     

In vitro anti-oxidant potential of new metabolites from Hypericum oblongifolium (Guttiferae)

Phytochemical investigations on Hypericum oblongifolium led to the isolation of a flavone named folicitin (1) and a bicyclic conjugated lactone, folenolide (2) from the ethyl acetate fraction of methanolic extract. Both metabolites were characterised as new compounds based on detailed spectroscopic analyses. In vitro anti-oxidant potential of both the compounds was evaluated by the DPPH radical scavenging assay. Compound 1 exhibited significant antioxidant activity while compound 2 was found inactive.     

Rapid preparative isolation of erythrocentaurin from Enicostemma littorale by medium‐pressure liquid chromatography,its estimation by high‐pressure thin‐layer chromatography,and its α‐amylase inhibitory activity

Erythrocentaurin is a relatively simple natural product present among the members of Gentianaceae. A preparative method for the isolation of erythrocentaurin from the ethyl acetate fraction of Enicostemma littorale using medium‐pressure liquid chromatography has been reported. The method consisted of a simple step gradient from 10 to 20% ethyl acetate in n‐hexane. Using a 70 × 460 mm Si60 column, this method is capable of processing 20 g of material in <3 h (purity ≈ 97%). The recovery of erythrocentaurin was 87.77%. Estimation of erythrocentaurin in extracts and fractions based on high‐pressure thin‐layer chromatography was carried out on silica gel 60 F₂₅₄ plates with toluene/ethyl acetate/formic acid (80:18:2 v/v/v) as the mobile phase. The densitometric analysis was performed at 230 nm. A well‐separated compact band of erythrocentaurin appeared at R_f 0.54 ± 0.04. The analytical method showed good linearity in the concentration range of 200–1500 ng/band with a correlation coefficient of 0.99417. The limits of detection and quantification were found to be ≈60 and ≈180 ng/band, respectively. Erythrocentaurin exhibited a concentration‐dependent α‐amylase inhibition (IC₅₀ 1.67 ± 0.28 mg/mL). The outcome of the study should be considered for pharmacokinetic and biotransformation studies involving E. littorale.     

Boroalkyl group migration provides a versatile entry into α-aminoboronic acid derivatives

A reaction exemplifying migration of boron-substituted carbon is described. We show that α-boroalkyl groups of transient boroalkyl acyl azide intermediates readily migrate from carbon to nitrogen. This process allows access to a new class of stable molecules, α-boryl isocyanates, from α-borylcarboxylic acid precursors. The methodology facilitates synthesis of a wide range of α-aminoboronic acid derivatives, including α,α-disubstituted analogues.     

Role of reversible dimerization in reactions of amphoteric aziridine aldehydes

Unprotected aziridine aldehydes belong to the amphoteric class of molecules by virtue of their dual nucleophilicity/electrophilicity. The dimeric nature of these molecules, brought together by a weak and reversible aminal "connection", was found to be an important element of reactivity control. We present evidence that reversible dimer dissociation is instrumental in aziridine aldehyde transformations. We anticipate further developments that will unveil other synthetic consequences of remote control of selectivity through forging reversible covalent interactions.     

Optical soliton and elliptic functions solutions of Sasa-satsuma dynamical equation and its applications

The Sasa-satsuma(SS) dynamical equation interpret propagation of ultra-short and femto-second pulses in optical fibers. This dynamical model has important physical significance.In this article, two mathematical techniques namely, improved F-expansion and improved auxiliary methods are utilized to construct the several types of solitons such as dark soliton, bright soliton, periodic soliton, Elliptic function and solitary waves solutions of Sasa-satsuma dynamical equation. These results have imperative applications in sciences and other fields, and constructive to recognize the physical structure of this complex dynamical model. The computing work and obtained results show the influence and effectiveness of current methods.     

Proficiency test exercise on the determination of natural levels of radionuclides in mushroom reference material

The results from a proficiency test exercise for the determination of natural levels of radionuclides in mushroom reference material carried out by laboratories in six different countries are discussed. These laboratories submitted data on seven radionuclides, namely ¹³⁴Cs, ¹³⁷Cs, ⁴⁰K, ⁹⁰Sr, ²⁴¹Am, ²²⁶Ra, and ²¹⁰Po. However, only the data received for three of these radionuclides could be statistically evaluated to obtain consensus mean values and confidence intervals (at a significance level of 0.05). The contents of ¹³⁴Cs, ¹³⁷Cs and ⁴⁰K were quantified as 4.4, 2,899 and 1,136 Bq/kg, respectively.     

