A second-order dynamical system for equilibrium problems

Numerical Algorithms - We consider a second-order dynamical system for solving equilibrium problems in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of strong global...     

Purification of the precursor for the automated radiosynthesis of [18F]FCWAY by counter-current chromatography

Radiolabeled FCWAY (N-(2-[4-(2-methoxyphenyl)piperazino])-N-(2-pyridinyl) trans-4-fluorocyclohexanecarboxamide) was prepared for human positron emission tomography (PET) studies by a simple one-step radiosynthesis. The LC-MS analysis of the products indicated that it contained impurities which may interfere with FCWAY uptake of 5-HT1A receptors and that these impurities were derived from an impurity originally present in the precursor preparation. Since preparative HPLC failed to resolve one of the impurities from the precursor, preparative-scale high-speed counter-current chromatography (HSCCC) was used for purification of this FCWAY precursor. A suitable two-phase solvent system composed of cyclohexane-ethyl acetate-methanol-water at a volume ratio of 1:1:1:1 or 4:5:4:5 was selected based on the partition coefficients of the precursor and impurity as determined by a LC-MS method. Using the second solvent ratio of 4:5:4:5 with the organic phase as a mobile phase, a 2.57 g amount of precursor preparation was successfully purified yielding 2.2 g of the pure precursor by a single run.     

Investigation of phytochemicals and antioxidant capacity of selected <Emphasis Type="Italic">Eucalyptus</Emphasis> species using conventional extraction

Eucalyptus species have found their place in traditional medicine and pharmacological research and they have also been shown to possess a large number of phenolic compounds and antioxidants. The present study sought to implement conventional extraction to yield maximal total phenolic content (TPC), total flavonoid content (TFC), proanthocyanidins, antioxidants, and saponins from E. robusta using different solvents. The most suitable extraction solvent was further employed for extracting phytochemicals from E. saligna, E. microcorys, and E. globulus to select the Eucalyptus species with the greatest bioactive compound content. The results emphasised the efficiency of water in extracting TPC ((150.60 ± 2.47) mg of gallic acid equivalents per g), TFC ((38.83 ± 0.23) mg of rutin equivalents per g), proanthocyanidins ((5.14 ± 0.77) mg of catechin equivalents per g), and antioxidants ABTS ((525.67 ± 1.99) mg of trolox equivalents (TE) per g), DPPH ((378.61 ± 4.72) mg of TE per g); CUPRAC ((607.43 ± 6.69) mg of TE per g) from E. robusta. Moreover, the aqueous extract of E. robusta had the highest TPC, TFC and antioxidant values among the other Eucalyptus species tested. These findings highlighted the efficiency of conventional extraction in extracting natural bioactive compounds from Eucalyptus species for pharmaceutical and nutraceutical applications.     

Levi Extension Theorems for Meromorphic Functions of Weak Type in Infinite Dimension

The aim of paper is to give some results, that prepare for studying the problem on cross theorems for separately \((\cdot , W)\)-meromorphic functions. Some general versions of extension theorem of Levi type are extended to the classes of meromorphic functions f on \(D \times (\Delta _r {\setminus } \overline{\Delta })\) with values in a locally convex space F. Here, the function f is assumed that, for each \(z \in D_*,\) the function \(f_z = f(z, \cdot )\) has a (F, W)-meromorphic extension to \(\Delta _r,\) where F is either a locally (or sequentially) complete locally convex space or a Fréchet space, the space \(W \subseteq F'\) is separating (or determines boundedness), \(\Delta _r = \{\lambda \in {\mathbb C}: |\lambda | < r\}\) with \(r > 1, \Delta = \Delta _1\) and D is either a domain in \({\mathbb C}^n\) or a balanced domain in a Fréchet space containing a non-pluripolar balanced convex compact subset, \(D_*\) is dense in D.     

Structural and Optical Properties of Zn1‐xMgxO Prepared by Calcination of ZnO + Mg(OH)2 after Hydro Micro Mechanical Activation

Zn_1‐xMg_xO microcrystals are produced in the 0.15 ≤ x ≤ 1 composition range by calcination of ZnO + Mg(OH)₂ after hydro micro mechanical activation according to the patent WO2018065735A1. The structural properties of the samples have revealed the cohabitation of wurtzite and rock‐salt phases for x values ranging from 0.15 up to 0.6 with a clear increase of the proportion of cubic phase with x. A single cubic phase is observed in the range 0.66 ≤ x < 1. From the purity of these samples produced at very low cost, it is expected that they will be used as precursors for growth of advanced light emitters integrated into an already existing process as they exhibit exceptionally efficient (and robust with T) light emission in the ultraviolet region.     

An extragradient-type method for solving nonmonotone quasi-equilibrium problems

In this paper, a quasi-equilibrium problem with a nonmonotone bifunction is considered in a finite-dimensional space. The primary difficulty with this problem is related to the fact that one must simultaneously solve a nonmonotone equilibrium problem and calculate a fixed point of a multivalued mapping. An extragradient-type method is presented and analysed for its solution. The convergence of the method is proved under the assumption that the solution set of an associated dual equilibrium problem is nonempty. Finally, some numerical experiments are reported.     

Nonlinear dynamics and collective excitations of spin-1 magnets

The Poisson brackets for macroscopic parameters are obtained and nonlinear dynamic equations of spin-1 magnets are derived. Two types of magnetic exchange Hamiltonians corresponding to two Kazimir invariants of SU(3) group are introduced. Thermodynamics of spin-1 magnets is studied and the flux densities of additive integrals of motion are found in terms of exchange energy density. The momentum of magnons is introduced and the corresponding dynamic equation is derived. The spectra of spin and quadrupole waves of magnets with various symmetry of equilibrium state with respect to time inversion are found.     

A note on the derivation of filter regularization operators for nonlinear evolution equations

Despite the strong focus of regularization on ill-posed problems, the general construction of such methods has not been fully explored. Moreover, many previous studies cannot be clearly adapted to handle more complex scenarios, albeit the greatly increasing concerns on the improvement of wider classes. In this note, we rigorously study a general theory for filter regularized operators in a Hilbert space for nonlinear evolution equations which have occurred naturally in different areas of science. The starting point lies in problems that are in principle ill-posed with respect to the initial/final data – these basically include the Cauchy problem for nonlinear elliptic equations and the backward-in-time nonlinear parabolic equations. We derive general filters that can be used to stabilize those problems. Essentially, we establish the corresponding well-posed problem whose solution converges to the solution of the ill-posed problem. The approximation can be confirmed by the error estimates in the Hilbert space. This work improves very much many papers in the same field of research.     

Synthesis of allyl end‐block functionalized poly(ε‐caprolactone)s and their facile post‐functionalization via thiol–ene reaction

A simple and facile strategy for the functionalization of commercial poly(ε‐caprolactone) diols (PCLs) with pendant functionalities at the polymer chain termini is described. Well‐defined allyl‐functionalized PCLs with varying numbers of allyl end‐block side‐groups were synthesized by cationic ring‐opening polymerization of allyl glycidyl ether using PCL diols as macroinitiators. Further functionalization of the allyl‐functionalized PCLs was realized via the UV‐initiated radical addition of a furan‐functionalized thiol to the pendant allyl functional groups, showing the suitability for post‐modification of the PCL materials. Changes in polymer structure as a result of varying the number of pendant functional units at the PCL chain termini were demonstrated. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 928–939