Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Some Hardy-type integral inequalities in general measure spaces, where the corresponding Hardy operator is replaced by a more general Volterra type integral operator with kernel , are considered. The equivalence of such inequalities on the cones of non-negative respective non-increasing functions are established and applied.

     

Comparative analysis of Raman spectra of PbS macro- and nanocrystals

A comparative analysis of the Raman spectra of bulk PbS and PbS nanocrystals with average diameters of 6.6 and 3.8 nm has been performed. It is shown that the bands due to the LO phonons at the Γ point of the Brillouin zone dominate in the first- and second-order Raman spectra of the nanocrystals. Based on the analysis of the relative band intensities for the first- and second-order spectra a qualitative conclusion is drawn: the electron-LO-phonon interaction in PbS nanocrystals increases with a decrease in their size.     

Configurational assignment of N-arylsulfonylimines of alpha-polychloroaldehydes

Configurational assignment of seven synthesized N-arylsulfonylimines of alpha-polychloroaldehydes has been carried out by means of experimental measurements and high-level ab initio calculations of their (13)C--(13)C, (13)C--(1)H and (15)N--(1)H spin-spin coupling constants. The title compounds were shown to exist in solution solely in the form of E isomers, in line with thermodynamic reasoning.     

The nature of ionic conduction of phases based on calcium thioytterbiate

The CaYb₂S₄ compound and the phases based on it are fabricated. The ranges of solid solutions of CaS and Yb₂S₃ in calcium thioytterbiate are determined using the methods of x-ray diffraction analysis and conductometry. Average ionic, electronic, cationic, and anionic transport numbers and the coefficients of self-diffusion and diffusion of majority carrier in the Yb₂S₃ solid solution based on CaYb₂S₄ are determined by the modified emf method, the polarization Hebb-Wagner method, and potentiostatic chronoammetry. To discuss the mechanism of ionic transfer, the data on the pycnometric and X-ray densities are compared.     

ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Real-time queueing theory: A tutorial presentation with an admission control application

Real-time scheduling, or scheduling with respect to a deadline, is critical in many application areas such as telecommunications, control systems, and manufacturing. This paper presents a novel approach to real-time scheduling based on a queueing theory model. Using real-time queueing theory (RTQT), one can analytically determine the distribution of the lead-time profile (i.e., the time until the deadline is reached) of customers waiting for service. Emphasis is placed on the development of the equations used to determine the lead-time profile distribution. The development of the GI/G/1 case is presented and confirmed using simulation. Simulation results confirm prior research for the M/M/1 and GI/M/1 case. As a practical application, RTQT is used to implement a packet admission control algorithm for a telecommunications network. Using this algorithm, packet lateness was reduced by up to 31%. This revised version was published online in June 2006 with corrections to the Cover Date.     

Supported Zr-and Hf-cene Catalysts for Propylene Polymerization

The supported metallocene catalysts were obtained on the layered silicate montmorillonite (MMT), using AlMe₃ and AliBu₃ for synthesis of alkylaluminoxane directly on a support surface, followed by metallocene supporting. It was shown that the MMT-H₂O/AliBu₃ forms with ansa-Zr-cenes of C₁ and C₂-symmetry the significantly more active supported metal-alkyl complexes in propene polymerization, than MMT-H₂O/AlMe₃. The MMT-H₂O/AliBu₃ is the effective activator of the ansa-Hf-cenes, in contrast to MAO and MMT-H₂O/AlMe₃, giving the high active supported catalysts for synthesis of isotactic and elastic polypropene. The character of influence of metallocene fixation on support on the isotactic pentad [mmmm] content in polymer, compared to homogeneous analogues, depends on the metallocene nature. The introduction of borate Ph₃CB(C₆F₅)₄ in the case of both Zr-cene and Hf-cene catalysts increases significantly the activity at the reduced ratio of Al/Zr, Hf (100–500 instead of 2000–3000) and stabilizes the catalytic complexes.     

A duality principle in weighted Sobolev spaces on the real line

An embedding inequality of Sobolev type is characterized in the paper with help of a duality principle and boundedness criteria for the Hardy–Steklov integral operator in weighted Lebesgue spaces.     

Improvement of extreme controls and the steepest ascent method in the norm maximization problem on the reachable set

The maximization of the terminal state norm of a linear system is considered in the sense of searching for and improving extreme points of the reachable set. A sufficient optimality condition is formulated in terms of a special maximum function. A steepest ascent method for level surfaces of the objective function is constructed, and related procedures for improving extreme controls are described.