Carter–Payne homomorphisms and Jantzen filtrations

We prove a q-analogue of the Carter–Payne theorem in the case where the differences between the parts of the partitions are sufficiently large. We identify a layer of the Jantzen filtration which contains the image of these Carter–Payne homomorphisms and we show how these homomorphisms compose.     

On the calculation of some mixed moments of aggregative characteristics of a homogeneous Markov chain for the polynomial scheme

Formulas are given for the calculation of some mixed moments of aggregative characteristics of a homogeneous Markov chain for the polynomial scheme. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 156–164, Perm, 1991.     

Thin layer gas electrode and its application to measurement of dissolved oxygen

A novel thin layer cell equipped with thin layer gas electrode (TLGE) was studied as electrochemical gas sensor for the measurement of dissolved oxygen in water or aqueous solutions. The working electrode (TLGE) is a hydrophobic gas diffusing electrode placed between the cell electrolyte and the solution to be tested. The hydrophobic pores in TLGE serve as a gas chamber. After the sampling period, in which the partial pressure of dissolved oxygen in test solution becomes in equilibrium with that in the gas chamber, the TLGE is polarized with square wave or linear potential signal. Then the Faradaic charge (Q) consumed in depletion of the oxygen contained in pores of TLGE is measured. The main merits of this system are good linearity between the partial pressure of dissolved oxygen in test solution and Q, low zero-reading, negligible liquid-gas difference, convenient calibration and very low temperature coefficient (ca. 0.5%/°C). This technique can also be applied to the measurement of oxygen partial pressure in gas phases.     

Pressurized hot water extraction (PHWE)

Pressurized hot water extraction (PHWE) has become a popular green extraction method for different classes of compounds present in numerous kinds of matrices such as environmental, food and botanical samples. PHWE is also used in sample preparation to extract organic contaminants from foodstuff for food safety analysis and soils/sediments for environmental monitoring purposes. The main parameters which influence its extraction efficiency are namely the temperature, extraction time, flow rates and addition of modifiers/additives. Among these different parameters studied, temperature is described as the most important one. It is reported that the extraction of certain compounds is rather dependent on pressurized water with different applied temperature. Thus, the stability and reduced solubilities of certain compounds at elevated temperatures are highlighted in this review. With some modifications, a scaled-up PHWE could extract a higher amount of desirable compounds from solid and powdered samples such as plant and food materials. The PHWE extracts from plants are rich in chemical compounds or metabolites which can be a potential lead for drug discovery or development of disease-resistant food crops.     

Stability of T. Chan＇s Preconditioner from Numerical Range

A matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix An, we discuss the stability properties of T. Chan＇s preconditioner cU（An） from the viewpoint of the numerical range. An application in numerical ODEs is also given.     

Two-phase flow distribution of air–water annular flow in a parallel flow heat exchanger

The air and water flow distribution are experimentally studied for a round header – flat tube geometry simulating a parallel flow heat exchanger. The number of branch flat tube is 30. The effects of tube outlet direction, tube protrusion depth as well as mass flux, and quality are investigated. The flow at the header inlet is identified as annular. For the downward flow configuration, the water flow distribution is significantly affected by the tube protrusion depth. For flush-mounted configuration, most of the water flows through frontal part of the header. As the protrusion depth increases, more water is forced to the rear part of the header. The effect of mass flux or quality is qualitatively the same as that of the protrusion depth. Increase of the mass flux or quality forces the water to rear part of the header. For the upward flow configuration, however, most of the water flows through rear part of the header. The protrusion depth, mass flux, or quality does not significantly alter the flow pattern. Possible explanations are provided based on the flow visualization results. Negligible difference on the water flow distribution was observed between the parallel and the reverse flow configuration.