New insights into photosynthetic oscillations revealed by two-dimensional microscopic measurements of chlorophyll fluorescence kinetics in intact leaves and isolated protoplasts

Chlorophyll fluorescence kinetic microscopy was used to analyze photosynthetic oscillations in individual cells of leaves and in isolated leaf cell protoplasts. Four Brassicaceae species were used: Arabidopsis halleri (L.) O'Kane & Al-Shehbaz, Thlaspi fendleri (Nels.) Hitchc, Thlaspi caerulescens J.&C. Presl and Thlaspi ochroleucum Boiss et Helder. With the latter two, the measurements were extended also to isolated protoplasts. The oscillations were induced under the microscope by exposing dark-adapted samples to actinic irradiance. Detailed analysis of the induced transients revealed that they consist of several processes oscillating with different frequencies and not only one component as reported earlier. Furthermore, it was found that most of these processes are controlled inside each individual cell. This was shown by differences in oscillations in neighboring cells and protoplasts that share a uniform intercellular environment. The frequency of the dominant oscillation frequency depended neither on irradiance nor on CO2 concentration and is, therefore, not controlled by the photosynthetic rate. Characteristic differences in the frequency spectrum and damping of oscillations have been found among the plant species examined.     

Gas-Phase Synthesis of Singly and Multiply Charged Polyoxovanadate Anions Employing Electrospray Ionization and Collision Induced Dissociation

Electrospray ionization mass spectrometry (ESI-MS) combined with in-source fragmentation and tandem mass spectrometry (MS/MS) experiments were used to generate a wide range of singly and multiply charged vanadium oxide cluster anions including V_xO_y ^n– and V_xO_yCl^n– ions (x = 1–14, y = 2–36, n = 1–3), protonated clusters, and ligand-bound polyoxovanadate anions. The cluster anions were produced by electrospraying a solution of tetradecavanadate, V₁₄O₃₆Cl(L)₅ (L = Et₄N⁺, tetraethylammonium), in acetonitrile. Under mild source conditions, ESI-MS generates a distribution of doubly and triply charged V_xO_yCl^n– and V_xO_yCl(L)^(n–1)– clusters predominantly containing 14 vanadium atoms as well as their protonated analogs. Accurate mass measurement using a high-resolution LTQ/Orbitrap mass spectrometer (m/Δm = 60,000 at m/z 410) enabled unambiguous assignment of the elemental composition of the majority of peaks in the ESI-MS spectrum. In addition, high-sensitivity mass spectrometry allowed the charge state of the cluster ions to be assigned based on the separation of the major from the much less abundant minor isotope of vanadium. In-source fragmentation resulted in facile formation of smaller V_xO_yCl^(1–2)– and V_xO_y ^(1–2)– anions. Collision-induced dissociation (CID) experiments enabled systematic study of the gas-phase fragmentation pathways of the cluster anions originating from solution and from in-source CID. Surprisingly simple fragmentation patterns were obtained for all singly and doubly charged V_xO_yCl and V_xO_y species generated through multiple MS/MS experiments. In contrast, cluster anions originating directly from solution produced comparatively complex CID spectra. These results are consistent with the formation of more stable structures of V_xO_yCl and V_xO_y anions through low-energy CID. Furthermore, our results demonstrate that solution-phase synthesis of one precursor cluster anion combined with gas-phase CID is an efficient approach for the top-down synthesis of a wide range of singly and multiply charged gas-phase metal oxide cluster anions for subsequent investigations of structure and reactivity using mass spectrometry and ion spectroscopy techniques.      

Exact Solutions of Schrödinger Equation for the Position-Dependent Effective Mass Harmonic Oscillator

A one-dimensional harmonic oscillator with position-dependent effective mass is studied. We quantize the oscillator to obtain a quantum Hamiltonian, which is manifestly Hermitian in configuration space, and the exact solutions to the corresponding Schrödinger equation are obtained analytically in terms of modified Hermite polynomials. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the position dependence of the mass vanishes.