A remark concerning Putinar’S model of hyponormal weighted shifts

The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar’s construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar’s theory does not lead to the extension that would provide a positive answer to the question.     

Fatty acid composition of lipids in pot marigold (Calendula officinalis L.) seed genotypes

Background

The process of thermal decomposition of dichloromethane (DCM) and chlorobenzene (MCB) during the combustion in an inert, bubbling fluidized bed, supported by LPG as auxiliary fuel, have been studied. The concentration profiles of C₆H₅CI, CH₂Cl₂, CO₂, CO, NO_x, COCl₂, CHCl₃, CH₃Cl, C₂H₂, C₆H₆, CH₄ in the flue gases were specified versus mean bed temperature.

Results

The role of preheating of gaseous mixture in fluidized bed prior to its ignition inside bubbles was identified as important factor for increase the degree of conversion of DCM and MCB in low bed temperature, in comparison to similar process in the tubular reactor.

Conclusions

Taking into account possible combustion mechanisms, it was identified that autoignition in bubbles rather than flame propagation between bubbles is needed to achieve complete destruction of DCM and MCB. These condition occurs above 900°C causing the degree of conversion of chlorine compounds of 92-100%.     

Single and networked CuO nanowires for highly sensitive p‐type semiconductor gas sensor applications

Development of high‐performance p‐type semiconductor based gas sensors exhibiting fast‐response/recovery times with ultra‐high response are of major importance for gas sensing applications. Recent reports demonstrated the excellent properties of p‐type semiconducting oxide for various practical applications, especially for selective oxidation of volatile organic compounds (VOCs). In this work, sensors based on CuO nanowire (NW) networks have been successfully fabricated via a simple thermal oxidation process on pre‐patterned Au/Cr pads. Our investigation demonstrates high impact of the process temperature on aspect ratio and density of copper oxide NWs. An optimal temperature for growth of thin and densely packed NWs was found to be at 425 °C. The fabricated sensors demonstrated ultra‐high gas response by a factor of 313 to ethanol vapour (100 ppm) at an operating temperature of 250 °C. High stability and repeatability of these sensors indicate the efficiency of p‐type oxide based gas sensors for selective detection of VOCs. A high‐performance nanodevice was fabricated in a FIB‐SEM system using a single CuO NW, demonstrating an ethanol response of 202 and rapid response and recovery of ～198 ms at room temperature. The involved gas sensing mechanism of CuO NW networks has been described. We consider that the presented results will be of a great interest for the development of higher‐performance p‐type semiconductor based sensors and bottom‐up nanotechnologies. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Weak solutions for fractional differential equations in nonreflexive Banach spaces via Riemann‐Pettis integrals

The aim of this paper is to develop fractional calculus for vector‐valued functions using the weak Riemann integral. Also, we establish the existence of weak solutions for a class of fractional differential equations with fractional weak derivatives.     

局部凸空间中最佳逼近研究纵览

通过对大量文献研究，回顾了最佳逼近论的研究进展．重点讨论了最有意义的可分离局部凸空间最佳逼近问题、以及最佳逼近问题与向量优化、Pareto有效性、多值函数等之间的直接联系．     

Semiclassical bosonic <Emphasis Type="Italic">D</Emphasis>-brane boundary states in curved spacetime

In this paper we discuss the existence of quantum D-brane states in the strong gravitational field and in the presence of a constant Kalb-Ramond field. A semiclassical string quantization method in which the spacetime metric g _AB and the constant antisymmetric Kalb-Ramond field b _AB are treated exactly is employed. In this framework, the semiclassical D-branes are defined at the first order perturbation around the trajectory of the center-of-mass of a string. The set of equations the semiclassical D-branes must satisfy in a general strong gravitational field are given. These equations are solved in the AdS background where it is shown that a D-brane coherent state exists if the operators that project the string fields onto the corresponding Neumann and Dirichlet directions satisfy a set of algebraic constraints. A second set of equations that should be satisfied by the projectors in order that the semiclassical state be compatible with the global structure of the D-brane are derived in the particle limit of a string in the torsionless AdS background.     

A class of discrete time generalized Riccati equations

In this paper, a class of discrete-time backward non-linear equations defined on some ordered Hilbert spaces of symmetric matrices is considered. The problem of the existence of some global solutions is investigated. The class of considered discrete-time non-linear equations contains, as special cases, a great number of difference Riccati equations both from the deterministic and the stochastic framework. The results proved in the paper provide the sets of necessary and sufficient conditions that guarantee the existence of some special solutions of the considered equations as: the maximal solution, the stabilizing solution and the minimal positive semi-definite solution. These conditions are expressed in terms of the feasibility of some suitable systems of linear matrix inequalities (LMI). One shows that in the case of the equations with periodic coefficients to verify the conditions that guarantee the existence of the maximal or the stabilizing solution, we have to check the solvability of some systems of LMI with a finite number of inequations. The proofs are based on some suitable properties of discrete-time linear equations defined by the positive operators on some ordered Hilbert spaces chosen adequately. The results derived in this paper provide useful conditions that guarantee the existence of the maximal solution or the stabilizing solution for different classes of difference matrix Riccati equations involved in many problems of robust control both in the deterministic and the stochastic framework. The proofs are deterministic and are accessible to the readers less familiarized with the stochastic reasonings.     

Optimal homotopy asymptotic method with application to thin film flow

A new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use.