Determining dynamic output feedback of the least order for SIMO systems to locate poles in a specified region†

This paper presents a new theory for determining dynamic output feedback of the least order for a linear, time-invariant, controllable and observable SIMO system, such that poles of the closed-loop system lie in a given region Γ in the complex plane. When some poles have prespecified stationary locations in the complex plane, dynamic output feedback is obtained in the sense that the remaining poles lie in Γ This theory applies to continuous-time as well as discrete-time systems. Here a design algorithm for complete system realization and an illustrative example are given.     

Fatigue Damage of the Gesso Layer in Panel Paintings Subjected to Changing Climate Conditions

Abstract: Numerical modelling was used to follow the moisture movement and strain in a composite system – an unrestrained, single wood panel coated with a layer of gesso, in response to cyclic sinusoidal variations in relative humidity (RH). The allowable magnitude of the variations, below which physical damage of the gesso layer on the wood does not occur over a selected time of exposure, was derived as a function of cycle duration, panel thickness and moisture diffusion configuration. The dimensional response of wood substrate becomes subject to restraint by the applied layer of gesso. The panels do not respond significantly to diurnal fluctuations or shorter irrespectively of the panel thickness. The panels respond more and more significantly when the duration of the fluctuations increases until a certain critical period at which the panel fully responds to each cycle. The analysis of the data obtained indicates that moderate RH variations within the approximate range 50 ± 15% are safe. This safe range was derived using the extremes of conservative criteria of the gesso’s fatigue fracture and assumption of worst‐case wooden substrate response. The reduction of allowable amplitude of RH cycles because of decrease in the gesso’s modulus of elasticity and thickness is discussed.     

Levels of polybrominated diphenyl ethers in house dust in Central Poland

Polybrominated diphenyl ethers (PBDEs) are used as flame retardants in numerous products, from which they are emitted to the environment, including house dust. House dust is a source of human exposure to these compounds by ingestion. The aim of this article was to determine the levels of selected PBDEs in the house dust and indicate their potential sources of origin. PBDE congeners: BDE‐47, BDE‐99, BDE‐153 and BDE‐209, were analyzed in 129 samples. The geometric mean levels (and 95% CIs) of the aforementioned congeners amounted to 3.8 (3.1–4.7) ng/g, 4.5 (3.5–5.6) ng/g, 2.2 (2.1–2.4) ng/g and 345 (269–442) ng/g respectively. BDE‐209 was the dominant congener in the majority of tested samples. We found a statistically significant correlation between the concentrations of BDE‐47 and the computer operating time per day (r_s – 0.18) and the living area (r_s – 0.20). Statistically significant higher levels of BDE‐99 were found in homes where the floor was not replaced during the last 2 years.     

Impact of precursor preparation on density of gadolinium iron garnets synthesized via reactive sintering

Gadolinium iron garnet was obtained from two different precursors, homogenized in isopropyl alcohol and in an aqueous environment with a fixed pH. In the first case, it was a mixture of goethite (FeO(OH)) and gadolinium oxide (Gd₂O₃); in the second, a mixture of GdIP (GdFeO₃) and α-Fe₂O₃. Conditions of homogenization in the aqueous environment were selected based on the zeta (ξ) potential measurements as the function of pH. DSC measurements of the output powder mixtures allowed the identification of the effects observed during the temperature rise. In the case of the material obtained from a mixture of goethite (FeO(OH)) and gadolinium oxide, with the increasing temperature, we observe three effects, the first of which corresponds to the phase transformation of goethite into α-Fe₂O₃, the second corresponds to the reaction of gadolinium iron perovskite (GdIP) formation, and the third to the reaction in which a gadolinium iron garnet (GdIG) is formed. However, in the case of heat treatment of the mixture of GdIP and α-Fe₂O₃, we only observe the effect responsible for a solid state reaction leading to the formation of gadolinium iron garnet. Dilatometric measurements allowed to determine the changes in linear dimensions at various stages of reaction sintering. The resulting materials were sintered at temperatures of 1200, 1300, and 1400 °C. In the case of the material obtained from a mixture of perovskite and iron (III) oxide, already at the temperature of 1300 °C, a density has been obtained at around 95% of the theoretical density, and the temperature of 1400 °C allowed achieving a density of 97% of the theoretical density. Whereas, for the material obtained from a mixture of goethite (FeO(OH)) and gadolinium oxide, a density above 95% of theoretical density was achieved only at 1400 °C.     

Sufficient conditions for instability of delay differential systems

The paper gives sufficient conditions for instability of linear systems of both the neutral and retarded types with commensurate and non-commensurate time delays. The conditions are given in terms of time delays and coefficients of the characteristic quasi-polynomials of these systems. Illustrative examples are presented.     

A Comparative Study of Mechanical Properties,Thermal Conductivity,Residual Stresses,and Wear Resistance of Aluminum-Alumina Composites Obtained by Squeeze Casting and Powder Metallurgy

Squeeze casting and powder metallurgy techniques were employed to fabricate AlSi12/Al₂O₃ composites, which are lightweight structural materials with potential applications in the automotive industry. The impact of the processing route on the material properties was studied. Comparative analyses were conducted for the Vickers hardness, flexural strength, fracture toughness, thermal conductivity, thermal residual stresses, and frictional wear. Our results show that the squeeze cast composite exhibits superior properties to those obtained using powder metallurgy.