Finding weak defining hyperplanes of PPS of the BCC model

Production possibility set (PPS) is intersection of the several halfspaces. Every halfspace corresponds with one strong or weak defining hyperplane (facet). This research proposes a method to find weak defining hyperplanes of PPS of BCC model. We state and prove some properties relative to our method. Numerical examples are provided for illustration.     

On a numerical technique for finding multiple zeros and its dynamic

An optimal method is developed for approximating the multiple zeros of a nonlinear function, when the multiplicity is known. Analysis of convergence for the proposed technique is studied to reveal the fourth-order convergence. We further investigate the dynamics of such multiple zero finders by using basins of attraction and their corresponding fractals in the complex plane. A fourth-order method will also be presented, when the multiplicity m is not known. Numerical comparisons will be made to support the underlying theory of this paper.     

Characterization methods for liquid interfacial layers

Liquid interfaces are met everywhere in our daily life. The corresponding interfacial properties and their modification play an important role in many modern technologies. Most prominent examples are all processes involved in the formation of foams and emulsions, as they are based on a fast creation of new surfaces, often of an immense extension. During the formation of an emulsion, for example, all freshly created and already existing interfaces are permanently subject to all types of deformation. This clearly entails the need of a quantitative knowledge on relevant dynamic interfacial properties and their changes under conditions pertinent to the technological processes. We report on the state of the art of interfacial layer characterization, including the determination of thermodynamic quantities as base line for a further quantitative analysis of the more important dynamic interfacial characteristics. Main focus of the presented work is on the experimental possibilities available at present to gain dynamic interfacial parameters, such as interfacial tensions, adsorbed amounts, interfacial composition, visco-elastic parameters, at shortest available surface ages and fastest possible interfacial perturbations. The experimental opportunities are presented along with examples for selected systems and theoretical models for a best data analysis. We also report on simulation results and concepts of necessary refinements and developments in this important field of interfacial dynamics.     

Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation

This Letter is concerned with bifurcation and chaos control in scalar delayed differential equations with delay parameter τ. By linear stability analysis, the conditions under which a sequence of Hopf bifurcation occurs at the equilibrium points are obtained. The delayed feedback controller is used to stabilize unstable periodic orbits. To find the controller delay, it is chosen such that the Hopf bifurcation remains unchanged. Also, the controller feedback gain is determined such that the corresponding unstable periodic orbit becomes stable. Numerical simulations are used to verify the analytical results.     

Monitoring real-time curing of epoxies in situ using single-sided NMR

Adhesively bonded joints using epoxy are widely used in aircraft and aerospace structures. Quality control and defect detection during epoxy curing in such applications is critical. We used single-sided nuclear magnetic resonance (NMR) to nondestructively probe and spatially resolve the change in the characteristic NMR relaxation time (T₂) of epoxies during curing on a substrate. Time-dependent T₂ values were fit to a Weibull function to model temporal changes in the NMR measurables. Our results demonstrate that the reduction in molecular mobility of various epoxy/curing agent mixtures occurs more rapidly at the interface than in the bulk. Further use of single-sided NMR to acquire spatially resolved T₂ data will provide a route for elucidatory epoxy curing studies. © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 616–623     

Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues

We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian,

     

Reactions of platinum complexes with 4,7-phenanthroline: crystal structures of mono- and binuclear platinum(II) complexes containing 4,7-phenanthroline

The reaction of a mixture of cis and trans-[PtCl₂(SMe₂)₂] with 4,7-phen (4,7-phen = 4,7-phenanthroline) in a molar ratio of 1 : 1 or 2 : 1 resulted in the formation of mono and binuclear complexes trans-[PtCl₂(SMe₂)(4,7-phen)] (1) and trans-[Pt₂Cl₄(SMe₂)₂(μ-4,7-phen)] (2), respectively. The products have been fully characterized by elemental analysis, ¹H, ¹³C{¹H}, HHCOSY, HSQC, HMBC, and DEPT-135 NMR spectroscopy. The crystal structure of 1 reveals that platinum has a slightly distorted square planar geometry. Both chlorides are trans with a deviation from linearity 177.66(3)°, while the N–Pt–S angle is 175.53(6)°. Similarly, the reaction of a mixture of cis and trans-[PtBr₂(SMe₂)₂] with 4,7-phen in a 1 : 1 or 2 : 1 mole ratio afforded the mono or binuclear complexes trans-[PtBr₂(SMe₂)(4,7-phen)] (3) and trans-[Pt₂Br₄(SMe₂)₂(μ-4,7-phen)] (4), respectively. The crystal structure of trans-[Pt₂Br₄(SMe₂)₂(μ-4,7-phen)].C₆H₆ reveals that 4,7-phen bridges between two platinum centers in a slightly distorted square planar arrangement of the platinum. In this structure, both bromides are trans, while the PtBr₂(SMe₂) moieties are syn to each other. NMR data of mono and binuclear complexes of platinum 1–4 show that the binuclear complexes exist in solution as a minor product, while the mononuclear complexes are major products.