On Some Mean Value Points Defined by Divided Differences and Their Hyers–Ulam Stability

The aim of this paper is to establish some stability results involving generalized divided differences.     

Impact of Strong Magnetic Fields on Collision Mechanism for Transport of Charged Particles

One of the main applications in plasma physics concerns the energy production through thermo-nuclear fusion. The controlled fusion is achieved by magnetic confinement i.e., the plasma is confined into a toroidal domain (tokamak) under the action of huge magnetic fields. Several models exist for describing the evolution of strongly magnetized plasmas, most of them by neglecting the collisions between particles. The subject matter of this paper is to investigate the effect of large magnetic fields with respect to a collision mechanism. We consider here linear collision Boltzmann operators and derive, by averaging with respect to the fast cyclotronic motion due to strong magnetic forces, their effective collision kernels.     

Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming

The problem of finding minima of weakly sequentially lower semicontinuous functions on reflexive Banach spaces is studied by means of convex and nonconvex subdifferentials. Finding a descent direction for a non-stationary point is a question of importance for many optimization algorithms. The existence or non-existence of such a direction is clarified through several theorems and a series of selective examples. For the general problem, a notion called radius of descent is proposed and shown to be useful for the analysis related to descent directions.     

Some singular value and unitarily invariant norm inequalities for Hilbert space operators

In this paper, we prove some singular value inequalities for sum and product of operators. Also, we obtain several generalizations of recent inequalities. Moreover, as applications we establish some unitarily invariant norm and trace inequalities for operators which provide refinements of previous results.     

Certification of nitrate in spinach powder reference material SPIN-1 by high-precision isotope dilution GC–MS

A high-precision exact-matching quadruple isotope dilution method (ID⁴MS) was employed for the quantitation of nitrate in an air-dried spinach powder Certified Reference Material (CRM). The analyte was extracted in hot water following addition of ¹⁵NO\({}_{3}^{-}\) internal standard. The blend was then treated with sulfamic acid to remove nitrite and with triethyloxonium tetrafluoroborate to promote aqueous conversion of nitrate into volatile EtONO₂. The derivative was analyzed by headspace GC–MS with 3-min elution time. The method performance was validated with a series of tests which demonstrated adequate selectivity and ruggedness. This method supported the development of novel SPIN-1 CRM giving a modest contribution to its uncertainty (u_char = 0.85%). With respect to previous attempts, the SPIN-1 was proven stable, homogeneous (u_hom = 0.44%), and suitable for spinach monitoring under EU regulations. On dried basis, the nitrate content of SPIN-1 was found to be 22.53 ± 0.43 mg/g (U_c = 1.9%, k = 2). The material was also used in an inter-laboratory study where four laboratories employed a total of ten measurement methods.

SPIN-1 Certified Reference Material for nitrate in spinach powder

     

Highly Efficient Copper(II) Ion Sorbents Obtained by Calcium Carbonate Mineralization on Functionalized Cross‐Linked Copolymers

A new type of Cu^II ion sorbents is presented. These are obtained by CaCO₃ mineralization from supersaturated solutions on gel‐like cross‐linked polymeric beads as insoluble templates. A divinylbenzene–ethylacrylate–acrylonitrile cross‐linked copolymer functionalized with weakly acidic, basic, or amphoteric functional groups has been used, as well as different initial inorganic concentrations and addition procedures for CaCO₃ crystal growth. The morphology of the new composites was investigated by SEM and compared to that of the unmodified beads, and the polymorph content was established by X‐ray diffraction. The beads, before and after CaCO₃ mineralization, were tested as sorbents for Cu^II ions. The newly formed patterns on the bead surface after Cu^II sorption were observed by SEM, and the elemental distribution on the composites and the chemical structure of crystals after interaction with Cu^II were investigated by EDAX elemental mapping and by FTIR‐ATR spectroscopy, respectively. The sorption capacity increased significantly after CaCO₃ crystals growth on the weak anionic bead surface (up to 1041.5 mg Cu^II/g sample) compared to that of unmodified beads (491.5 mg Cu^II/g sample).     

Boundary behaviour of the mappings satisfying generalized inverse modular inequalities

We study the geometric properties of the mappings for which generalized inverse modular inequalities hold. We generalize in this way known theorems from the theory of analytic mappings and the theory of quasiregular mappings, like the theorems of Fatou, M. and F. Riesz, Beurling and Lindelöf and their extensions given for quasiregular mappings by Martio, Rickman and Vuorinen.     

Thermostable Trioxane-Dioxolane Copolymers Obtained with Boron Trifluoride: Acrylonitrile Complex as Initiator

Trioxane was copolymerized with small amounts of dioxolane in benzene in the presence of a boron trifluoride:a crylonitrile complex as initiator. The kinetics of reactions was expressed in terms of topoenergetic principles. The copolymerizations had no induction periods and the maximum reaction rate was found proportional to the square of both the initiator and monomers concentrations. A zwitterionic mechanism is suggested for initiation. The activation energy for the system with 5% dioxolane was determined as 18.3 kcal/mol. The melting behavior of the copolymers is briefly discussed as a function of the dioxolane initial content, and is indicative of the amorphous-crystalline coupling phenomenon. The copolymers with ～ 5% dioxolane are thermostable in air up to 250%deg; and are recommended for practical purposes.     

Synthesis of Drim-7,9(11)-diene and Its Hydroxylated Derivatives

This article describes a new efficient synthesis of drim-7,9(11)-diene and its hydroxylated derivates from drim-8-en-7-one. Reduction of this ketone with NaBO₄ in the presence of CeCl₃ · 7H₂O afforded regio- and stereoselectively drim-8-en-7β-ol in a high yield. Its dehydration with H₂SO₄ under mild conditions led to drim-7,9(11)-diene. Noncatalytic oxidation of drim-7,9(11)-diene with OsO₄ and the catalytic oxidation with the pair OsO₄–NMO gave, in a high yield, depending on conditions, driman-7β,8β,9α,11-tetraol or its mixture with drim-7-en-9α,11-diol and drim-9(11)-en-7α,8α-diol. Under optimal conditions the total yield of these diols reached 89%. The separate, noncatalytic oxidation of drim-7-en-9α,11-diol and of drim-9(11)-en-7α,8α-diol with OsO₄ afforded driman-7α,8α,9α,11-tetraol.